j

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

PROCEEDINGS

OF

THE ROYAL SOCIETY

E D I N B U I! G H.

VOL. XLI.

1920-1921

n (\ 0 r* I o q f !j

/

EDINBURGH:

PRINTED BY NEILL AND COMPANY, LIMITED.

MDCCCCXXII.

CONTENTS.

PAGE

1. Size, A Neglected Factor in Stelar Morphology. Opening Address by Professor

F. 0. Bower, M.A , D.Sc , LL.D., F.R.S., F.L.S., President. Issued separately
December 30, 1920, ........ 1

2. On the Equations of Motion of a Single Particle. By J. H. M. Wedderburn,

M.A., D.Sc. Issued separately January 24, 1921, . . . .26

3. iEther and the Quantum Theory. By H. Stanley Allen, M.A., D.Sc. Issued

separately January 24, 1921, . . . . . .34

4. On the Transverse Galvanoinagnetic and Therm omagnetic Effects in several

Metals. By F. Unwin, M.Sc. Communicated by Professor F. G. Baily,

Issued separately March 17, 1921, . . . . . . 44

5. Observations on the Interruption of the Endodermis in a Secondarily Thickened

Root of Draccena fruticosa , Koch. By Annette G. Mann, B.Sc. Communi-
cated by Professor F. O. Bower, F.R.S. Issued separately March 17, 1921, . 50

6. On Fechner’s Law and the Self-Luminosity of the Eye. By Professor William

Peddie, D.Sc. [Abstract], ....... 60

7. The Relation of the Soil Colloids to the Thermal Conductivity of the Soil. By

Capt. T. Bedford Franklin, B.A. (Cantab.). Issued separately May 9, 1921, 61

8. On a Graphical Method of determining Shear Influence Lines and Diagrams of

Maximum Shearing Force for a Beam subjected to a Series of Concentrated
Rolling Loads. By Alex. R. Horne, B.Sc. (Lond.), Professor of Engineering,

Robert Gordon’s Technical College, Aberdeen. Issued separately May 9,

1921, .......... 68

9. The Confluent Hypergeometric Functions of Two Variables. By Pierre

Humbert. Communicated by Professor E. T. Whittaker, F.R.S. Issued
separately May 9, 1921, ........ 73

10. An Experimental Analysis of the Losses by Evaporation of Liquid Air con-

tained in Vacuum Flasks. By Professor Henry Briggs, D.Sc., Ph.D., A.R.S.M.

Issued separately June 20, 1921, . . . . . . . 97

11. Note on a Continuant of Cayley’s of the Year 1874. By Sir Thomas Muir, F.R.S.

Issued separately August 23, 1921, . . . . . .111

VI

Contents.

PAGK

12. On the. Old Red Sandstone Plants showing Structure, from the Rhynie Chert

Bed, Aberdeenshire. Part IV. Restorations of the Vascular Cryptogams,
and discussion of their bearing on the General Morphology of the Pteridophyta
and the Origin of the Organisation of Land -Plants. Part V. The Thallo-
phyta occurring in the Peat Bed ; the Succession of the Plants throughout a
Vertical Section of the Bed, and the Conditions of Accumulation and Preser-
vation of the Deposit. By R. Kidston, LL.D., D.Sc., F.R.S., and Professor
W. H. Lang, D.Sc., F.R.S. Issued separately August 23, 1921 [Abstract], . 117

13. The Adsorption of Gas under Pressure. By Henry Briggs, D.Sc., Ph.D., *

A.R.S.M., and William Cooper, M.A., B.Sc. Issued separately August 23,

1921, .......... 119

14. Utilisation of Solid Caustic Soda in the Absorption of Carbon Dioxide. By

Elizabeth Gilchrist, M.A., B.Sc., A.I.C. Communicated by Professor Henry
Briggs, D.Sc., Ph.D. Issued separately September 5, 1921, . . . 128

15. On the Criterion for Stable Flow of a Fluid in a Uniform Channel. By H.

Levy, M.A., D.Sc., Assistant-Professor of Mathematics, Imperial College of
Science, South Kensington. Issued separately December 13, 1921, . . 136

16. Note on Conditions for Mirage on the Queensferry Road. By Alex. G. Ramage.

Issued separately December 13, 1921, ...... 148

17. The Annual Incidence of Intelligence, and its Measurement by the American

Army Tests. By M. M‘Callum Fairgrieve, M.A. Issued separately December
13, 1921, .......... 150

18. Experiments with an Electrified Pith Ball in an Ionised Atmosphere. By

Dr Dawson Turner and Mr D. M. R. Crombie. Issued separately December
13, 1921, .......... 154

Obituary Notices : —

Robert Munro, M.A., M.D., LL.D. By Dr George Macdonald, C.B., . . 158

John George Bartholomew, LL.D. (Edin.), F.R.G.S., Geographer and Carto-
grapher to the King. By Geo. G. Chisholm, M.A., B.Sc., Reader in
Geography, Edinburgh University, Secretary to the Royal Scottish Geo-
graphical Society, . . . . . . . .170

John Aitken, LL.D., F.R.S. By C. G. Knott, D.Sc., LL.D., F.R.S., 177

Yves Delage. By Professor J. H. Ashworth, F.R.S., .... 182

Edward William Prevost, Ph.D., F.I.C. By Dr Henry Barnes, O.B.E., M.D., . 184

Sir Thomas R. Fraser. By Harry Rainy, M.A., M.D., F.R.C.P. Ed., . .186

T. Lindsay Galloway, M.A., F.G.S., A.M.Inst.C.E., M.Inst.M.E. By Professor

W. P. Ker, F.B.A.; M.A., . . ... . . .193

Henry Barnes, O.B.E., M.D., LL.D. Contributed by his daughter, Miss E.

Barnes, ......... 195

Obituary Notices of Fellows, Honorary and Ordinary. By Mr George A.

Stewart, Assistant Secretary, . . . . . • .197

Contents. vii

PAGE

Appendix —

Proceedings of the Statutory General Meeting, October 1920, . - .211

Proceedings of the Ordinary Meetings, Session 1920-1921, . . .213

Proceedings of the Statutory General Meeting, October 1921, . . . 219

The Keith, Makdougall- Brisbane, Neill, Gunning Victoria Jubilee, and James

Scott Prizes, ......... 221

Awards of the Keith, Makdougall-Brisbane, Neill, and Gunning Prizes, . 224

Accounts of the Society, Session 1920-1921, ..... 230

Voluntary Contributors under Law VI (end of para. 3), . . . . 236

The Council of the Society at October 1921, . ■ . . . 237

Alphabetical List of the Ordinary Fellows of the Society, . . . 238

List of Honorary Fellows of the Society, ...... 258

List of Honorary and Ordinary Fellows of the Society elected during Session

1920-1921, ......... 260

Changes in Fellowship during Session 1920-1921, ... 260

Additions to Library by Gift or Purchase, ..... 261

Laws of the Society, . . . . . . . 265

Index, .... ...... . 272

Index, under Authors’ Names, of Papers published in Transactions , . . 275

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

SESSION 1920-21

Part I]

YOL. XLL

CONTENTS.

[FpJrS-.,^

\nstit6

°0

&

☆ JUN - 6 1921

I. Size, A Neglected Factor in Stelar Morphology. O^&^g0na| ^
Address by Professor F. O. Bower, M.A., D.Sc.,

F.R.S., F.L.S., President, 1

( Issued separately December 30, 1920.)

II On the Equations of Motion of a Single Particle. By J. H. M.

Wedderburn, M.A., D.Sc., 26

(. Issued separately January 24, 1921.)

III. AEther and the Quantum Theory. By H. Stanley Allen,

M.A., D.Sc., . . . 34

(. Issued separately January 24, 1921.)

IV. On the Transverse Galvanomagnetic and Thermomagnetic

Effects in several Metals. By F. Unwin, M.Sc. Com-
municated by Professor F. G. Bajly, .... 44

(. Issued separately March 17, 1921.)

V. Observations on the Interruption of the Endodermis in a
Secondarily Thickened Root of Dracaena fruticosa, Koch.

By Annette G. Mann, B.Sc. Communicated by Professor
F. O. Bower, F.R.S., . 50

{Issued separately March 17, 1921.)

VI. On Fechner’s Law and the Self-Luminosity of the Eye. By

Professor William Peddie, D.Sc. [Abstract], ... 60

[Continued on page iv of Cover .

EDINBURGH:

Published by ROBERT GRANT & SON, 107 Princes Street, and
WILLIAMS & NORGATE, 14 Henrietta Street, Covent Garden, London, W,C. 2.

Price Eleven Shillings.

THE ROYAL SOCIETY OF EDINBURGH.

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

The Council beg to direct the attention of authors of communications to
the Society to the following Regulations, which have been drawn up in
order to accelerate the publication of the Proceedings and Transactions,
and to utilise as widely and as fairly as possible the funds which the
Society devotes to the publication of Scientific and Literary Researches.

1. Manuscript of Papers. — As soon as any paper has been passed
for publication, either in its original or in any altered form, and has been
made ready for publication by the author, it is sent to the printer.

2. Method of Publication. — As soon as the final revise of a Trans-
actions paper has been returned, or as soon as the sheet in which the last
part of a Proceedings paper appears is ready for press, a certain number
of separate copies or reprints, in covers bearing the title of the paper and
the name of the author, are printed off and placed on sale. The date of
such separate publication will be printed on each paper.

3. Additions to a Paper after it has been finally handed in for
publication, if accepted by the Council, will be treated and dated as
separate communications, and may, or may not, be printed immediately
after the original paper,

4. Brief Abstracts of Transactions Papers will be published in
the Proceedings, provided they are sent along with the original paper.

5. Special Discussion of Papers accepted for Publication. —
Where a paper has been accepted for publication, the Council may, with
the consent of the author, select this paper for Special Discussion. In the
case of such papers advanced proofs will be sent to the members of the
Society desiring copies, and copies will be supplied to the author for dis-
tribution. A paper selected for Special Discussion will be marked with an
asterisk (*) and placed first on the Billet for the day of reading. Any
following papers for that day may be adjourned or held as read if the
discussion prevents their being read.

6. Communications not submitted for Publication, such as
Demonstrations of Experiments, Statement of Scientific Problems, etc.,
may be received by the Council, and may also be selected for Special
Discussion. The Council does not undertake to publish any notice of such
communications in the Proceedings or Transactions of the Society.

[ Continued on next page.

PROCEEDINGS

OF THE

ROYAL SOCIETY OF EDINBURGH.

VOL. XLI. 1920-21.

I. — Size, A Neglected Factor in Stelar Morphology. Opening
Address by Professor F. O. Bower, M.A., D.Sc., LL.D.,
F.R.S., F.L.S., President.

(Read October 25, 1920. MS. received November 1, 1920.)

The principle of similar structures was first enunciated by Galileo.
Applying it mechanically, it appears that the strength of a structure varies
as the square of the linear dimensions, and the weight as the cube. This
principle and its mechanical applications have been widely illustrated
by reference to the bodies of animals, and many of their peculiarities are
necessary consequences of its effect in the course of their evolution. For
instance, the columnar legs of the elephant or of the moa are held to be the
inevitable sequel to the large size and consequent weight of those animals,
while the thin arched legs of insects are only possible where the body
itself is small and light. Such questions have been adequately dealt with
in D’Arcy Thompson s book on Growth and Form. Botanists have, how-
ever, been slower in applying the principle to the study of plants. It
is true that the question of the practicable limit of size of trees has long
ago been discussed from this point of view, and it is recognised that a
change either of material or of method of construction would be necessary
for effective growth beyond the limits already reached by some of the
largest of them. In fact, that about 300 feet is the extreme height that
can be self-supporting with the usual type of construction of the trunk.
But the principle is also applicable to other points of construction, such
as the size and constitution of individual cells, and even to the forms

of chloroplast : as well as to various problems of distribution of tissue-
VOL. XLI. ' 1

2

Proceedings of the Royal Society of Edinburgh. [Sess.

masses, and their relation to the physiological functions which they
perform. So far, however, the principle of similar structures has not been
applied in botanical science as freely as its importance would justify. An
attempt will be made in this address to show how the principle has
affected the internal morphology of the Vascular System of Plants. The
most marked illustrations will be taken from the Ferns, a class of plants
in which the vascular system has always attracted attention by reason
of the complexity and peculiarity of its details. But further evidence
will be brought to show that it has its application in other types of
plants as well.

The stems and roots of most plants are approximately cylindrical.
The same is the case as a rule for their conducting tracts also. The
cylinder is one of those solid forms in which the proportion of external
surface to bulk is exceptionally low. Any deviation from the cylindrical
form, either by external projections or by involutions, necessarily leads to
increase in the proportion of surface to bulk. The surface varies only as
the square of the linear dimensions, but the bulk as the cube. It follows
therefore that in carrying out any of those physiological functions of a
living organism which depend upon surface, as do all those of the
acquisition and interchange of material, the actual size of the part which
exercises that function is a matter of the greatest moment. It may be
assumed that, if other things be equal, such as the structure and quality
of the tissues that form the surfaces in question, the rate of interchange by
diffusion of soluble gases or salts through a tissue-surface will be directly
proportional to the area of the diffusing surface. If that be so, then for
each such function there will be a limit of size beyond which its exercise
with sufficient rapidity will become impossible if the form be maintained,
or if the quality of the- surface-tissue through which the transit occurs
remains the same. This suggests that the larger the plant is the more
dependent it will be upon its form and detailed structure, not only for its
stability, but also for the performance of its functions of absorption and
transit of liquids and gases. This will apply not only to the external
surface, but also to those internal surfaces which limit one tissue-tract
from another. Not only the outer surfaces, but also the limiting surfaces
of the internal tissue-tracts should then be carefully examined, both as to
area and as to their detailed structure.

In point of fact stems and roots are only approximately cylindrical.
Fluctuations of size either by increase or by decrease are common. But
the most general and the most important of them all is that primary
increase of dimensions which is found in the stems of most plants as they

3

Size, a Neglected Factor in Stelar Morphology.

1920-21.]

pass from the juvenile to the adult
state. For the moment only the
primary increase is meant : all second-
ary or cambial increase may be
ruled out of this discussion, however
interesting its problems may be.
Here the intention is to concentrate
upon those problems which any land-
living organism having no cambial
increase must face as it passes from
the juvenile to the adult state. It is
the facts of ontogenetic development
in plants without secondary growth
which provide the most cogent evi-
dence of the effect of increase in size
upon internal structure. Good illus-
trations are provided by the Filicales.
Here the first leaves are small : the
later leaves are successively larger.
The stem which bears them is rela-
tively small at its base, but in propor-
tion as larger leaves are formed the
supporting stem becomes progres-
sively larger, till the adult size is
reached. The same is the case for
the stele that lies within (fig. 1). It is
small at the base, and approximately
cylindrical; but passing upwards its
transverse section gradually increases,
till finally in most ferns it takes one
of those complicated forms that are
so characteristic of the class (fig. 2).
The form of the stem at its base, and
of the stele within, is then not a
cylinder but a gradually enlarging
cone. Consequently problems depend-
ing on the proportion of surface to
bulk, whether of the stem as a whole
or of the stele which it contains, will
be progressively changing in each

Fig. 1.— Plan of stelar construction of a juvenile plant
of Gleichenia pectinata, after Dr J. M. Thompson,
showing in median section the way in which the
stele enlarges conically upwards, and widens into
a solenostele, with leaf-gaps. a-L= the insertions
of the successive leaves. J£« = endodermis.

4

Proceedings of the Koyal Society of Edinburgh. [Sess.

successive transverse zone from the juvenile to the adult region. It may
be anticipated that at some point of size a critical proportion of surface
to bulk will be reached, where the interchanges between stele and cortex
will demand some alteration of structure if they are to be satisfactorily
carried out.

Conversely, however, an axis or root may diminish progressively in
bulk from the base upwards. In a fern that has been starved by
unfavourable culture the size of its stem is less than in the region
developed under normal conditions, and the internal tissues follow suit,
with simplification of structure. Certain strut roots of palms develop

lr

1,

thinner after entering the ground than
above it. These should then show pro-
gressively converse structural changes, if
the reasoning be correct. For them the
problem, so far as it depends upon size,
would be progressively simplified, and the
evidence of this might be expected to
appear in their structure. It will be
shown later that this expectation is justi-

An illustration already familiar to

Fig. 2. — Median longitudinal section fied by the facts,
through the prothallus and embryo
of Polypodium vulgare. x 6. Leaves

A h> et(L roots, op = apex of botanists of the way in which form may
stem. the drawing shows the J J

widely expanding conical stem— be modified so as to secure an increase of
small at the base, where it is pro-

tostelic; larger above, where it is surtace-area, and so to facilitate transit
dictyostelic. through that surface, is seen in the case

of submerged leaves. In Hottonia, Potamogeton pectinatus, Ranunculus
aquatilis , and Gabomba, etc., the submerged leaves are cut into narrow
segments, differing thus in marked degree from the undivided blades of
the aerial leaves of allied plants. In the cases of Gabomba and R.
aquatilis {heterophyllus) the difference appears even in the leaves of the
same plant. On the other hand, in Ouvirandra the submerged leaves
are perforated by many oblong holes. The biological reason for these
peculiarities is to be sought in the fact that, by being thus subdivided
or perforated, they expose a relatively large absorbent surface to the
water, out of which they abstract the materials for their food. In par-
ticular, oxygen and carbon-dioxide are exchanged with the water through
the epidermis, which has here no stomata, so that their external surface
is the only available surface for the purpose. In this respect their struc-
tural difference from the entire and slightly lobed aerial leaves which bear
stomata makes an increase of absorptive surface all the more necessary.

5

1920-21.] Size, a Neglected Factor in Stelar Morphology.

This example of a readily intelligible case, involving elaboration of
external form and increase of the surface thereby, is held as an important
parallel to certain cases of surface-adjustment of internal tissues which
are to be described later.

In the young stems of Vascular Plants generally, and in those of the
Ferns in particular, the conducting tracts are strictly delimited from the
surrounding tissues by endodermis. The same is the case also for roots.

Fig. 3. — Helminthostachys zeylanica : part of transverse section of root (Gwynne- Vaughan collection,
slide 589 ; x 66). The endodermis, recognised by the characteristic structure of its radial walls,
marks a boundary between the outside cortex, with large starch-grains (here above), and the
inner conjunctive parenchyma (here below), with small grains. Drawn by Dr J. M. Thompson.

This endodermis forms not only a morphological, but also a physiological
boundary that is without any gap or imperfection. Its physiological
importance consists in the fact that the structure of the endodermis places
the contents of the conducting tract under strictly protoplasmic control.
All the lateral walls of its cells are so specialised in substance that, instead
of being permeable like ordinary cellulose walls, they are impervious to
fluids. Thus all possible leakage is stopped, and the only channel of transit
for substances into or out of the stele is under the control of the living
protoplasts of the endodermal cells. This control applies not only to salts,
sugars, and other similar soluble substances, but also to gases. Since in

6

Proceedings of the Royal Society of Edinburgh. [Sess.

young and primitive plants the mantle is unbroken by intercellular spaces,
even the respiration of the living cells within the barrier can only be
conducted by interchange of gases passed in solution through the cells of
the endodermis. These structural facts, which can be verified by sections
of the stem of any young fern-plant, or of any root, form the foundation
of a theory which may account for some of the most extraordinary vascular
developments seen in plants.

Evidence of the effectiveness of the endodermis as a physiological

Fig. 4. — Part of transverse section of stem of Acrostichum ctureum , showing the
centre of the solenostele, with endodermis surrounding a small central pith
with large starch-grains ; outside the endodermis is conjunctive parenchyma
with small starch-grakis. Drawn by Dr J. M. Thompson. ( x 66.)

barrier is afforded by comparison of the cell-contents outside and inside
it ; sometimes starch is absent from the stelar tissues but present in thfe
surrounding cortex. Marked cases may commonly be found of difference
in size of the starch-grains on either side of the barrier. This is seen
in the storage-rhizomes of Pteridium, and fig. 3 shows it in the case
of the rhizome of Helminthostachys. In the young stem of Acrostichum
aureum the difference is still more striking (fig. 4). Such facts indicate
that the endodermis controls the passage of soluble sugar. It has been
shown by de Lavison (Rev. gen. de Boh, 1910, p. 225), and by Priestley
(New Phyt., 1920, p. 192), that it is an effective barrier to the passage of
such soluble substances as are incapable of penetrating the protoplasm, but
whose passage through the walls can be followed by their colour, or by

7

1920-21.] Size, a Neglected Factor in Stelar Morphology.

staining reactions. Such evidence points to the endodermis as a selective
screen, or even an effective barrier to physiological transit between the
outer tissues and the conducting system. Hence the constant diminution
of the proportion of surface to bulk as the stele increases in size becomes
a matter of the utmost importance. A conical increase in size of the stele
is illustrated in all ferns, as well as in other plants. It starts from the
minute stele of the sporeling, and expands as a support for the successively
larger leaves of the established plant (figs. 1, 2). Often the increase is rapid,
especially in ferns with short internodes. For each plant which thus
enlarges its stele in conical form, a limit must ultimately he reached where
the facility for interchange through the endodermis will not suffice for the
needs of the tissues within. This facility for interchange will then become
a “ limiting factor.” Either some means of increasing the surface area of
the stele, and so of increasing the means of transit, must be supplied, or
the conical enlargement of the stele must be checked, and the later regions
of the stele will be cylindrical. The increase cannot be continued
indefinitely in the form of a cone. But on the other hand, any deviation
from the simple conical form, by involution of surface or by excrescence,
will give an increase of the proportion of surface to bulk, and thus tend to
overcome the difficulty. We may now proceed to see how these demands
following on increase in size have been met in the stems of ferns.

It is generally admitted that the protostele is the most primitive stelar
type. It is present in the juvenile stage of all ferns, and it is permanently
retained in the adult stems of some of them. It consists of a central core
of xylem often composed only of tracheides, as in Botryopteris cylindrica
(fig. 5). This is surrounded by a band of phloem, followed by the
pericycle, and finally the stele is delimited externally by the continuous
sheath of the endodermis. No intercellular spaces have been found in the
protostele, and the endodermis serves as a complete gas-barrier limiting the
ventilating system of the cortex internally. Thus constructed, the stele
receives the trace of each successive leaf, and it is important to note that
its entry is effected without any break of continuity of the endodermal
envelope, which thus forms a gas-tight barrier surrounding the whole
vascular system. The protostelic structure is retained in the adult stems
of Botryopteris, Gleichenia, Lygodium, and Gheiropleuria. It is also
characteristic of the stems of the Hymenophyllacese, which with others are
relatively primitive types, having stems of moderate dimensions.

In the ferns named the stele is often minute, and never actually large.
In Botryopteris cylindrica it is about • 5 mm. ; in Lygodium 1 mm. to 2 mm. ;
in Gheiropleuria about 1 mm.; .in Trichomanes scandens, one of the larger

8

Proceedings of the Royal Society of Edinburgh. [Sess.

Hymenophyllacese, it is *5 mm. in diameter. In all of them its form is
conical at first, but after reaching a certain size it retains that size through
life, as a cylinder traversing the cylindrical rhizome. The limiting factors
have come into play, one of which is the proportion of surface of the stele
to its bulk. When the stele attains larger dimensions, as it did in certain
fossils while still retaining its protostelic state, is is seen to have undergone
a modification of form. For instance, in Ankyropteris Grayi (fig. 6, ii),
which is 2-8 mm. in diameter, it is corrugated, the insertions of the leaf-

Fig. 5. — Transverse section of a stem of Botryopteris cylindrica, showing
a protostele with a solid central cure of xylem, and peripheral
phloem. The endodermis is not clearly shown in this fossil Fern.

traces projecting, and the surfaces between being hollowed. Moreover, the
curvatures of the hollows are deeper in the larger than in the smaller
specimens (fig. 6, iii). A still more extreme case of this is seen in the stele
of Asterochloena laxa, which may be as much as 15’5 mm. in diameter
(fig. 6, iv). Here the stele is thrown into deep involutions of the surface.
It is obvious that this will give a very greatly increased proportion of
surface to bulk. It seems natural to conclude in such cases that the more
elaborate form of the stele has made the larger size possible, by overcoming
the limiting factor. But notwithstanding the complicated outline, and the
well-known differentiation of the xylem of these fossils, their steles are
still of the nature of protosteles: their non-medullated structure is
maintained.

9

1920-21.] Size, a Neglected Factor in Stelar Morphology.

In other primitive ferns, as a larger size of the stele is attained in the
growing plant a change of internal structure appears, leading to medulla-
tion. Since the leaf-traces are inserted peripherally, it is in the outer
xylem that the water-transit will be most active. As the stele enlarges,
the water in the central region will tend to stagnate, and thin-walled cells

Fig. 6. — Outlines of xylem of steles, all drawn to the same scale ( x 5),
to show approximately relative size.

i. Botryopteris cylindrica, diameter 'C5 mm. iii. Ankyropteris Grayi, diameter 2-5 mm.

ii. Ankyropteris Grayi, diameter 2’0 mm. iv. Asterochloena laxa, diameter 12*0 mm.

The elaborateness of outline increases with the size.

will serve for its storage as well as thick- walled tracheides would do.
This is probably the rationale of the conditions of “ mixed pith,” and of
the formation of a parenchymatous medulla. Medullation in one form or
another is common to the great majority of ferns. Its intra-stelar origin
has been followed most convincingly for upright stems in the stratigraphical
sequence of the fossil Osmundacese, described in our Transactions by Kidston
and Gwynne-Vaughan. It has also been demonstrated in Gleichenia
pectinata and other ferns by Dr Thompson {Trans. R.S.E vol. Iii, pt. iv,
p. 715). The parenchymatous pith once established may serve not only

10

Proceedings of the Royal Society of Edinburgh. [Sess.

as a place of storage for water, but also for plastic substances. In the
living Osmundacese it contains large quantities of starch. As usual in
storage tissues, intercellular spaces are present, though these are absent
from the simplest steles. Here they form an internal ventilating system,
quite separate from that of the cortex, excepting that in some species there
is communication at the point of dichotomy of the stem. A careful
examination of Osmunda regalis and of Todea barbara shows no con-
nection at the xylic gaps between the outer and inner ventilating systems.
The endodermis surrounds the stele completely as well as each leaf-trace.
Consequently the inner ventilating system is here as isolated and self-
contained as is the intercellular system of a submerged plant. Where the

Fig. 7. — Traces of the actual sizes of steles of living and fossil Osmimdacese,
all to the same scale, i.e. approx, nat. size.

i. Todea barbara (3 mm.). iv. Thamnopteris schlechtendalii (13 mm.).

ii. Osmunda cinnamomea ( 4 mm.). v. Osmundites skidegatensis { 25 mm.).

iii. Osmunda regalis (5 mm.). vi. Osmundites Carnieri (35 mm.).

size is small this condition is possible. It is so in T. barbara with a stele
3 mm. in diameter, or in 0. regalis (5 mm.). In such instances the propor-
tion of surface to bulk of the small stele is relatively high (fig. 7, i, ii, iii);
but the case is different for the large steles of Osmundites skidegatensis
(25 mm. in diam.), or of 0. Carnieri (33 mm. in diam.), and in them the
problem is solved by breaking down the barrier. In the former fossil each
leaf-trace at its departure interrupts the whole vascular ring, and the pith
is continuous with the cortex through each leaf -gap. Moreover, no layer

resembling an endodermis can be distinguished, so that it is practically
impossible to set a definite limit to the stele. In 0. Carnieri , though a
line of delimitation appears which is believed to be endodermis, it is
discontinuous at irregular intervals, and the ventilated cortex is directly
related to the greatly distended pith (fig. 8). Thus in both of these
large fossil stems a concomitant, and it probably was even a necessary
condition of their large size, was this interruption of the endodermal

11

1920-21.] Size, a Neglected Factor in Stelar Morphology.

barrier and the completion of a common ventilating system for cortex and
pith. The “ limiting factor ” was met by interruption. This is in point of
fact a more effective device than that seen in the enlarged protosteles,
which maintained their endodermis but enlarged its area.

Lang has shown in the living Ophioglossacese a method of resolving the
difficulty similar in effect to that of the Osmundacem. In Botrychium
and Helminthostachys the young plant has a complete endodermal barrier,
as in other ferns, shutting off the vascular system from the surrounding
cortex. But as the plant advances, the conical stele enlarges, and a pith is

Fig. 8. —Osmundites Carnieri , Schuster. Arrangement of meristeles.
The endodermis is shown by dotted lines. After Kidston and
Gwynne- Vaughan.

formed which serves for storage, and contains starch. Intercellular spaces
appear in it, but the internal ventilation-system is at first wholly shut off
from the cortical, and it remains so till the plant is well advanced.
As the stem enlarges free communication is established by foliar gaps,
which naturally open outwards to the cortex, but here they are always
open inwards also to the pith. This has the disadvantage of laying open
the conducting tract, and destroying the completeness of endodermal con-
trol ; but it resolves the difficulty of communication between the outer and
the inner tissues, which becomes more acute as the stem enlarges. The
advantage gained is probably greater than the disadvantage that follows.

What is thus seen in less complete form in Botrychium and Helmintho-
stachys is carried much further by the genus Ophioglossum. Here the
endodermis is discarded early. The stele dilates with a distended pith,

12

Proceedings of the Royal Society of Edinburgh. [Sess.

which communicates directly with the cortex through very wide leaf-gaps.
The extreme condition is seen in the tuberous stocks of 0. palmatum,
which may be as much as 2 cm. in diameter. This seemingly reckless
discarding of the protective endodermis goes along with a leathery foliage.
Such plants have only a sluggish circulation of fluids, and the protection
of their conducting tracts seems less vital for them than the establishment
of free gaseous and other interchange between the tissues of their sappy
stocks.

The parallel condition seen in the Marattiacese indicates the truth of
this. The massive stocks of these ferns are also soft and sappy, and their
leaves are as a rule leathery and thick. They dispense early in their
ontogeny with the endodermis, and the stele at once breaks up into small
parts which are widely scattered through the transverse section. The stem
grows to a large size, with no limit between the distended pith and the
cortex. Consequently after the brief juvenile stage is past no question of
proportion of surface to bulk arises. But, on the other hand, by discarding
the endodermis the conducting tracts have lost that protoplasmic control
which the endodermis gives. This state may serve for semi-xerophytic
plants, such as the Ophioglossaceae and Marattiacese, with sappy stocks and
leathery leaves, and sluggish fluid-transit. But it would not serve for
plants where fluid-transit requires to be rapid, and in particular for those
with delicate leaf-structure.

The Leptosporangiatse, which are mostly delicate hygrophytes, com-
prise the vast majority of living species of ferns. They have taken a
quite different course of structural development, in which the endodermal
barrier is strictly maintained in its complete form, while intercellular
spaces are as a rule absent from their vascular tracts. They show in their
peculiar vascular structure to what shifts a plant is put as it increases in
size by primary and not by cambial activity, maintaining meanwhile its
vascular system under complete protoplasmic control. All of them start
from the protostelic state. It appears from comparison along phyletic
lines parallel but yet distinct, that a transition has taken place from the
protostele to a disintegrated stelar structure. The successive steps of this
may be seen with varying degrees of clearness of detail in the successive
stages of the individual life. These steps appear as the stele enlarges.
According to the reasoning already brought forward, it is on enlargement
that the problem of proportion of surface to bulk of the stele becomes
insistent. The modifications of form of the stele seen in the advanced
Leptosporangiate Ferns may be held as the means of its solution. The
critical point in the individual development of the solenostelic type is

13

1920-21.] Size, a Neglected Factor in Stelar Morphology.

where the transition is effected from the protostele. Medullation may
precede this, as it does in Gleichenia pectinata. In others no previous
medullation may be seen. In either case a condition of physiological
success appears in the Leptosporangiate Ferns to be the continuity of the
sheath, so as to allow no leakage. In the Eusporangiates, as already
explained, this appears to be less important.

The chief steps in the advancing complexity of the vascular system of

Fig. 9. — Series of solenostelic and dictyostelic stems of Ferns, all drawn
to same scale. ( x 2. )

1, Metaxya ; 2, Dipteris conjugata ; 3, Mat onia pectinata ; 4, Plagiogyria pycnophylla ; 5, Thyrsopteris
elegans ; 6, Saccoloma elegans ; 7, Platycerium alcicorne ; 8, Platy cerium cethiopicum.

These drawings show that the disintegration of the stele does not depend
on absolute size alone.

the Leptosporangiate Ferns are known as solenostely, polycycly, per-
foration, and dictyostely . Such advances may be traced either in the
ontogeny, or in the race by comparison of distinct species or genera. They
all result in increase of surface in proportion to bulk of the stelar tissue,
and in all of them the endodermal barriers are strictly maintained, while
intercellular spaces are consistently absent from the vascular tissues. They
all follow on a very considerable increase in size of the system as a whole
and are believed to be causally related to it. In solenostely the solid
protostele is replaced by a hollow tube lined within and without by con-
tinuous endodermis (fig. 9:1,2). At each leaf-insertion a foliar gap leads

14

Proceedings of the Boyal Society of Edinburgh. [Sess.

from the cortex through the tube to the inner pith, giving ready com-
munication by intercellular spaces, and by continuous tracts of living cells

between the cortex and the pith.
But the lips of the gap are en-
tirely sheathed by endodermis,
so that the barrier between
vascular and non-vascular tissue
is maintained intact: and it is
continued without any leak or
imperfection to the base of the
plant. The passage from the
protostele to the solenostele in
the individual plant is marked

Fig. 10. — Histiopteris incisa (Thunbg.) J. Sm. Trans- by a great increase of the trans-
verse section of internode .of rhizome ( x 10) show- verse secti0n of the stele (fig.
mg corrugation oi solenostele. (Gwynne- Vaughan v °

collection, slide 1163, by Tansley.) 11). Clearly the proportion of

Fig. 11. — Series of transverse sections of the stem of Pcesia podophylla, all drawn
to the same scale, showing the great increase of stelar complexity as the
conical stem expands upwards. ( X 4.)

surface to bulk of the stele is greatly increased by the tubular form.
But sometimes a still further increase is secured by corrugation of the tube,
as in Histiopteris incisa (fig. 10). A still more remarkable way in which

1920-21.] Size, a Neglected Factor in Stelar Morphology. 15

this end is attained is by the further advance to polycycly, which is seen
in beautiful examples in Matonia (fig. 9 : 3), or Pcesia podophylla (fig. 11).
Three or even four concentric cycles of vascular tissue have been observed,
while open communication is maintained at or near to the nodes between
the outer and inner cycles, as well as between the tissues that embed them.
The proportion of surface to bulk is still further advanced by such means
as these, which are exemplified in numerous cases
of ferns not otherwise resembling one another.

From this it may be concluded that a general
cause has been at work, which has affected the
development in distinct phyletic lines.

The same ends as are gained by solenostely
are still further promoted by the appearance of
perforations in the vascular tube. These are
often very numerous, and are specially found
in ferns of advanced type, such as Davallia,

Platycerium (fig. 9 : 7, 8), Polypodium, or Steno-
chlcena (fig. 12). Each perforation is entirely
lined by endodermis, which still shuts in the
vascular tissue completely, while interchange
between the tissues within and without the tube
is promoted. The perforated stele may be com-
pared structurally and physiologically with the
perforated leaf of Ouvirandra : the problem of
surface-interchange has been solved in both cases
by increased surface. The attenuated network of
vascular tissue which after perforation represents
the solenostele is characteristic of the most recent fig. 12 —Stenochlo&natmuifolia
and advanced ferns, and their prevalence in genera
and species now living is a testimony to the
physiological success which perforation brings.

Another step, distinct in time and manner of
its origin from perforation though resembling it in its effect, is the over-
lapping of foliar gaps in short stems with crowded leaves. The result is
what is described as dictyoslely. If a foliar gap underlies each leaf-
insertion, and the leaves are crowded on the axis, any transverse section
will cut through more than one of them, and in a transverse section the
vascular ring will appear divided into a number of isolated tracts. This is
seen in the Male Fern or in large Tree Ferns (fig. 13, B). It is frequently
combined with perforation. Though the perforations and the leaf -gaps are

into a single plane, showing
perforations.
l.t. = leaf -trace.

br. = vascular supply to a branch.

16

Proceedings of the Royal Society of Edinburgh. [Sess.

essentially different in their real origin, the physiological effect of them
is alike. By either means the endodermal surface is increased, and inter-
change facilitated ; while the complete investment of the vascular tracts
with endodermis is maintained. The final effect of these several factors,
separately or in combination, is to break up the vascular tracts as seen
in transverse section into relatively small circular or oval masses, each
with a relatively large proportion of surface to bulk. The physiological

Fig. 13. — Transverse sections of stems, drawn to the same scale, showing that stelar complication
does not depend directly upon size alone. ( x 2.)

A = Cibotium Barometz. B = Hemitelia setosa.

difficulty following on increase of size is thus fully met in Leptosporangiate
Ferns (fig. 9 : 4, 6, 8).

If, as the anatomy of the ferns seems to suggest, actual Size is one
of the factors determining the form which the stelar tissues take, and that
increase beyond certain dimensions leads to those peculiarities which are
seen in them, and particularly to the breaking up of the stele into
meristeles, then tuberous development should lead to such disintegration.
More especially should the change be apparent where the normal part
shows a relatively simple stelar structure. A good example of this is
seen in the tubers borne upon the protostelic stolons of Nephrolepis (fig.

17

1920-21.] Size, a Neglected Factor in Stelar Morphology.

14, A). It has been shown by Lachmann ( Thesis , Paris, 1889), and by
Sahni (New Phyt., vol xv, p. 72, 1916) that the protostele of the stolon
expands at the base of the distended tuber. As seen in transverse section
it first acquires a central mass of phloem, followed successively by peri-
cycle, endodermis, and ground-parenchyma. In fact it becomes soleno-
stelic. As the base of the tuber expands the ring breaks up by irregular
perforations, as it does in leafy shoots of many Leptosporangiate Ferns.
But here there are only perforations : since no leaves are borne on the
stolon there are naturally no foliar gaps. A network of meristeles is thus

A, Stolon bearing a tuber, in which the protostele breaks up into a cylindrical network,

contracting again at the apex. After Sahni.

B, Transverse section of protostelic stolon. (x5.)

C, Transverse section of tuber (also x 5) showing ring of meristeles each limited

by endodermis.

Diameter of stolon, 1*6 mm. Diameter of tuber, 11*0 mm.

formed, each limited by a complete endodermis, and arranged in an ex-
panded ring (fig. 14, C). At the distal end, where the tuber contracts again,
the network narrows down through stages of condensation the reverse of
the previous disintegration. In a given case the diameter of the stolon
was 1*6 mm., and of its protostele -6 mm. The diameter of the tuber was
IT cm., and of its ring of meristeles *74 cm. : that is, nearly fifteen times
that of the original protostele. It thus appears that, while complete
endodermal control is maintained, when the stolon of Nephrolepis dilates
into a tuber the same features of stelar expansion appear as in the
conically enlarging axis of many Leptosporangiate Ferns. This suggests
that the increase in size in both cases determines the structural change,
while the reversal of that change which follows on the apical contraction

of the tuber strongly supports that conclusion.

VOL. XLI.

2

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

A somewhat similar result is found in the tubers formed on the
rhizomes of certain species of Equisetum. Each tuber results from the
dilatation of an internode of the rhizome to a size beyond the normal,
and this is found to be accompanied by a disintegration of the stele. E.
arvense is one of those species in which the stele is strictly circumscribed
by an unbroken external endodermis. In the internode of the rhizome
the stele is relatively compact, and in an average case it measures about
1 mm. in diameter. The individual vascular strands may vary in number.

In fig. 15, A, six are seen. In the
distended tuber the strands appear
widely apart, each surrounded by its
own endodermal sheath, which closes
round it as the strands separate at
the base of the tuber. The ring
which they form may be 3 mm. or
more in diameter, fully three times
that of the original stele (fig. 15, B).
As in Leptosporangiate Ferns, the
stele has divided into meristeles, and
as in them the disintegration accom-
panies an increase in bulk, which
may be held to be one of the factors,
or perhaps the chief factor in deter-
mining it. As the next node is

B

Fig. 15. — Equisetum arvense.

Transverse section of internode of rhizome : stele approached the tuber Contracts, and
with encircling endodermis, 1 mm. in diameter.

Transverse section of tuber, to the same scale,

showing ring of meristeles, each with its own
endodermal sheath, 3 mm. in diameter. (xlO.) m0i»isteleS

the stele is reconstituted from its
The significance of these
two examples in supporting the theory cannot be mistaken.

In the petiole of the fern-leaf the leaf -trace has as a rule the form of
an arc concave on the adaxial side. In many relatively primitive ferns
the leaf-trace is undivided. Being thus a continuous curved tract limited
by endodermis, it may form in large leaves a formidable obstacle to com-
munication from the outer surface inwards, and especially at the leaf -base,
where naturally interchange would be active and the petiole is at its
largest. In many ferns the leaf-trace is broken up at, or near to, the
base into separate strands. There is often a median slit dividing the
trace into equal halves, as in the type of Asplenium, Athyrium, or
Gymnogramme (fig. 16). But often the subdivision may be carried further,
as in the case of many Cyatheoid Ferns (fig. 17 : 6). Sometimes the slits
close again upwards and downwards, as is very well seen in Plagiogyria f

19

1920-21.] Size, a Neglected Factor in Stelar Morphology.

semicordata. The slits are in fact perforations of essentially the same
nature as those which occur in the axis, and their function is the same.

They are most prominently
seen in leaves of large size,
and especially where the
margins of the curve ap-
proach one another, as in
Thyrsopteris or Alsophila
(fig. 17 : 5, 6). It may.

Fig. 16. — Transverse section of petiole of Athyrium then, be concluded that in

filix fcemina, ferns of advanced type the

(a) Near base ; (&) higher up. After Luerssen. (x7.) . „ . , .

leat-trace is subject to per-
foration in essentially the same way, and with the same physiological effect,
as is the stele of their axes.

The stele in the root of ferns is always small, so that no difficult problem
of proportion of surface to bulk arises. The general tendency to concentrate
the vascular tissues at the centre of the transverse section of the root, which
is so general in the Pterido-
phytes at large, leads to the
same result. Even in the
large roots of the Marattiacese
there is no need for any dis-
ruption of the compact stele.

The triumph of the Lepto-
sporangiate Ferns which show
disintegration of the stele in
stem and leaf in all their more
advanced types, is witnessed
by their 6000 living species
over the face
of the earth. That triumph
has been won by a compro-
mise, effected without cambial
increase in the enlarging stem. The conducting stele has enlarged with
the conically enlarging shoot: it has maintained its endodermal barriers
complete, and has met the difficulty of physiological interchange conse-
quent on that enlargement by various steps of moulding and disintegration
of the stele. This has given those conducting tracts the requisite propor-
tion of surface to bulk even for stems as large as those of the Tree Ferns.

The analogy between what is seen in ferns and the “ polystelic ” state

Fig. 17. — Transverse sections of petioles, all drawn
to the same scale. ( x 2. )

1, Dipteris conjugate/, ; 2, Dipteris Lobbiana ; 3, Metaxya ;

4, Phlebodium aureum ; 5, Thyrsopteris ; 6, Alsophila australis.

These show that while greater size leads to vascular
disintegration, there is no definite proportion.

20

Proceedings of the Royal Society of Edinburgh. [Sess.

of certain of the larger species of Selaginella suggests that they should
also be examined from the physiological-anatomical point of view. The
similarity between the vascular arrangements in S. Icevigata and that in
solenostelic ferns seems to indicate that there is some common underlying
cause which has brought such likeness into existence. It is suggested that
the need for physiological interchange over the surface of an enlarged stele
has been the determining factor in both cases, though the need for a
larger surface seems less apparent in Selaginella with its peculiar structure
of the endodermis than elsewhere. The Medullosse with their recurrent
“polystely” also provoke comparison. Scott {Studies, vol. ii, p. 444)
remarks that their polystely has no relation to leaf-gaps, and he suggests
that “ the breaking up of the original stele depended on some other cause.”
Does it not appear probable that the cause may have been connected with
questions of proportion of surface to bulk in the original steles of these
large stems, before cambial increase set in ? With the knowledge of their
primary steles and of their sheaths so incomplete as it is, one cannot do
more than suggest that this is an aspect worthy of consideration, especially
as it has been found to illuminate the cognate structure in ferns.

Having thus seen how firmly established the disintegrated stelar state
is among Pteridophytes, the question arises whether Flowering Plants
show any similar modifications of stelar structure with enlarging size.
Most of the Flowering Plants have met their problem of enlargement in
other ways, as will be noted later. But the large prop-roots of certain
palms have advanced structurally along lines that show a close analogy
with what has been seen in the ferns. Such roots are often thick. They
have normally a cylindrical stele delimited by an endodermis that is
sclerotic. There is a cortical system of large intercellular spaces, and an
intra-stelar ventilating system that is often also large. These are separated
by the barrier of endodermis. Consequently the same problem arises with
increasing size as in the stems of ferns. Modifications in the direction of
disintegration, or of “ polystely ” as it is sometimes called, have been
produced by involution and finally by disruption of the endodermis, in
Areca catechu, Archontophcenix cunninghami, Dictyosperma aurea,
Verschaffeltia splendida, and other palms. The departure from type
appears in roots about 1 cm. in diameter, and it is still more marked in
those of larger size. In roots about 1 cm. in diameter the stele takes a
fluted form. In larger roots the involutions are deeper, and the endodermis
and ring of vascular tissues within it are interrupted by bands of parenchyma
with continuous intercellular spaces (fig. 18). In roots of the largest size,
as occasionally in Areca, but more markedly in Verschaffeltia, the separate

1920-21.] Size, a Neglected Factor in Stelar Morphology. 21

vascular tracts may be rounded off, and each completely surrounded by its
own endodermis (fig. 19). The stele is thus disintegrated into a number

of meristeles, and the analogy
with the ferns is significant.
But all large Angiospermic
roots do not behave in this
way. A prominent exception
is seen in Pandanus, the large
prop-roots of which may he
as much as 5 cm. in diameter,
and yet show no stelar dis-
integration. Thus size does
not always prescribe it. These
Fig. 18. — Transverse sections of root of Areca. references by no means ex-

i-iv, Successive sections from the same root: i is 15 mm. from L0110i. f n. 0 avomnloa wViinVi
apex ; ii at 77 mm. ; iii at 115 mm. ; iv at 150 mm. v is a naUSt me examples WUlCn
section from another, larger root. After Cormack. might be quoted £rom the

higher vascular plants, in which distension, with or without a definite
cambial zone, results in a distended mass of tissue. In such cases the
texture is often sappy, and the
vascular system broken up into
numerous isolated strands. This
is seen in Welwitschia, Gycas,

Gunnera, and Nymplicea. It is
worthy of remark that these
plants, which resemble the Marat-
tiacese in their general construc-
tion of the stem though not in its
details, are all either actually
xerophytes, or they live under
circumstances in which a rapid
fluid-transit is not necessary.

Nevertheless, that actual size Fig. 19, — Transverse section of a large strut-root

is causally related to these abnor- °J rersclutfeUia splendida, showing high state
J 01 stelar disintegration.

malitieS in the roots of palms is st.— a completely cylindrical meristele.

. 1 i n lr. = lateral roots. (x2). After Cormack.

shown by the tact that when the

root diminishes progressively the abnormality ceases. It was demon-
strated by Cormack (Trans. Linn. Soc., vol. v, pt. 6, 1896) that there is
a continuous transition to normal monostelic structure in the younger
and thinner parts of roots that are fluted in their older and thicker
region (fig. 18). He was led to conclude that this difference of structure

22

Proceedings of the Royal Society of Edinburgh. [Sess.

is due to a progressive change in the mode of differentiation of the
apical meristem. It is in fact here, as it is also in ferns, a question of
procambial destination. But how it is, and why it is, that the meristem
of a part beyond a certain size should in fern-stems and in palm-roots
differentiate its procambium so as to produce a disintegrated stele, and
the same root below that size so as to produce an integral stele: and
why the latter type of meristem should pass into the former, as in the
ontogeny of the Leptosporangiate Ferns: or the former into the latter,
as in certain individual roots of palms, must for the present remain an
open question. It is in fact as great a mystery as is the power of the
root-tip to receive the stimulus of gravity, and to pass it on to the
point of reaction. The behaviour of meristems remains now, as it has
always been, the greatest enigma of the plant-body, and not the least of
the questions which it raises is this : How does the meristem forecast in its
embryonic tissues those proportions of surface to bulk which will be
necessary when the tissues still embryonic shall have matured to their full
size ? In this the biologist of the present day may see a new application
for the old word “ Prolepsis.”

It may be asked, if certain plants show these modifications of structure
according to size, why are they not more common among the higher plants,
many of which seem to be of such size as to justify, or even to demand
them ? The reply is that in the stems and roots of very many seed-bearing
plants, the difficulty of a delimiting endodermis does not arise, except in
the young state, and while they are relatively small. In many small
Monocotyledon-stems, such as the creeping rhizomes of Convallaria
majalis. a well-marked endodermis may exist. Even in this plant
Schwendener has recorded a “ perforation v similar in nature to those
seen in Ferns. But in plants of larger size where the stele is dilated so
as to take up almost the whole of the transverse section, as is the case
in the palm-type generally, the endodermis is inconspicuous, and does not
appear as an efficient barrier. These plants have in fact adopted a con-
dition which for practical purposes is like that of the Marattiaceae, though
it has been reached by a different developmental method. Isolated vascular
strands traverse the parenchyma of the distended stele, and neither they
nor the stele have an efficient endodermal barrier.

Those plants which possess secondary thickening, such as the Dico-
tyledons and Gymnosperms, stand in a different position. Frequently they
show in their young stems and roots a well-marked endodermis. But
before the stem or root enlarges to that size which appears to be critical
in so many plants (that is about 1 cm. in diameter), the secondary cambial

23

1920-21.] Size, a Neglected Factor in Stelar Morphology.

increase within has already so stretched and disorganised the endodermis
that it can no longer act as a physiological barrier. It would be worth
while to examine it carefully as to the manner of its functional change,
from the point of view here suggested, and to trace in detail the disruption
or disorganisation of the sheath. But such observations would not be easy.
It is only in cases where the endodermis is marked by special structure
that this can be readily seen. An example has been worked out by Miss
Mann in the large roots of Dracaena, which show secondary thickening.
The effect of internal expansion of tissues is shown in bursting asunder the
thickened cells, and communication is thus established between the cortical
and stelar systems by tracts of ventilated parenchyma. Once the
endodermal barrier is interrupted, communication is continued radially
inwards along the medullary rays of Dicotyledons and Gymnosperms, as
Strasburger showed long ago. It is in some such way as this that the
problem is solved for trunks and roots of the largest size The same holds
also for the dendroid stems of Monocotyledons, such as Dracaena and
Cordyline. In them tangential sections show that intercellular spaces run
radially inwards in the hardened tissues that lie between the secondary
strands.

The success with which the flowering plants have thus met the
requirements of increasing size stand in strong antithesis to the difficulties
with which the ferns have had to contend. Doubtless the strictly enclosed
conducting system of ferns is a more effective means of transport for
plants so dependent as they are upon a constant water-supply. But the
problems which increasing size has raised in them could only be solved
by extraordinary modifications of structure : and that seems to be the
physiological explanation of those remarkable vascular systems which
they show, often in clearly marked succession in their individual develop-
ment. The ontogenetic evidence is in fact more weighty than that from
comparison.

Those who pursue sciences of exact measurement may expect me to
give precise statements as to the actual size of stele which will be possible
with a certain structure, and of the exact dimensions at which the
“ limiting factor ” will become operative : that at which either a new form
of stele must be adopted, or a change be made in the visible structure of
the endodermis, so as to alter its permeability. At present it is not
possible to put forward measurements of that nature. The difficulty is
illustrated by the drawings, all to the same scale, in figs. 9 and 17 ; and
especially by the cases of Dipteris and Matonia, two genera of allied
ferns, with many analogies of structure. They are both rhizomatous and

24

Proceedings of the Royal Society of Edinburgh. [Sess.

solenostelic : transverse sections of them drawn to the same scale are
shown in fig. 9 : 2, 3. Dipteris conjugata is the larger, and shows only
a simple solenostele : Matonia pectinata is the smaller, and shows three
concentric rings. A further example is seen in fig. 13, A, B, where in stems
of equal size that of Cibotium is a simple solenostele, that of Hemitelia is
a dictyostele with medullary strands. A comparison of drawings illus-
trating the origin of the solenostele in individual plants of Gleichenia
pectinata , Loxsoma, and Histiopteris incisa, shows that no absolute size-
limit rules for them, though in each individual a great increase of size
accompanies the structural change. There need be no surprise that this
difficulty should arise, for it is common knowledge that the character-
istics of plants, and ultimately of their protoplasts, differ. One is more
resistant to temperature, or drought, or insolation than another. The
incidence of the “limiting factor” will depend upon the specific perme-
ability of the endodermis, and particularly of its protoplasts. It seems
probable that this may vary from plant to plant without any visible
difference of structure, just as much as other characteristics of the pro-
toplasts do. It is only when the specific permeability of the endodermis
has been measured for any plant that we can reasonably expect to be
able to state in terms of exact measurement where for it the incidence
of the limiting factor may come. With our present knowledge it is
only a rough suggestion of the existence of a critical point that can
be indicated. But this gives a sufficient ground for recognising the
underlying principle of similar structures as applicable to vascular tissues.
It appears to have determined certain of their peculiarities, which have
hitherto appeared as strange and unexplained phenomena. It is believed
that by directing attention to the sheaths surrounding the vascular
tracts, their presence or absence, their structure and permeability, and their
relations however roughly to absolute size, a better understanding of the
vascular systems of plants, and of the ferns in particular, will be obtained
than by the most carefully drawn comparisons of mere formal anatomy.
Size must then be considered not only in its bearing on external form and
the strength of materials, but also as it may tend to modify, or even in
some cases to rule decisively the structure and disposition of internal
tissues.

As far as I am aware only one definite attempt has hitherto been made
to correlate size with internal structure in the massive plant-body.
Professor Compton, in a very remarkable comparative study of the
seedling structure in the Leguminosse {Linn. Journ., vol. xli, p. i, 1912), has
shown that in determining the level of transition from root-structure to

1920-21.] Size, a Neglected Factor in Stelar Morphology. 25

stem-structure in the hypocotyl, the diameter of the axis is a most
important factor. He found that low transitions are characteristic of
massive hypocotyls, high transitions of those which are slender. Here
again it was not possible to put forward exact measurements, but the
principle emerges from the average taken from a large number of seedlings
of different species. The correlation in that case was, however, between
size and the readjustment of intra-stelar tissues : the form of the stele itself
was throughout approximately cylindrical. Questions of permeability of
the endodermal barrier will hardly have affected them. That size may
thus be correlated on the one hand with the internal disposition of the
stelar tissues, and on the other with the actual conformation of the stele
itself, shows how important it may be in determining features which are
habitually used in comparison. The effect should be to impose caution in
drawing phylogenetic or classificatory conclusions from characters so
pliable : for at once the door is opened for frequent homoplasy in stocks
phyletically quite distinct from one another. Thus the recognition of the
principle of similar structures and its consequences, while it involves
interesting points in physiology and anatomy, may react finally even upon
classification.

(Issued separately December 30, 1920.)

26

Proceedings of the Royal Society of Edinburgh. [Sess.

II —On the Equations of Motion of a Single Particle.
By J. H. M. Wedderburn.

(MS. received August 9, 1920. Read November 1, 1920.)

§ 1. When solved for the second derivatives, the Lagrangian equations of
motion for a system in which there are no extraneous forces have the form *

d2xk ^ ( i j \ dxidx1_
dt 2 ^ ) i j dt dt ~ ’ h-

ij ’

h 2, . . . tz),

or, disregarding the parameter t ,

(1) . . <^+z{y (*=i,2

ij

| Y J- being the second Christoffel symbol j* of the matrix associated with

the kinetic energy. If there are extraneous forces and, denoting t by
xn+1, we add d?xn+1 — 0 to the set of equations, the equations of motion are

(2) d2xk + 2 | Y \dxidXj-¥kdxn+2 = 0, (k= 1, 2, . . . n), d2xn+1 = 0.

ij '

These equations have a general similarity to (1) with the number of
variables increased by one, and would in fact have exactly the same
mathematical form if there existed a matrix \js for which

(3)

u i “Ur

\i 7

U

+iy=o,

fn + 1 7

\ i

\'nAi

o, (i,j= b

= -Ffc, (i,j,7c=l, 2, . . . n),

71+ 1),

where the dashes indicate symbols belonging to the new matrix \js. It is
readily seen, however, that these relations cannot hold in general, and it is
the principal object of this note to investigate the circumstances under which
they can be approximately satisfied. If ordinary dynamics can be modified
so that this is so, and the time f variable is regarded as a special case of the
space variables, it will follow that the equations of motion in the modified

* Of. Whittaker, Analytical Dynamics , p. 39 ; or Wright, Invariants of Quadratic Differ-
ential Forms , p. 83.

t The definition and properties of these symbols may be found in Wright, loc. cit., p. 10.

I If there is more than one particle in question, it may be necessary to introduce more
than one time variable. In many ways it is best to consider these as strictly space variables
and. to assume that particles in our universe are moving in the direction of the fourth space
direction so nearly uniformly in straight lines that the distances measured in this direction
are, to a first approximation, proportional to the time.

27

1920-21.] The Equations of Motion of a Single Particle.

system will have the same form independently of the system of coordinates
used, and all forces will appear as geometrical constraints.

§ 2. For the present we shall consider only the motion of a single particle
whose position is defined by rectangular coordinates xv x2, x3, the time
variable being denoted by x4 and the potential function by V. The
Newtonian equations of motion are then

(4)

= dx% {h= 1, 2, 3), d%= 0,

OXi,

and our problem is to determine a symmetric matrix \js = (ars) such that
the equations

(5) d<2xk+^j | \

or the equivalent set
(5') . .

dxidxi — 0,

(*= 1, 2, 3, 4)

* 3
k

dxidxj = 0, (k= 1, 2, 3, 4)

are approximately satisfied when (4) is satisfied, and vice versa. To
determine the conditions for this, we substitute the values of d2xk from (4)
in the first three equations of (5'), thus obtaining

(6)

0V

ddij, 'da at. da.

dx n dXn dxj

so that the term under the 2 on the right is zero except when i and j are
both 4. It follows immediately that the part of the matrix whose sub-
scripts do not exceed three, i.e. the part which refers to the subspace
xv x2, x3> is independent of xv x2, x3 ; and therefore, since \/s is symmetric,
there is a real orthogonal transformation, with coefficients independent of
xv x2, x3, which reduces this part of \fs to the main diagonal. We may
therefore assume without loss of generality that aij = 0, (i,j = 1, 2, 3; i-^j)

—% 4"

and da4i/dXj = 0 (i}j = l, 2, 3). Further, since ^

= 0 (i, 4), we have

and similarly

t dai1c daH = Q
dxj dxi dxk 5

ca>j 4 da^k dak4

dxk dx4 dx^ ’

so that daile/dxi = 0 (showing that the coefficients of the orthogonal trans-
formation used above are also independent of x4) and

so that we may set
(7) . . .

da i4
dxk

dajg

dx,

0A

(i, k=f= 4)

an = (z== fj 2, 3).

28

Proceedings of the Royal Society of Edinburgh. [Sess.

(8)

If a.

a--i) <*=1’2’3>-

Finally, comparing coefficients of dx\ in (6) and using the relations just

derived, we have

0Y dak. . da.. d

• —=

dxk dx4 z dxk dxk

a22, a33 are all different, we infer that Y has the form
9i(xi)+92(x2)+9s(x3)’ or if say an = ‘Wa33>it has the form g1(xvx2)+gs(x3) ;
but since the x’s are ordinary rectangular coordinates, this form does not
agree to a first approximation with the Newtonian potential, so that when
we are dealing with Newtonian dynamics we must have au = a22 = a33 and,
being constant, we may set each equal to unity. This gives immediately

0A

(9)

a, , = 2Y 4- 2;

di

the arbitrary function of x4 introduced by the integration being included
in A. The fourth equation of (5') then becomes

dxidx.

* V - 1>. - - i - 2i(S ■ *££)

so that in order that d2x4 may be a second order quantity it is sufficient
to assume that Y + 0A /dx4 is large compared with the other coefficients in
the equation, a condition that can be readily attained, since V + 0A/0as4
contains an arbitrary function of x4 which can have terms not entering
into any other coefficient.

We assume, therefore, that \js has the form

10 0 A,

(10)

Ac

A3 2 Y + 2A4

(12)

where we have set A{ for dA/dxt. The corresponding quadratic form is
(11) . . . . . 2 dx\ + 2 Y dx\ + 2dAdx4 ,

and the corresponding Lagrangian equations can be readily reduced to

d2xk + A kd2x4 - Y kdx\ =0 [k = 1, 2, 3),

(2Y + A4)d2x4 + d2A + 2 dVdx4 - Y 4dx\ = 0,

the form (11) equated to a constant being, as is well known, a first integral
of (12).*

* This seems the most natural way of introducing the form (11) into the dynamical
system. Jt suggests that it is natural to consider this form as defining time rather than
distance, thus leaving open the possibility of using a different form to define the geometry
of space.

f dh

■ |(2f

1920-21.] The Equations of Motion of a Single Particle. 29

When the potential is independent of the time x 4, and dA/dx 4 is constant,
equal to —a, say, a first integral of the last equation of (12) is

(2V - a)dx± + dA = const.,
or

2(Y - a)dx 4 + 2 t^dx^ = const.

§ 3. An important case of the equations of the preceding paragraph
arises when (i) the potential Y is a function of r alone, and (ii) A= — axi} so
that A4= — cl, & constant.

When (ii) holds and also V4 = 0, equations (11) and (12) become, on
introducing a parameter r,

(13) .

(14) .

whence
(14') .

dxA2

da

(H constant)

d2x$
~d 7-

Y A

( dx.

\dr J

V-

0, (*=1,2,3)

2(V - a)^i + 2~ dp = 0,

dr 2 dr dr

— £ = ------ (K constant)

dr Y — a

so that, setting U = — k2I( V — a),

(15) .
(15') .

d2x^

d ?

U* (*=1,2,3),

dx^ U

dr k

2U = H.

If now V, and therefore U, is a function of r alone, it follows by the
usual methods that the motion is in a plane, and, choosing spherical polar
co-ordinates so that this plane is <p = 0, the equations of motion become

d?r _ (d,6\2 _ k2 dY = dU '2d0 = j

dr 2 \dr) (V - a)2 dr dr’ dr

where h is constant, or setting u—l/r,

(16) .

dU

d2u _ _ dr _ 1 dU dO _ , 2
’ dO'2 h2u 2 h2 du dr

If we now assume that Y has the Newtonian form m/r, and set /c = — a so
that equals r when r* is large, then the equation for n becomes on
neglecting terms in 1/a2,

(16') .

d2u

dO2

5 +

~Wa

m

h2'

30

Proceedings of the Boyal Society of Edinburgh. [Sess.

which gives

(H) • • •

so that the orbit has the approximate period %ir(l + in 0. To agree

with Einstein’s result this would require a = c2/3, and then when r is large
the quadratic (11) would approach Hdx\ — %c2dx\. The Newtonian form of
Y therefore leads to results which clash with the classical form of the
relativity theory.

The usual form of the quadratic is easily obtained by assuming that
the Newtonian form of V is merely the first term in the expansion of V
in negative powers of c 2 ; but the method of the next paragraph is more
satisfactory.

§ 4. The Newtonian potential is a solution of Laplace’s equation. If
this equation is regarded as associated with the form 'Edx* — c2dx\, Y
being independent of xif the analogous equation associated with the form
'Zarsdxrdxs is, as is well known*

(17) . . . ... . A2Y = 0,

where A2Y is the Beltrami parameter 2arsYrs
reciprocal to (cbr8), and

(18)

82Y _ ^ fr sy_V
dxrdxs j \ J fdxj

being the covariant derivative.

In the case considered in §3, (17) becomes

(ars) being the matrix

which leads to
(19) .

dW 2 dV 1 (d V\2_0

dr2 + r dr + 2( Y — a)\ dr ) ’

Y-a

Setting k= —ai= -\c2, 2/3 = 3 ma1, this gives in place of (16')

(20)

d2u f 5 m2\ m
W+V~£h‘2)w = h?’

which leads to f of Einstein’s value f for the motion of the perihelion of
Mercury, a result which is slightly closer to the observed value. The
corresponding form does not, however, lead to the correct deviation of a
ray of light in a gravitational field.

There are other methods of deriving an equation analogous to Laplace’s

* Of. Wriglit, loc. cit p. 53.
t The Einstein value is obtained by setting

31

1920-21.] The Equations of Motion of a Single Particle.

which lead to results different from those just obtained.* It will be seen
below that in certain important cases, in addition to the case discussed
above, a change of variable enables us to bring (11) into the form

2 (a-V)dyl ,

where dsl depends only on x1: x2, x3, and dyjdty 4=1. Comparing this form
with ds20 — c2dt2, it is natural to interpret y 4 as t and to regard 2{a — Y) as
the square of a variable velocity of light. From this point of view, then,
we should expect V2(<x — V) to satisfy the generalised Laplace equation
rather than V itself, especially as when a is large the value of V so
determined will agree with the Newtonian potential to a first approxima-
tion. In the case discussed in the preceding paragraph this second method
of determining V leads without approximation to the Newtonian form.

§ 5. From the dynamical point of view, there does not appear to be any
reason for imposing any particular form of restriction on V and A in addi-
tion to the general restrictions of § 1 and § 2, which are sufficient to ensure
that the equations of motions are equivalent to the Newtonian equations
to a first approximation. In view of the particular case partially developed
in § 3, it is, however, natural to investigate the case in which A depends on
V alone except for an additive term of the form — ax 4 (a constant) introduced
in the integration of (8). This makes the equations of the system depend
solely on the potential. We shall not impose this condition in its entirety
at first, but will introduce it as required in the course of the discussion.

We shall first determine conditions under which it is possible so to
transform the variables as to remove the term dkdx± in (11). Setting

Vi — (i= 1, 2, 3), 2/4 = dfai) *^3J ‘*'4)’

Xi - Vi (i=l, 2, 3), X^=f(yv y2, ys, y4),

in (11), and equating the coefficient of dy^dy^ to zero, we get

(21)

dg 0A
chq dx^

2(v+a4>S,.

=0 (*“ 1, 2, 3).

If A is a function of V and x} alone and V is independent of ,x4, this leads to

(22)

0A3A_2/^+y)Y=o,

dx, 0Y \dxL

0V

any solution of which will give the required result. If 0A/0V and 0A/0x4
are functions of V alone, f i.e. A= — acc4+/(V), the solution of (22) is

dV

(23)

2/4 = F(*4 + j|^

av (V-a

* Gf. Levi-Civita, “Statica Einsteiniana,” Rom. Acc. L. Rend., xxvi (1917), p. 458, where
the connection with Einstein’s equations is discussed.

+ There are, of course, other cases in which an explicit solution of (21) can be obtained,
e.g. when 2Y + A is a function of A and xi alone, or if A has the form AfiY) + x4 A2( Y).

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

ie i

*ji

where F is an arbitrary function, the most important case being

'0A dV

lav (V^a) *

When (23') is used, the quadratic (11) becomes

'0A\2 dV2

(24)

+ 2(V -- a)dyl .

v0V/ 2 (V-a)

We shall now assume that Y x = Y — a = constant is one of a triply
orthogonal system of surfaces. Making a slight change in notation, we
denote the corresponding curvilinear coordinates by y1 = Yv y2, yZi and
set the square of the element of distance in the space xv x2, x3, equal to
Hicfa/5 + H2efa/! -\-H3dy% so that (24) becomes

(25) . . . (Hi-^-)^|h^ + H3*/1+2V1^>

where Ax = 0A /dyv or say

(25') .... a1dyl + a2dy% + a3dyl + a^dyl.

As a further restriction on Y, we now assume that it, and therefore also
Y1, satisfies the Laplace equation which is covariant relatively to (25),
namely

/0fi, AW_ la^aw ivito(sw\ .

' ^ ci/i 2a? dyt dt /( 2«,2 a. dy. di/j)

or, if W is a function of y1 only,

■ 32W j 0 log (a2a3a4/a1) 0W

5- +

dVi

= 0.

dVi

In particular, if W = Y1=y1,

0 f a^aQa
dy

where / is an arbitrary function of y2 and y3, y± being absent since the a’s
are independent of ytl. Inserting the values of the a’s from (25), we get

;(“) = 0, or f{y»«s),

(27)

HoHsV, „

“ A2 %)>

H1-2V,

so that H2H3 is the product of a function of Vx alone and a function of y2
and yz alone.

If now Vj_ is a function of r= Jx\ + x\ + xl, we may use spherical polar

co-ordinates with y2 = S and ys = </>, so that 1^ = 1/
H3 = r2 sin2 0. (27) then becomes

= /dViX

dr 7 ’

H0 = r2 and

TT JL(dA\2
2Y1\0Y1/

y riVv (y constant)

1920-21.]/ The Equations of Motion of a Single Particle. 33
and in place of (25) we get

(29) . . ^ yr*Y dr2 + r2d62 + r2 sin2 6d<f)2 + 2Y ^y'l .

The values of A and y 4 are given by

Here Y1 is completely undetermined except that (i) it is a function of r
alone, (ii) it agrees with the Newtonian potential to a first approximation
apart from the additive constant a.

If, in addition, we impose Kottler’s * condition that the determinant of
the form (29) equals — c2 when expressed in rectangular coordinates, we
readily deduce that Y1 = — J(a + /3/r ), a being constant and /3 = — 2c/ JZ- 2y,
and then (29) becomes

c2

(31) . . . — -^ydr2 + ?,2d02 + r2 sin2 6d(j>2 + 2Y1di/f ,

which is equivalent to the Einstein-Schwarzschild form,

A similar discussion can be easily made if the second form of Laplace’s
equation is adopted, the result being that Y has the form given in (19) and
that (29) is replaced by

~(d~Y dr2 + rW2 + r 2 sin2 0dd>‘i+ 2V, A/j.

?nz' dr * 1

* F. Kottler, Ann. d. Phys., lvi (1918), p. 401.

( Issued separately January 24, 1921.)

VOL. XLI.

3

34

Proceedings of the Royal Society of Edinburgh. [Ses§.

III. — -ZEther and the Quantum Theory. By H. Stanley Allen,

M.A., D.Sc.

(MS. received October 30, 1920. Read November 22, 1920.)

§ 1. Extreme supporters of the principle of relativity find no place for an
aether. Thus Lord Haldane in discussing the theory of Einstein writes :
Space, as a physical thing with unvarying geometrical properties, is to be
banished, just for the same sort of reasons as the aether was banished
before it. Only observable things are to be recognised as real in the new
system of modern physicists.” On the other hand, many followers of
Faraday and Maxwell have regarded aether as the primary real substance ;
all mass, momentum, or energy being mass, momentum, or energy of the
aether. Without entering into a discussion of the significance of physical
“ reality,” we may, with most physicists, agree to use the concept of aether
as giving a model, inadequate though it is at present, for the interpretation
of physical phenomena.

§ 2. During the present century it has been recognised that certain
classes of observations cannot be explained on the basis of Newtonian
mechanics, and a new theory has been developed which has proved
extraordinarily fertile. “ The quantum theory is believed to have disclosed
in nature a certain atomicity of a kind unsuspected by the older mechanics.”
The theory centres round the idea of spasmodic interchanges, losses or
gains of energy of amount hv, where h is Planck’s constant, and ;/ is a
frequency (number of oscillations per second). According to Poincare, the
hypothesis of quanta is the only one leading to the law of Planck which
represents the distribution of energy between different wave-lengths in
“ black-body ” radiation. In his invaluable report on Radiation and the
Quantum Theory, Jeans has pointed out that if the aether is part of the
dynamical system, then the energy in the aether must be treated as part
of the energy of the system, and to arrive at Planck’s formula it would
appear to be necessary to suppose that the vibrations in the # aether
themselves gain or lose energy by whole quanta. The assumptions
underlying the quantum theory have been stated in somewhat different
forms by various theoretical physicists. For our present purpose we may
adopt the hypotheses proposed by W. Wilson,* as these have been employed

* W. Wilson, Phil. Mag ., vol. xxix, p. 795 (1915) ; vol. xxxi, p. 156 (1916).

35

1920-21.] iEther and the Quantum Theory.

by Sommerfeld * * * § with marked success in explaining the fine structure of
spectral lines of hydrogen and helium. During certain intervals each
dynamical system behaves as a conservative one, and between these
intervals are relatively very short ones during which definite amounts of
energy may be emitted or absorbed. The motion of a system in the
intervals between such discontinuous energy exchanges is determined by
Hamiltonian dynamics as applied to conservative systems. Let qv q2, . . .
pv p2, . . . be the Hamiltonian positional and impulse coordinates of a
system in one of its steady states. The kinetic energy, T, can be expressed
as a quadratic function of the form

T = + 2 A2<?22 + * • •

= T1 + T2 + . . .

Further, 2T1 = ^1p1, ^T2 = £2p2, etc.; pv p2 being Hamiltonian “moments’'
corresponding to the canonical coordinates qv q2. Wilson’s hypothesis is
that the discontinuous energy exchanges always occur in such a way that
the steady motions satisfy equations of the form

— nJl or ^ /Tjdtf = njlt

the integration being extended over the period corresponding to the q
considered, and n being a positive integer (including zero).

§ 3. Planck’s constant h, which has the value 6'558 x 10-27 erg sec., may
be regarded as a quantum of action. It is, however, simpler to look upon
this universal constant as an angular momentum, a view suggested by
J. W. Nicholson]- in June 1912, and employed by Bohr J in his theory of
the origin of spectral lines. S. B. McLaren § identified this natural unit
of angular momentum with the angular momentum of the magneton.
“ Rejecting entirely the idea of magnetic or electric substance, the
magneton may be regarded as an inner limiting surface of the aether,
formed like an anchor-ring. The tubes of electric induction which
terminate on its surface give it an electric charge, the magnetic tubes
linked through its aperture make it a permanent magnet.” For a
magneton of any shape of cross-section the angular momentum, according
to M‘Laren, is proportional to the product of the number of tubes of
electric induction, Ne, and the number of tubes of magnetic induction, Nm.
In a paper communicated to the Philosophical Magazine I have shown

* Sommerfeld, Ann. d. Physik , vol. li, pp. 1, 125 (1916).

t Nicholson, Monthly Notices , R.A.S. , June 1912.

I Bohr, Phil. Mag., vol. xxvi, pp. 1, 476 (1913).

§ M‘Laren, Nature , vol. xcii, p. 165 (1913).

36 Proceedings of the Koyal Society of Edinburgh. [Sess.

that this result may be proved in a very general way, and that in ordinary
units we have

Angular momentum = — NeNw.

Ji7T

It is to be noted that this expression is quite independent of the
quantum hypothesis. If we now apply the quantum theory to this case
we have

r2ir

rz*

i pd<f> = nh ,

J o

or as p, the angular momentum, is constant

2 irp = nh.

Identifying these two expressions for the angular momentum, we obtain

If we regard the charge of the magneton as equal to e, the electron charge,
the relation may be written

or the number of magnetic tubes passing through the aperture of the
magneton is directly proportional to an integer n.

§ 4. It seems probable that this result may be applied not only to
M'Laren’s magneton, but also to the case of a classical electron circulating
in a closed orbit. Such an extension has in fact been suggested in an
interesting, but not altogether convincing, paper by A. L. Bernoulli.* This
author has given an electrodynamic interpretation of Planck’s constant by
introducing a principle which he terms the “ Principle of the Universal Flux
of Induction,” defined as follows : — “ If electrons are moving in identical
closed trajectories in a molecular magnetic field, the number of lines of
force cut by the radii vectores at each revolution is. one and the same
universal constant.” In other words, all the electron-resonators are
traversed by a like tube of magnetic force. The product of the induction
flux and the charge is equal to Planck’s constant.

In the paragraph immediately following I have attempted to give a
more general proof of this principle, with the object of avoiding as far
as possible particular assumptions as to the character of the electrical
distribution.

§ 5. Consider a system composed of any number of point charges ev e2,
. . . rotating with angular velocity <*> about a common axis. These will be
the starting-points of electrostatic tubes rotating about the same axis.

* Bernoulli, Archives des Sciences , vol. xlii, p. 24 (1916).

1920-21.] x^Ether and the Quantum Theory.

37

2 H2

may be written 4^^^- ] = - X . Hence the total angular momentum

Such an electrical system might correspond to an atom in one of its steady
states. The equivalent mass per unit volume of a tube is 4tt/xD2 sin2 0,
where D is the electric polarisation or displacement, and 0 is the angle
between the direction of the tube and its velocity. Hence the angular
momentum for unit volume of the tube is ^tt/ulD2 sin2 Or2 co. The moving
Faraday tubes are accompanied by a magnetic field, at right angles to their
length and to their direction of motion, given by H = 47rD sin Oreo. Hence
D sin dr = H/47ro), and the angular momentum for unit volume of the tube

of the system takes the form — , the summation extending over the

whole space occupied by the magnetic tubes.

If the frequency of rotation be sufficiently high, the movement of the
charges ev e2, . . . may be regarded as equivalent to currents iv i2, . . .

1 • 6-i ft) . Soft)

where h = ^, . . .

H2

The sum , which represents the electrokinetic energy, may be

expressed in the form JL1i12+ . . +M 12vi2+ . . . , where Lx is the self-
inductance for the circuit iv M12 the mutual inductance for the circuits
i,, i2, etc.

Hence the total angular momentum

2Mi2^2

0)

where Nx = Lxix + M12i2 + . . , and denotes the total number of magnetic
tubes passing through the circuit ir

In this case the application of the quantum theory to the steady state

tZv

pd<p = nh (n an integer), since the integration is to be

extended over the full period, which is common to all the rotating charges.
Hence

27 rp — nh.

Identifying p with the above expression for the angular momentum we
find

2eiN i=nh-

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

According to the electron theory, the charges ev . , . must be integral
multiples of the fundamental charge e, so that e1 = k1e, where \ is an
integer, which may be either positive or negative. Therefore

The simplest interpretation to give to this result is to regard the quantity
h/e as defining a unit magnetic tube ; the equation then expresses the fact
that in the steady state of such a system the number of magnetic tubes is
an integral number of such unit tubes.

If we now generalise this result we may say that as, according to
the quantum theory, the steady motions of any dynamical system satisfy
equations of the form

J pdq = rih ,

such a steady motion is always associated with an integral number of unit
magnetic tubes. In fact we postulate an atomicity not merely of electric
charges, but of magnetic tubes.

§ 6. The unit magnetic tube is determined by the ratio of Planck’s
constant, h , to the fundamental electron charge, e. Taking h = 6*558 x 10~27
erg sec. and e = 4*774 x 10-10 E.S.XJ.,

TT . . ^ . h 6*558 xlO"27 , i rv 17 yi n TT

Unit magnetic tube = - = ,n = 1*374 x 10-17 E.S.U.

0 e 4*774 x 10-iU

Assuming for the velocity of light the value c = 2*999xl010 cm./sec., we
find in electromagnetic measure one unit magnetic tube = 4*120 x 10~7 C.G.S.

Thus one C.G.S. line of magnetic force (one “ Maxwell ”) contains
2*43 x 106 unit tubes, or “ quantum tubes ” as they might be termed.

§ 7. Since there is a strong presumption that things which can be
counted must have a physical existence, we are led to regard these discrete
quantum tubes of magnetic force as physical realities. In view of the fact
that one C.G.S. magnetic line is a bundle of nearly two and a half million
quantum tubes, it is scarcely surprising that the smaller tubes have not
revealed their existence as such in ordinary magnetic experiments. There
is, after all, nothing novel in the suggestion of the actual existence of
magnetic lines of force. Students of Faraday’s Experimental Researches
will find that in vol. iii he insists again and again on this point of view.
Starting from the consideration of such lines in the abstract “ as expressing
accurately the nature, condition, direction, and amount of the force in any
given region either within or outside of the bar [magnet],” he passes on to
the inquiry “ of the possible and probable physical existence of such lines ”
(p. 438). If the existence of curved lines of magnetic force be conceded,

39

1920-21.] iEther and the Quantum Theory.

then the physical nature of the lines must be granted also. The question
of the existence of physical lines of force he regards as “ both important,
and likely to be answered ultimately in the affirmative” (p. 437). Again,
in the celebrated letter published under the title “ Thoughts on ray-
vibrations” (p. 447) he writes: “The view which I am so bold as to put
forth considers, therefore, radiation as a high species of vibration in the
lines of force which are known to connect particles and also masses of
matter together. It endeavours to dismiss the aether, but not the
vibration.” “ It may be asked, what lines of force are there in nature
which are fitted to convey such an action and supply for the vibrating
theory the place of the aether ? ” “ The lines of weight or gravitating

force are, certainly, extensive enough to answer in this respect any
demand made upon them by radiant phaenomena ; and so, probably, are the
lines of magnetic force. . . .”

As is well known, Clerk Maxwell developed and gave mathematical
expression to the views of Faraday, and one of his earliest papers deals
with the illustration of Faraday’s lines of force by the lines of flow of a
liquid (1856). As early as 1857 Faraday was speculating whether the
velocity of propagation of magnetic action is of the same order as that of
light, but Maxwell’s memoir, entitled “ A Dynamical Theory of the Electro-
magnetic Field,” in which the electromagnetic theory of light was
formulated, was not completed till 1864.

Sir Joseph Thomson has developed extensively the theory of moving
tubes of force, but unlike Faraday he regarded magnetism as a secondary
effect, ascribing magnetic fields, not to the presence of magnetic tubes, but
to the motion of electric tubes. The conception of lines of electric force
stretching from positive to negative charges presents certain difficulties,
as in the case where magnetic fields occur without any manifestation of
electric force. In order to account for such facts it may be supposed that
two sets of Faraday tubes exist starting from positive and negative
charges respectively. In a steady magnetic field the positive and negative
tubes may be thought of as moving in opposite directions with equal
velocities. Such difficulties have led many physicists to reject the idea of
the discrete existence of electrostatic tubes, in spite of the fact that “ they
give a natural and simple explanation of the electrokinetic momentum in
the aether ” (Jeans).

The results of the present paper suggest that the magnetic tubes may
be more fundamental than the electrostatic.

§ 8. Faraday’s proposal to “ dismiss the aether ” seems to have reference
to the particular view of the aether then prevalent. His own hypotheses

40

Proceedings of the Royal Society of Edinburgh. [Sess.

as to the existence of lines of force may be regarded as leading to a new
mode of representing the luminiferous medium. During the latter half of
the nineteenth century many attempts were made, especially by British
physicists, to construct mechanical models to illustrate the properties of the
aether. These are described in Sir Oliver Lodge’s Modern Views of
Electricity (1907), and in Professor Whittaker’s History of the Theories of
Hither and Electricity (1910). The rotatory character of magnetism,

suggested to W. Thomson (Kelvin) by a study of the magnetic rotation of
the plane of polarisation of light, was adopted by Maxwell,* and elaborated
in a series of papers on “ Physical Lines of Force,” in which a theory of
molecular vortices was applied to magnetic phenomena. He assumed the
existence in the magnetic field of vortices or eddies, having their axes in
the direction of the lines of force, and having their direction of rotation
determined by that of the lines of force. The vortices are separated from
each other by a single layer of round particles, which are in rolling contact
with both the vortices which they separate, and, acting as “ idle wheels,”
allow neighbouring vortices to revolve in the same direction. This
conception, says Maxwell (p. 346), “ may appear somewhat awkward. . . .
It is, however, a mode of connection which is mechanically conceivable
and easily investigated, and it serves to bring out the actual mechanical
connections between the known electromagnetic phenomena; so that I
venture to say that anyone who understands the provisional and temporary
character of this hypothesis, will find himself rather helped than hindered
by it in his search after the true interpretation of the phenomena.”

The theory of vortex motion has been applied in constructing models
of the aether by W. Thomson (Kelvin), f FitzGerald,} and Hicks. § A fluid
in which portions in rotational and irrotational motion are finely mixed
together has been termed a vortex-sponge. Laminar disturbances are
propagated through such a vortex-sponge in the same manner as waves of
distortion in a homogeneous elastic solid. Kelvin came to the conclusion
later that hollow vortices are better adapted than ordinary vortex filaments
for the construction of such models.

A model of another type is found in Kelvin’s || gyrostatic model of the
luminiferous working of the aether. This type has been developed and its
limitations pointed out by Larmor.lf In a lecture delivered before the

* Maxwell, Phil. Mag., vol. xxi, pp. 161, 281, 338 (1861).

f Kelvin, Brit. Assoc. Report , p. 473 (1880) ; Math, and Pays. Papers , vol. iv, p. 308.

| FitzGerald, Scient. Proc. Roy. Dublin Soc. (1885).

§ Hicks, Brit. Assoc. Report , p. 595 (1895).

|| Kelvin, Math, and Phys. Papers , vol. iii, p. 466.

Larmor, JEther and Matter, Appendix E.

41

1920-21.] iEther and the Quantum Theory.

International Congress of Mathematicians at Strasbourg on September 23,
1920, Larmor said: “The vortex theory and the elastic solid aether theory
had had their day, but there was no reason at present why we should
not admit the existence of an aether — a new aether the properties of which
were so different from those of ordinary matter that they could be
expressed only in terms of non-Euclidean space. The alternative was
complete abstraction, the absence of a basis on which to found our
theories.” *

The difficulties to be faced on the older view of the aether in connection
with the principle of relativity have been clearly explained by N. R.
Campbell in his books on Modern Electrical Theory .*(■ “ Our original idea

of the aether was ‘ the body in which radiant energy is localised ’ ; if, in
that statement, we put ‘ bodies ’ for ‘ body/ all our difficulties vanish ; if the
energy from different sources is localised in different bodies, then it is
obvious that the velocity of an observer relative to the body in which the
energy of one source is localised may be different from that relative to the
body in which the energy from another source is localised. If we speak of
‘ aethers ’ and not ‘ the aether,’ all our experiments prove is that the
particular aether with which we are concerned in any case is that which is
at rest relatively to the source and may be regarded as forming part of it.”
One way of visualising such a conception is by employing the electrostatic
tubes of Faraday in the manner sketched by J. J. Thomson. The results
of the present paper suggest that the magnetic tubes have at least an equal
claim to be considered as constituting “ the sethers.”

§ 9. Assuming the existence of discrete magnetic tubes in accordance
with the hypothesis of Faraday and the indications of the quantum theory,
we have to consider the possible nature of the tubes. The method by
which the magnitude of the unit tube has been arrived at suggests un-
mistakably that the distinguishing feature of the tube is spin about an
axis in the direction of its length. This is essentially the view developed
by Maxwell in his theory of molecular vortices, but it is not necessary to
adopt the particular mechanism by means of which neighbouring vortices
were enabled to rotate in the same direction. A classical electron moving
round the periphery of the spinning tube is, however, not unlike one of the
“idle wheels” imagined by Maxwell. This mode of representation re-
sembles that suggested by Larmor in the Physical Society Discussion on
the Ring Electron (1918) — “ One or more electrons constrained to move
round a channel would be like an amperean current. It is not unlikely

* Nature, vol. cvi, p. 196 (1920).

t Modern Electrical Theory , First Edition, ch. xiv ; Second Edition, Appendix I.

42

Proceedings of the Royal Society of Edinburgh. [Sess.

that constraint of this kind will have to be introduced into molecular
models to give an account of paramagnetism and ferromagnetism — namely,
structure in space or atom involving channels more or less definite for the
electrons to circulate in.” It would seem that such a view is consistent
with Bohr’s theory of stationary orbits and with the later developments of
that theory by Sommerfeld and others in connection with the fine structure
of spectral lines. In these applications of the quantum theory it is not
merely the size of the orbit, but also its shape and its position in space
which must be determined by the quantum principle, and can assume
certain prescribed values only. Consequently, as Sommerfeld puts it, the
stationary paths of the electrons in the atom, and also in the molecule,
form not a continuum but a network. The “ phase-space ” is interwoven
by the curves of the stationary paths as by the meshes of a net. The size
of the mesh is determined by Planck’s h.

On the present hypothesis the network is formed by the magnetic
tubes, between and around which the electrons are able to circulate. It
may prove necessary to proceed a step further and suppose that the tubes
can be divided up in the direction of their length so as to form “ aether
cells,” but such a subdivision need not at present be discussed, beyond
pointing out that in considering how the theory of molecular vortices
could be applied to statical electricity Maxwell * assumed the rotating
matter to be the substance of certain cells, such substance possessing
elasticity of figure. On this hypothesis he was able to explain electrostatic
phenomena, and showed that the velocity of transverse undulations in a
medium so constituted was in almost exact agreement with the velocity of
light, so that “ we can scarcely avoid the inference that light consists in
the transverse undulations of the same medium which is the cause of
electric and magnetic phenomena.”

§ 10. It is commonly assumed that an explanation of magnetic
phenomena can be obtained from the theory of the classical electron on
the basis of ordinary mechanical laws. That this supposition is incorrect
was shown by W. Voigt, f who proved that, assuming the electronic motions
are undamped, changes in the velocities of the electrons in consequence of
the formation of magnetic fields will not give rise to magnetic phenomena.
This result, recognised by Bohr J in his application of the quantum theory
to an atomic model, received confirmation in the work of M‘Laren,§ who

* Maxwell, Phil. Mag., vol. xxiii, p. 12 (1862). It should be noted that this paper is
two years earlier than that which gives “ A Dynamical Theory of the Electromagnetic Field.”
f Voigt, Annalen d. Physik , vol. ix, p. 115 (1902).

I Bohr, Studier over Metallernes Elektrontheori , p. 106.

§ M‘Laren, Phil. Mag., vol. xxv, p. 43 (1913).

43

1920-21.] iEther and the Quantum Theory.

proved that the classical dynamics cannot explain magnetism. No one, in
fact, has been able to explain how an electron orbit can be tilted under the
influence of a magnetic field.

Sir Alfred Ewing has directed attention recently to the resemblance
between the form of the curve showing the relation between specific heat
and temperature deduced from Planck’s theory and that representing the
magnetisation of a specimen of iron. The resemblance in mathematical
form between Planck’s equation and that of Langevin for the intensity of
magnetisation of a paramagnetic gas had previously attracted the attention
of Benedicks.* These similarities suggest that the same type of action
underlies the quantum theory as the various physical phenomena here
referred to.

All these results seem to be in harmony with the view put forward in
the present paper, that the “ quantum ” is itself essentially magnetic. It
must not, however, be supposed that the view “ reconciles ” the quantum
theory and classical dynamics. My object is rather to seek to understand
more clearly the nature of the quantum, whilst accepting the conclusion
that some modification of the old theories is inevitable.

* Benedicks, Annalend. Physik , vol. xlii, p. 133 (1913).

(Issued separately January 24, 1921.)

44

Proceedings of the Koyal Society of Edinburgh.

IV.— On the Transverse Galvanomagnetic and Thermomagnetic
Effects in several Metals. By F. Unwin, M.Sc. Communicated
by Professor F. G. Baily.

(MS. received November 10, 1920. Read January 10, 1921.)

Introduction.

In a previous paper * the author has described experiments to determine
the Hall effect and the two transverse thermomagnetic effects in several
metals. The fourth transverse effect — namely, the galvanomagnetic tem-
perature effect — was not measured at that time, as the measuring arrange-
ment was not sufficiently sensitive for this purpose.

In the present state of the electron theory of metals the ratios of these
transverse effects to each other is of very considerable interest, and hence
it is desirable to have determinations of all four transverse effects. Deter-
minations have been made by other workers, but, so far as the author is
aware, only in the case of a few metals. The present paper records the
determinations for eight different metals — iron, nickel, cobalt, silver,
copper, zinc, cadmium, aluminium.

Description of Effects and Definition of Coefficients.

Galvanomagnetic Effects.

Suppose a strip of metal, carrying an electric current, to be placed
between the poles of an electromagnet. When the magnet is excited it is
found that there are set up between the edges of the plate a difference of
potential and a difference of temperature. These constitute respectively
the Hall Effect and the Galvanomagnetic Temperature Effect. The co-
efficients R and P are the values of these effects in a plate 1 cm. wide
placed in magnetic field of unit strength when the potential gradient along
the plate is 1 c.g.s. unit per cm.

Thermomagnetic Effects.

If with the above arrangement a heat current is sent along the plate
instead of the electric current, it is again found that a transverse potential
difference and a temperature difference are set up.

These constitute the Thermomagnetic “ Potential Effect ” and “ Tem-
perature Effect ” respectively, and the coefficients Q and S are the magni-
tudes of these effects under the standard conditions named, the temperature
gradient along the plate being one degree Centigrade per cm.

* Proc. Boy. Soc. Edin ., vol. xxxiv, p. 208 (1914).

Transverse Galvanomagnetic and Thermomagnetic Effects. 45

Signs of the Effects.

The diagram (fig. 1) indicates the directions of the effects corresponding
R S Q P

“f- Warm

Fig. 1.

Cold

Electric

Current

Wat

>

to positive values of the coefficients ; it being understood that the magnetic
field is acting downwards perpendicular to plane of paper.

Apparatus.

The apparatus and measuring arrangements have been described in
detail in the author’s earlier paper, and the description need not be repeated
here. In dealing with the galvanomagnetic temperature effect it was found
necessary to introduce a modification in order to make the measurement
possible. This effect consists in a temperature difference set up between
the two edges of a small plate of metal, carrying an electric current, when

it is placed in a magnetic field whose direction is perpendicular to the plane
of the plate. This temperature difference is extremely small, and cannot be
measured in the usual way by thermocouples attached directly to the plate,
since with this arrangement the deflections of the galvanometers in circuit
with the couples are due mainly, not to the temperatures of the junctions, but
to electromotive forces set up by the current in the plate. Under these cir-
cumstances it was useless to increase the sensibility of the galvanometers.

The difficulty was overcome by using, in place of the two couples, a
small thermopile of ten pairs of junctions. This was built up (see fig. 2) on

46 Proceedings of the Royal Society of Edinburgh.

a support, and arranged so that one set of junctions could be pressed against
one edge of the plate and the other set against the other edge, a very thin
sheet of mica being placed between the junctions and the plate to prevent
any direct action of the electric current.

This sheet of mica, of course, prevents perfect thermal contact between
the junctions and the plate, and a large correction is necessary on this
account. The values of the galvanomagnetic temperature effect have
therefore not the same degree of accuracy as the other transverse effects.
Nevertheless they are sufficiently accurate to allow interesting conclusions
to be drawn in connection with the electron theory.

The thermopile readings were corrected in the following manner : —
The value of the coefficient S was calculated from readings taken with
the thermocouples before the thermopile was placed on the plate. It was
also calculated from observations made with the thermopile. The ratio of
these two values of S was taken as the correcting factor for the thermopile
readings in the determination of P.

Results.

The values of the four coefficients, R, S, Q, P, for the eight metals tested,

R 0 R 0

and the values of the ratios, g, p, p, g, are given in the following tables.

R x 107.

S x 107.

Q x 1 04.

j P x 1013.

Iron ....

+ 6-1

+ 5-2

+ 9-5

+ 30

Nickel

-33

-25

-io-o

-34

Cobalt

+ 2-5

+ 1-1

- 7-8

-22

Silver

-3-2

— 2-7

+ 1-8

+ 6*3

Copper

-2-8

-2*1

+ 1-9

+ 8-2

Zinc ....

+ T2

+ 1*1

-f- 0*7 3

+ 4-2

Cadmium .

+ 1-2

+ 0-89

+ 1-2

+ 39

Aluminium

- i-o

-0-62

- 0-42

- 2-8

R

S'

5 x 10~8.

5xl0-3.

lb

Iron ....

+ 1-2

+ 3-2

+ 2-0

+ 1-8

Nickel

+ 1’3

+ 2-9

+ 0-97

+ 4-0

Cobalt

+ 2‘2

+ 3-4

-IT

-7*3

Silver

+ 1-2

+ 3-0

— 5T

-0-68

Copper

+ 1-3

+ 2-3

-3 4

-0-95

Zinc ....

+ 1-1

+ 1-7

+ 2-9

+ 0-68

Cadmium .

+ P3

+ 3-0

+ 3-0

+ 1-3

Aluminium

+ P6

+ 1-5

+ 3-6

+ 0*68

Effects Transverse Galvanomagnetic and Thermomag netic. 47

Discussion of Results.

An inspection of the table shows that the four effects have not always
a common sign, but that in some cases two of the effects are positive and
two negative.

Zahn * put forward the suggestion that, while R and S may have different
signs from Q and P, it will always be found that R has the same sign as S,

R P

and Q the same sign as P,f so that the ratios and ~ are always positive.

Zahn appears to have drawn this conclusion from slender experimental
evidence, but its truth is borne out by the observations recorded in
this paper.

R Q

It will be observed that the values of g and ^ do not vary very widely

from metal to metal, although the individual effects vary both in magni-
tude and sign. The ordinary electron theory of conduction in metals,
taken in conjunction with J. J. Thomson’s suggestion of a local magnetic
field in the immediate neighbourhood of a molecule, is sufficient to account
for the variation in the sign of the effects from metal to metal, but it
cannot account for the difference between the signs of R and S, and those
of Q and P, in the same metal.

For this some other modification of the theory must be sought.

G. H. Livens J has recently developed a theory of conduction in metals
in which he arrives at the four expressions quoted below :

* Ann. d. Phys ., vol. xiv, p. 886 (1904).

t Zahn’s actual statement is that Q and P have always opposite signs, but the definition
of the positive direction of P used by the author is opposite to that used by Zahn.

X Phil. Mag., vol. xxx, p. 526 (1915).

48 Proceedings of the Royal Society of Edinburgh.

3

where q — ^ — ~2 , um2 being the mean square velocity of the electrons; and

Zum

s is given by the relation

m

~o

= potential energy relative to atom at distance r.

It will be seen that the signs of Q and P vary according as s is greater
or less than 4, while the signs of R and S are always the same ; so that,
taken in conjunction with J. J. Thomson’s suggestion, this statement of the
theory is capable of accounting for at least the signs of the four effects.

The four expressions given above are rather complex, but by taking
ratios we obtain the values :

2 +

R

7s2 + 8s + 16 e

8s(s + 1 )

These are comparatively simple, and the only unknown is s, which can
be calculated from the ratios found by experiment.

The following table gives the values of s for the different metals,

R 0

calculated from the observed values of p and g respectively.

Values of s.

R

From

H

O

^j<D

Iron

57

57

Nickel

10*0

9-7

Cobalt

2-4

1-8

Silver

3-6

3-6

Copper

3-3

3*5

Zinc

5T

4-6

Cadmium

5*1

5-2

Aluminium

4-8

4-6

The two values of s agree reasonably well except in the case of cobalt.*
The value of s for silver differs widely from the value for nickel, and

* The cobalt plate was prepared with some difficulty by electrolysis, and was not so
satisfactory as the plates of the other metals used. On this account the results for cobalt
cannot be considered as having the same accuracy as those for the other metals.

Transverse G-alvanomagnetic and Thermomagnetic Effects 49

/1_2\

consequently the term 2 s)> which enters into the expression for the
Hall effect, will differ greatly in value from the one metal to the other.
This is difficult to reconcile with the experimental fact that the Hall
effect has about the same value in both metals.

Summary.

The four transverse galvanomagnetic and thermomagnetic effects were
determined in the case of iron, nickel, cobalt, silver, copper, zinc, cadmium,
aluminium.

The results were considered in the light of the electron theory of
conduction in metals as formulated by G. H. Livens, and were found to
be in fair accord with the theory as regards the ratios of the effects, but
they could not be reconciled with the expressions given for the effects
themselves.

( Issued separately March 17, 1921.)

VOL. XL1

4

50

Proceedings of the Royal Society of Edinburgh. [Sess.

V. — Observations on the Interruption of the Endodermis in a
Secondarily Thickened Root of Dracaena fruticosa, Koch.
By Annette G. Mann, B.Sc. Communicated by Professor F. O.
Bower, F.B.S.

(MS. received October 25, 1920. Read December 6, 1920.)

It is generally accepted that the position and development of any one
tissue in a plant is to be studied from the point of view of function :
nevertheless the physiological need for it may alter as the plant develops.
The endodermis is an illustration of this. Its primary function (1) is to
restrict the passage of water and soluble substances to certain definite
channels : it follows that its best development is in those parts nearest to
the source of supply, e.g. in roots and young stems. The cell-walls are at
first relatively thin, with the characteristic suberised strip on the radial
and transverse walls. Its cells are in uninterrupted contact one with
another, there being no intercellular spaces. This leads incidentally to its
being also a barrier to gaseous interchange. The ventilating system of the
cortex is limited by it internally, and cut off from such intercellular spaces
as may lie within.

A secondary function which is mechanical is often assumed by it, as
shown by Schwendener (2). In older roots the cell- walls, particularly the
radial and inner tangential walls, become indurated and resistant. When
in this latter condition the endodermis forms a rigid structure enclosing
the stele, and forming a very effective barrier between stele and cortex.

It has been shown by Professor Bower (3) that size is a factor which
has to be considered in this connection. Since the surface of a cylinder
varies as the square, and the bulk as the cube of the linear dimensions, the
larger the cylinder is, the greater will be the difficulty of adequate transit
through the barrier, and a limit may be expected when the barrier must
be extended or be interrupted in some way or another, otherwise the check
on interchange through the endodermis would become a serious risk. In
roots of Dicotyledons the cortex and endodermis peel off as secondary
growth occurs. In thickening stems it disappears, though the steps by
which this is carried out have never been accurately followed. But the
roots of some Monocotyledons, in particular Draccena, offer a favourable
opportunity for tracing the disruption. Draccena, which has a well-
marked and indurated endodermis, has also, in some of its largest roots, a

51

1920-21.] Interruption of Endodermis.

process of cambial increase similar in its nature to that seen in the stem ;
accordingly it was selected as an object likely to throw light on the method
of breaking down the barrier in an enlarging part.

The following observations were made on transverse hand sections cut
from two roots of a plant of Draccena fruticosa grown in Glasgow Botanic
Gardens.

The first root examined was about 5 inches in length, and the first

section was cut at a distance of 1| inches from the apex, and section-
cutting was continued upwards towards the junction of root and stem.
The first sections showed the root to be about \ inch in its greatest
diameter, and the endodermis was a complete, almost regular ring, with all
the cells typically thickened on the inner tangential and the two radial
walls, the primary stele being undisturbed (fig. 1). The upward sequence

of sections from the apex showed a gradual beginning of growth and
division of the cells of the pericycle within the endodermis to form a
cambium (fig. 2), and, with the slight increase in girth of the root thus
brought about, the endodermal cells became somewhat distorted in shape,
and the ring itself irregular ; then, finally, the sequence of endodermal cells
was interrupted (figs. 3, 4, 5). The development of this inner or internal
cambium began first at one part only of the sections, and was most active
in the middle of this area, where the cambial cells divided quickly, and
often showed four to six radial rows of cells. Above this area of active

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

growth and division there occurred interruption and separation of the
cells in the endodermal ring by the intrusion and growth between the
endodermal cells of one or more parenchymatous cells either from the peri-
cycle or from the cortical cells just outside the endodermis (see cells x, x,
fig. 4). In either case there arose bending of the endodermal ring, and
displacement of the cells as shown in fig. 5. The next few sections showed
a rather quick disappearance of cambial activity until there was practically

no division of pericyclic cells, and the endodermis was again a complete
ring of typically thickened cells. Internal cambium then began again
with a quick division of its cells, resulting in a considerable amount of
separation of the cells of the endodermis by intrusive parenchyma. Again
occurred a falling off of cambial activity, and a consequent linking up of
the endodermal cells into a more complete ring. There were now If inches

of root left uncut, and sections were continued at about If inches from its
junction with the stem. The first sections cut here showed still a very
small amount of internal cambium, and the endodermis almost complete ; but,
in addition, there was a slight division of certain cortical cells just outside
the endodermis. These formed small isolated patches of outer or external
cambium made up of ten to twenty cells in two radial rows. The succeed-
ing sections showed the endodermis complete and no cambial development
on the inside, but there was increasing cambial development on the outside
(fig. 6). The cells often divided by obliquely tangential walls, therefore did

53

1920-21.] Interruption of Endodermis.

not appear at first in even typical radial rows. The external cambium
spread gradually round the sections, the cells dividing by periclinal walls,
and their arrangement becoming regular and broader, while the endodermis
remained undisturbed. A few sections further up showed cambium
appearing in parts of the pericycle also, and from this point upwards
the internal cambium caused breaking of the endodermal ring in the
manner already described and figured. For a considerable number of
sections the pericyclic cambium showed only a slight development of
secondary tissue, and the external cambium none at all, but about f of an
inch from the attachment of the root on the stem, there appeared the
beginnings of two small secondary bundles — typical xylem elements
surrounding central phloem — on the outside of the endodermis, which was
continuous below them. The following sections showed rapid development
of secondary tissue both from
external and internal cam-
bium. In consequence of the
activity of the latter, single
cells or groups of two or more
endodermal cells were forced
to the outside of the second-
ary tissue, or were left lying
between the bundles in the
midst of this tissue. This follows from the division and growth of the
cambial cells on either side of an endodermal group being quicker than
that of the cells immediately beneath it. The last sections made, about \
inch from the end of the root, showed internal cambium and development
of secondary tissue to a more or less degree practically all round, but the
thickening was much more strongly developed on that side of the root
which showed both internal and external cambial activity. The endodermis
appeared almost completely broken up into patches of cells, and even into
isolated cells (Photo II).

The .second root examined was of slightly greater diameter than the
first throughout all the series of sections, and its tissues had become much
more sclerotic and woody, even the pericycle being comparatively thick-
walled. The only thin-walled cells apparent were those of the cortex, and
of the cambium to the outside of the secondary tissue. The development
of cambium first began here in the cortex just outside the endodermis, and
spread round, giving rise to secondary bundles to a greater or lesser degree
in several isolated places, the endodermis being complete below the bundles
(fig. 7). When a considerable amount of external secondary tissue had

54

Proceedings of the Royal Society of Edinburgh. [Sess.

been developed, two or more cells in isolated parts of the pericycle, in
conjunction with several tracheids just below, were found to have enlarged

Fig. 7.

and extended outwards towards the endodermis. This enlarging of peri-
cyclic cells appeared in a number of places, the endodermis becoming

curved and broken as one cut
further up from the root apex.
The pressure of these thick-
walled cells must have caused
first that curving and then
that splitting apart of the en-
dodermal cells which is shown
in fig. 8 and Photo I. The
changes in the endodermal ring
due to inside pressure occurred
where there was greatest de-
velopment of secondary tissue
outside it, the cells of the
secondary conjunctive tissue
appearing to assist in the
process of separation of its
cells (see fig. 8, cells xv x2). When the endodermis had been ruptured
and the isolated parts pushed slightly outwards (fig. 9), the pericyclic

1920-21.]

Interruption of Endodermis.

55

Fig. 8.

Fig. 9.

56

Proceedings of the Royal Society of Edinburgh. [Sess.

cells below the curves, and also elsewhere in the pericycle, where there
was previously no external cambium, divided up rapidly by periclinal
walls. They thus formed a typical cambium from which were developed
secondary bundles and conjunctive tissue. Such developments have
already been noted by Haberlandt (1) and verified by Miss Spratt (4)
as being of the nature of fibrous tracheids. As secondary growth from

Fig. 10.

the internal cambium spread round and became more active, the secondary
tissue formed from it joined up through the gaps in the endodermis with
that formed by the external cambium. The endodermal ring now
appeared much broken, many of the cells being carried up on the outside
of the internal cambium, and left lying in little groups of a few cells
each in the midst of the thick- walled conjunctive tissue between the
secondary bundles (fig. 10). The last sections cut from root 2 showed a

1920-21.]

Interruption of Endodermis.

very similar appearance to those of root 1 at the same stage in secondary
growth, i.e. they showed endodermal strands lying between the secondary
bundles, and also on the extreme outside of the secondary tissue where
internal cambial activity was very marked (Photo II).

In both roots the pericyclic cambium, once it was fairly established,

was most active, whether or no
it was developed before the
cortical cambium, since endo-
dermal cells were always found
external to the cambium out-
side the greatest development
of secondary tissue. There
appears to be no rule whether
the cambium shall appear first
in the pericycle or in the cortex
just outside the endodermis.
Both the roots examined show
that the formation of external
cambium does not, as Miss
Spratt suggests, necessarily
follow after the formation of
pericyclic cambium, but may precede it. In that case the endodermal ring
still continues to form a serious barrier to ventilation, though there is
abundant evidence of intercellular spaces in the secondary tissue. Where
the cambium originates first from the inside the parenchyma cells pene-
trating the endodermis
show air-spaces between
them (see figs. 3, 4, 5),
so that the endodermal
barrier to ventilation is
broken. But I imagine
the primary cause of the
interruption is not to
allow of greater ventila-
tion of the inner tissue — though this of course follows — but rather is it an
adaptation to allow of a greater increase in girth of the root for the forma-
tion of new vascular tissues, and for a quicker interchange between the outer
and inner tissues of the enlarging root. If greater ventilation was the prim-
ary object, then internal cambium would, of necessity, be developed first.

Professor Scott and Mr Brebner (5) have described a somewhat similar

58

Proceedings of the Royal Society of Edinburgh. [Sess.

behaviour of endodermis in the secondarily thickened roots of other species
of Dracaena, and the phenomenon of the penetration of parenchyma cells
between thicker-walled cells, with the consequent splitting apart of the
latter, has been shown by others to occur elsewhere. Schwendener (2)
figured a cross-section of a root of Convallaria majalis showing the
interruption of the endodermis by thin- walled parenchyma ; and Miss A. M.
Clark (6) has described an ingrowing of parenchyma among secondary
xylem elements in the stem of Kendriclcia Wallceri. In fig. 11 I have
demonstrated an example of the intrusion of parenchyma from the cortex
which seems to correspond in its nature and origin to the case of
Convallaria mentioned by Schwendener. This intrusion into the endo-
dermis occurred before the appearance of cambium at that point, though
secondary thickening was active at the opposite side of the root.

In conclusion, I wish to acknowledge my indebtedness and grateful
thanks to Professor Bower for so kindly supervising the work, and to
Dr J. M. Thompson for valuable criticism.

REFERENCES.

(1) Haberlandt, G., Physiological Plant Anatomy, 1914, Oxford translation.

(2) Schwendener, S., Die Schutzscheiden und ihre Verstdrkungen , 1882.

(3) Bower, F. O., Professor, Presidential Address to Royal Society of
Edinburgh, 1920, Proc., vol. xli, p. 1.

(4) Spratt, A. V., Miss, “ Some Anomalies in Monocotyledon Roots,” Annals of
Botany, 1920.

(5) Scott and Brebner, “The Secondary Tissues in certain Monocotyledons,”
Annals of Botany, 1893.

(6) Clark, A. M., Miss, “ Secondary Thickening in Kendrickia Walkeri,” Annals
of Botany, 1907.

ILLUSTRATIONS.

E. = endodermis : p. = pericycle : c. = cambium : phi. = phloem: xy. = xylem:
Pr. tis. = primary tissue : Sec. tis. = secondary tissue : cor. = cortex.

Text-Figures.

Fig. 1. Endodermis complete without cambium on either side. x 250.

Fig. 2. Endodermis complete with pericyclic cambium. x 250.

Fig. 3. Separation of endodermal cells by internal cambial activity. Inter-
cellular spaces are numerous in the thin-walled tissue. x 250.

Figs. 4 and 5. Steps in the breaking up and displacement of endodermis by
intrusion of parenchyma cells. x 250.

59

1920-21.] Interruption of Endodennis.

Fig. 6. Endodermis complete, and beginning of external cambium. x 250.

Fig. 7. Endodermis complete, and formation of secondary tissue from external
cambium, x 250.

Fig. 8. Endodermis curved and continuity broken by pressure of tissues within.
Cells Xj x2 show the beginning of separation of endodermal cells. x 250.

Fig. 9. Three endodermal cells are shown pushed out from the ring. The bundle
just within was formed from internal cambium ; tissues to right and left from
external cambium. x 250.

Fig. 10. Endodermal cells pushed right out to cortex by the activity of internal
cambium. Those cells on right have been left behind among secondary elements.

x 200.

Fig. 11. Separation of endodermis by intrusion of cortex. x 250.

Photographs.

I. Curving and splitting of endodermis ( x ) due to inside pressure. x 24.

II. Endodermal cells (x) pushed out to cortex by internal cambial activity, x 24.

{Issued separately March 17, 1921.)

60

Proceedings of the Royal Society of Edinburgh. [Sess.

VI. — On Fechner’s Law and the Self-Luminosity of the Eye.

By Professor William Peddie, D.Sc.

(MS. received November 22, 1920. Read November 22, 1920.)

(Abstract.)

Fechner’s law states that change of visual perceptivity is proportional to
the fractional change in the intensity of the light. At weak intensities a
term, regarded as constant, has to be added to the intensity of the external
light on account of the self-luminosity of the eye. By integration over the
whole stimulated part of the retina, Helmholtz obtained an expression for
the perceptivity which agreed with observation in so far as the general
nature of the relation between perceptivity and external stimulus is
concerned. Close correspondence can be obtained by assuming that the
self-luminosity term in Fechner’s expression is itself a simple function
of the external stimulus, rising rapidly to a maximum and thereafter slowly
falling to a steady value.

/

1920-21.] Relation of Soil Colloids to Conductivity of Soil. 61

VII. — The Relation of the Soil Colloids to the Thermal Con-
ductivity of the Soil By Capt. T. Bedford Franklin, B.A.
(Cantab.).

(MS. received December 28, 1920. Read February 7, 1921.)

SUMMARY.

SECTION

I. Introduction .........

II. Scope of the Investigation and Effect of Change of Period on Values

r4

of

R.

Rr

III. Evidences of Changes in Values of

Temperature of Soil

(а) In sand ....

(б) In clay loam

(c) In clay loam, ignited clay loam, and sand

IV. Conclusions ....

with Changes in Mean Surface

page

61

62

63

63

64
64

67

I. Introduction.

Early investigators regarded the soil as an inert framework of soil grains
of various sizes covered with a continuous film of water, and the properties
which in theory it should possess under such a hypothesis were found
not to accord too well with the results of experiment. But when the
existence of soil colloids was understood, the differences between theory
and experiment tended to disappear one by one, as shown by the work of
Bouyoncos in America in 1915 and of Keen in England in 1914, 1919,
and 1920.*

These and other investigators have shown that it is essential to take
into account the colloidal properties of the soil before its physical pro-
perties can be understood properly, and in doing so have cleared up many
of the points of difference between experiment and the old theory which
was based on a hypothesis that disregarded these soil colloids.

In a previous paper on soil temperature I have discussed the effect of

* “ The Effect of Temperature on the most important Physical Processes in Soils.”
G. J. Bouyoncos, Technical Bulletin No. 22, Michigan Experimental Station , 1915.

“The Evaporation of Water from Soil,” B. A. Keen, Journal of Agricultural Science,
vol. vi, part iv, Dec. 1914.

“ A Quantitative Relation between Soil and the Soil Solution,” B. A. Keen, ibid.,
vol. ix, part iv, Oct. 1919.

“The Relations existing between the Soil and its Water Content,” B. A. Keen, ibid.,
vol. x, part i, Jan. 1920.

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

rain, snow, frost, a dry surface mulch, etc., on the soil temperatures at
various depths ; * in this present paper I propose to show that soil
temperatures are also affected by soil colloids, since the properties of these
colloids bring about changes in the conductivity of the soil.

II. Scope of the Investigation and Effect of Change of

Period on Values of

For this investigation it was essential that variations in the value of

R

due to any cause other than temperature should be eliminated. To this
K0

end hourly readings were made from minimum to maximum only, and no
observations were taken on days of precipitation or when the ground was
frozen or covered with a dry surface mulch : moreover, to ensure the
more or less uniform water content of the soil, observations in summer were
made on those days only when rain has fallen in the previous twenty-four

R

hours, so that any observed variations in the values of p-4 were due

apparently either to variations in the length of the interval from minimum
to maximum or to temperature changes in the soil.

It was assumed that the temperature curves from minimum to
maximum could be regarded as half a sine curve of period double the
interval from minimum to maximum ; we were thus able to use the formula

10

R

where ~ is the ratio of the ranges of temperature at the
-tC

4-inch depth and the surface from minimum to maximum, h 2 is the
diffusivity of the soil, and T is the period, i.e. double the interval from
minimum to maximum, reckoned in seconds.^

From chosen observations in June 1920, when the mean surface

R

temperature was 10° C. and the period 24 hours, — in sand and clay loam

were found to be ‘52 and *42 respectively.

Thus ^4=52 = e

X -006

for sand, giving a value of *09 for h in sand ;

in clay loam the corresponding value for h was *07.

Assuming that for the rest of the observations these values for h
remained constant for the two soils, and this seemed probable since

* “ The Effect of Weather Changes on Soil Temperature,” T. B. Franklin, Proc. Roy .
Soc. Edin ., vol. xl, part i, No. 8, 1920.

t Mathematical Theory of Heat Conduction , Ingersoll and Zobel.

1920-21.] Relation of Soil Colloids to Conductivity of Soil.

63

observations were made only when the soils had more or less the same

R

water content, we could find the values of p-4 for each soil corresponding

K0

to various values of the period T.

These values are given in Table I alongside some observed values of

r4.

Rn

*4

in clay loam for those periods.

Table I. — Change of — J with Change of Period.

XVn

Interval

Min.

to

Max.

Period

T

in Hrs.

R0

Sand.

5t

R0

Clay Loam.

|

Observed Value
of
R

-i in Clay Loam
R0

Mean
Surface
Temperature
for Period.

in Hrs.

for that Period.

6

12

•41

•30

•26

2-5° C.

8

16

•44

•33

•30

5-0° C.

9

18

•46

•35

•32

3-0° C.

10

20

•475

•375

12

24

•52

•42

•42

100°’ c.

24

48

•54

•50

•52

5-0° C.
5*0° C.

36

72

•60

•60

•61

8-5° C.
9*0° C.

It will be seen that good agreement was obtained between the calculated
R

and observed values of p^ in clay loam when the mean surface temperature
R0

during the period was about 10° C. — the temperature at which the standard

R

observation was made, — but that ^ fell considerably below the calculated

rt0

value when the mean surface temperature was below 10° C.

R

This suggested plotting the values of at various temperatures but

K0

the same period against the corresponding mean surface temperatures ; the
results for sand and clay loam are given in the next section.

R

III. Evidences of Changes in Values of ^-4 with Changes in

JLvq

Mean Surface Temperature of Soil.

(a) In Sand.

Owing to the strict conditions under which observations were made for

R

this investigation, only about sixty values of in each soil were recorded

64

Proceedings of the Royal Society of Edinburgh. [Sess.

as being sufficiently trustworthy out of the whole year 1920; of these 32
were arranged according to their length of period : —

11 for a period of 12 hours — Min. to Max. 6 hours.

14 „ 18 „ „ 9 „

7 „ 22 „ „ 11 „

These values for the two soils are shown plotted according to their length
of period against the mean surface temperature in figs. 1 and 2 ; in both
figures it will be noticed that the distribution of the plotted values of

R,

R„

at low mean surface temperatures is wider than at high temperatures :

R

this is due to the difficulty of computing exactly the value of p4 in winter

1C0

when both R4 and R0 are small, and the least error in either makes a

R

considerable difference in the value of

R0

The vertical dotted lines on the graph are the lines on which the values
R

of -p4 in sand should lie at periods of 12, 18, 22 hours respectively if there
R

R,

was no variation in value of with a change of mean surface
temperature.

The plotted points do fall so nearly on these lines that it seems justifi-
able to assume that there is no change in conductivity of sand with change
of temperature.

(b) In Clay Loam.

R

Here we have quite a different picture, as the groups of points for ^ lie

diagonally and not vertically as in sand, and it seems that there is a
distinct change of conductivity in clay loam with a change in the mean
surface temperature. The chief difference between clay loam and sand- —
apart from the size of the soil grains — is that clay loam contains organic
matter and soil colloids, while sand contains neither; therefore it would
appear that the change in conductivity of clay loam with temperature is
due to one of both of these constituents.

R

(c) in Clay Loam, Ignited Clay Loam, and Sand.
tv0

R

During the autumn of 1920 I compared the values of ^ in clay

R0

loam, ignited clay loam, and sand ; the interval from minimum to maximum
was about 8 hours — period 16 hours — for most of the time during which
the observations were made.

1920-21.] Relation of Soil Colloids to Conductivity of Soil. 65

The expected values for for a mean surface temperature of 10° C.

K0

would be *45 in clay loam, and ’55 in sand ; it happened that the ignited clay

20

I

o o

19

MEAN

SURFACE

TEMP.

17

FIG. I *

SAND

CHANGE /N VALUE OF ■— iV/TH •
CHANGE OF MEAN SURFACE TEMPER f

o

o

16

o

15

14

13

12

10

*

9

8

I »

I

o

o

7

6

5

4

3

2

•30 -32

*- I •
* t

*

*-

l

•34 -36 -38 -40 -42 -44

I

I

I

1

I

t

1

•46 -48

= 6 HOUR /NTERZAL
MIN. TO MAX.

@ - 9
0 — 1/

1

•50 -52

AV

Ro

•54 -56

loam had a value of ^ equal to '55 also, and the curves for it and sand have

run together faithfully day by day for over two months, during which the

mean surface temperature has fluctuated between 9° C. and just above 0° C.
VOL. xli. 5

66

Proceedings of the Royal Society of Edinburgh. [Sess.

R

The values of ^ 3 in ignited clay loam and sand have only varied between
■54 and *57 during this time, while for clay loam the variation is from

'13

30

MEAN

SURFACE

TEMP.

fig. n

CLAY LOAM

0

1

o

°c.

CHANGE /N VALUE OF ^ W/TH

I

o •

CHANGE OF MEAN SURFACE TEMPER f

I

0

1

0

1

o

*

if

0

0

I

#

if

if

if =6 HOUR INTERVAL

M/M. TO MAX..

m = 9

o = //

| | | ES

II \ Ro

•28 -30 -32 - 34 - 32 -38 -40 - 42 -44 - 46

*40 to '48, according as the mean surface temperature was near 0° C.
or 9° C.

Now, ignition destroys the organic matter and soil colloids, so that the

R

similar small fluctuations of p^-in ignited clay loam and sand — neither of

1920-21.] Relation of Soil Colloids to Conductivity of Soil. 67

which contain organic matter or soil colloids — compared with the larger

It

fluctuations of =p-3 in clay loam, which is rich in colloids, is a point of great
significance in the present investigation.

IV. Conclusions.

The addition of organic matter to a soil reduces the conductivity of that
soil. Thus Bouyoncos found that sand with the addition of 332 per cent,
organic matter was a better conductor than sand with 6'95 per cent, organic
matter ; moreover, in the soils he tested, the conductivity, both dry and wet,
was in the inverse ratio to the organic matter present.*

Therefore the change in conductivity of clay loam cannot be due to the
organic matter present, but must be caused by the colloids present in that
soil. This change of conductivity is probably brought about by the
colloidal films surrounding the soil grains swelling with the rise in
temperature, and so automatically compacting the soil, and reducing the
transfer resistance to heat between the particles within the soil.

* “ An Investigation on Soil Temperature and some of the most important factors
influencing it,” G. J. Bouyoncos, Technical Bulletin No. 17, 1913, Michigan Experimental
Station .

{ Issued separately May 9, 1921.)

68

Proceedings of the Royal Society of Edinburgh. [Sess.

VIII. — On a Graphical Method of determining Shear Influence
Lines and Diagrams of Maximum Shearing Force for a
Beam subjected to a Series of Concentrated Rolling Loads.
By Alex. R. Horne, B.Sc. (Lond.), Professor of Engineering, Robert
Gordon’s Technical College, Aberdeen.

(MS. received November 30, 1920. Read March 7, 1921.)

The shear influence line is a line the ordinates of which give the values
of the shearing forces at any one point in a beam or bridge as a load, or a
series of loads, pass over it. There is thus, for any one beam, an influence
line for every point in it.

These influence lines are of great value in the design of structures, such
as bridges and arches, where it is necessary to determine the greatest maxi-
mum and minimum shearing forces which occur at every point in them.

The methods generally used to obtain these lines prove laborious in
practice, especially when there are, as is often the case, several loads, such
as the wheel loads of a locomotive. The ordinates of each influence line
are generally determined by calculation, when it becomes necessary to
estimate the shearing forces for many positions of the loading. Alterna-
tively, a graphical method, which requires the construction of funicular
polygons, and which affords only approximate results, is resorted to. This
latter method is inconvenient when the load length exceeds the span, as is
often the case in practice.

In this paper, a simple graphical method of constructing an influence
line is explained ; and the system is extended to provide a ready means of
drawing the influence lines for as many points in the beam as may be
desired. From these a diagram of maximum positive and negative shears
can be constructed. No calculation whatever is required, and the method
is an exact one. Moreover, the system is not limited to the case where the
total length of the load does not exceed the span of the beam.

Let a series of loads, W2, W2, W3 (fig. 1) cross a beam AB, of span L,
moving towards the right. When the leading load, Wl5 is over the right
abutment B, the bending moments at A, due to Wv W2, W3, are M1? M2, M3
respectively. Let the total bending moment at A, due to these loads, be
represented by cd to a scale of 1 " = m units.

If the beam is freely supported at A, the resultant bending moment
there is zero. It follows that, if R is the reaction of the support at B,

RL = Mj + M2 + M3 = cd (in inches) x m,

1920-21.] Graphical Treatment of Shear Influence Lines. 69

771

hence R = cd x ~ ;

/T)rb

therefore cd represents the reaction R to a scale of 1" — — =n units.

JL

If, now, the loads move to the left by a distance lv it is easy to show
that R is represented by c ±d± = the depth of the diagram at a distance lx to
the right of A.

Again, if the loads move a distance l2 to the right , the sum of the
moments at A due to all the loads will be represented by ed2, where ce = l2.
But since is now off the beam, the bending moment, ec2, due to it is
ineffective. The true bending moment is now c2d2 ; and, from what has

v

gone before, it follows that the new value of R is represented by c2d2 for
this position of the loading.

When Wj is at an infinitely small distance to the left of B, R = cd ; but,
immediately it passes off the beam, R is reduced by W2 or eg. Similarly,
just when W2 leaves the beam at B, the reaction is suddenly reduced by
W2. This reduction is shown by hk( = W2), which is drawn at a distance
p from A, where p is the spacing between W1 and W2. A similar treatment
is adopted for the adjustment of the reaction R when W3 passes B. This
is not shown on the diagram.

Generally, the vertical intercept between the lines oxcghht — conveni-
ently termed the “ control ” line, and the line oxo2ozv, which may be
referred to as the “ moment ” line, at a distance l , where l is the motion
of the loads, measured horizontally from A in a direction opposite to that
in which the loads have moved from the position where Wx is over B,
gives the then value of R.

70

Proceedings of the Royal Society of Edinburgh. [Sess.

Consider now the general case, where the load length exceeds the span
(fig. 2). The “ control line <x64 is drawn exactly as has been described,
where b1a1 = W4, b2a2 = W2, bza3 — W3, and b^a^ — W4, and the horizontal
distances between these lines are equal to the respective spacings of the
loads. The “ moment ” line aa^ which forms the base line of the influence
line, is constructed in the manner already explained. The vertical ordinates
between these two lines give the values of the reactions R as the loads
move from the position where W4 is at A until W4 reaches B.

The ordinate under A has two values, differing by Wr according as W4
is just to the left, or just to the right, of B.

Considering the point X on the beam, distant x to the left of B. When
W4 is immediately to the left of X (and the other loads are in corresponding
positions), the positive shear at B is eqttal to the reaction mxo, where m1 is
distant x to the right of A. The shearing force is considered positive when
the portion of the beam to the right of X tends to move upwards relatively
to the portion on the left of X, and vice versa.

Immediately the loads move so that W4 is between X and B, the positive
shear at X — R — W4, R varying as the loads proceed to the right. When
W4 has moved a distance p to the right of X, W2 comes over X, and the

1920-21.] Graphical Treatment of Shear Influence Lines. 71

shear at X is now either m2o or — n2o according as W2 is just to the left or
just to the right of X. Clearly m2nx=p, the distance between W4 and W2;
and m2n2 = W2.

Similarly, if n2a.2m3 is drawn everywhere parallel to the control line
mA°h^2a2m3> the horizontal distance from n2 to n3 being equal to q—
the distance between W2 and W3, — the ordinate between the line n2a2m3
and the moment, or base, line at the appropriate point gives the shearing
force at X. Finally, m3n3 is made equal to W3 ; n3a3mx is drawn parallel
to the control line for a distance r — the spacing between W3 and W4;
m4^4 is set down equal to W4, and is joined to a4.

The line am1n1 . . . m4%a4 is the influence line for the point X, and
is easily traced on the diagram by the small circles, to the base line aooa 4.

Where the influence line falls above the base line the shear at X is
positive; while, when it falls below the base line, the shear at X is
negative.

By an extension of the diagram of fig. 2, a simple means is afforded by
which to obtain the appropriate influence line for any point in the beam.
The process is indicated in fig. 3, and is as follows : —

Place the loads so that W4 is over the right abutment. Produce the
load lines through W4, W2, W3, and W4 vertically downwards (dotted lines),
and draw vertical (chain-dotted) lines, similarly spaced, from A.

Draw abx = L, the span. Set down bxax = W1 at A. In the direction aax
draw ac and a^b2 in the spaces p. Set down b2a2 — W2.

In the direction ca2 draw cd and a2b3 in the spaces q. Set down

= W3.

In similar manner, draw de and <x3fe4 in the spaces r. Set down
bpi/y = W4, and join e to ct4.

The line acdea9 is the base line of all the influence lines, and abxa^b2a2
. . . 64a4 is the control line.

From av a2, a3, and <x4 draw lines axhv a2h2 . . . ajii everywhere
parallel to the control line above, to meet the verticals through W1? W2, W3,
and W4 respectively, and so obtain a series of parallel-sided figures, each
of horizontal length L.

To draw the influence line relative to the point X in the beam, distant
x from B, draw verticals mxnv m2n2 . . . mpi4 distant x from the left-hand
ends of the parallel-sided figures. The resulting influence line is indicated
by the circles, to the base line acdea 4.

In the design of structures, only the greatest maximum positive and
negative shears at each point in the span may be required. An inspection
of the diagram shows that these occur on the lines m1n1, m2n2 . . . m4r^4,

72

Proceedings of the Poyal Society of Edinburgh. [Sess.

and the inclined portions of the influence lines are not necessary in
such cases.

In the case dealt with, the several maximum positive shears are
omv onv om2, om3, and om4, of which om. is the greatest; while the
maximum negative shears are on2, onz, and on 4, the last being numerically
the greatest.

By dividing the span into a number of equal parts, say ten, and the

four parallel-sided figures into an equal number of parts, the greatest
positive and negative shears for each of the several points in the beam
may be determined by inspection. From these a diagram of maximum
shears (fig. 4) can be drawn. In practice, the maxima values can be
obtained by means of tracing paper.

To save confusion, only one of the four diagrams has been so divided.
It is to be observed that the ordinates of the figures — 1 to 10 — are
numbered in the reverse direction to the points on the beam.

The diagrams, figs. 3 and 4, have been drawn to scale for the case where
W4 = 2, W2 = 7, W3 = 3, and W4 = 9 tons; p = 3, q = 4*5 and r = 6 feet. A
scale of shearing force is attached to the diagram in fig. 4.

{Issued separately May 9, 1921.)

1920-21.] Hypergeometric Functions of Two Variables.

73

IX. — The Confluent Hypergeometric Functions of Two Variables.
By Pierre Humbert. Communicated by Professor E. T. Whit-
taker, F.R.S.

(MS. received December 6, 1920. Read January 10, 1921.)

Introduction.

This memoir is devoted to the study of certain new functions, which may
be regarded as limiting cases of the “ hypergeometric functions of two
variables ” discovered by Appell.* The relation which the new functions
bear to Appell’s functions is, in fact, analogous to that which the
“ confluent hypergeometric functions,” *j*

and

z \ , aX , a(a +1) 9

*(w)=i + _+_y_^
B(y? x) — 1 +

7 2 ! 7(7 + 1)"

x x 5

+ .

+ . . . ,

I.7 2 ! 7(7 + 1)

bear to the ordinary hypergeometric function.

There are four hypergeometric series of two variables. If we denote
the product

X(X + 1) . . . (X + n-1),

where \ is arbitrary and n a positive integer, by the symbol

(X, n),

with the convention (X, 0) = 1, these functions are as follows: —

F3(a> a'> A P' ; y;^?) = 22

F4(«, P; y,y; x,

= + 0O

(a, m + n)(p,

n)

Xmi/n

Zj

1=0

(7, m + n)

m\ n\

■ (a,

m + n)({3, n)

xmyn

i

(7, m)( 7', n)

m

! n !

(a,

m)(a\ n)(f3, m)(/3',

n)

xmyn

1

(7, m + n)

m\ n\

(a,

m + n)(/3, m + n ) xmyn

1

V

T

! n

t ’

* J. math, pures appl. , 1882, p. 173 ; 1884, p. 407.

+ For an account of the confluent hypergeometric functions, see chapter xvi of
Whittaker and Watson’s Modern Analysis.

74

Proceedings of the Royal Society of Edinburgh. [Sess.

These functions satisfy partial differential equations, and can be
expressed as definite integrals. Appell has given some applications of
them to certain problems of celestial mechanics, and expressed in terms
of them the polynomials of Hermite and Didon and some more general
polynomials.

An interesting advance in the theory has been made recently by Appell,
who has shown that the polynomials Vm n of Hermite, which are particular
cases of the function F2, are solutions of the potential equation in hyper-
spherical co-ordinates, and can be considered as hyperspherical harmonic
functions on the hypersphere

x2 + y2 + z2 + 12 = 1.

PART I.

DEFINITION AND PROPERTIES OF THE FUNCTIONS.

Chapter I.

FORMATION OF THE CONFLUENT HYPERGEOMETRIC SERIES.

The confluent hypergeometric functions of two variables may be formed
by confluence from Appell’s functions in the following way : —

First, in Appell’s function F3(a; ft, ft' ; y , x, y), make ft' oo , at the
same time dividing y by ft': we thus obtain the first of our confluent
functions,

^i(a ; ft; y; x,

Jy y (a, m + n)(ft, m) xmyn .
^ ^ (y, m + n) m \ n\

A second function can be obtained from Ft by dividing x and y by a, and
causing a to tend to infinity : we are thus led to the function

%(ft> ft' ; y; ^ y ) = 2 2

(ft, m)(ft', n) xmyn
(y , m + n) mini

A third new function can be derived from F1 by making the two para-
meters a and ft' infinite, after replacing x and y by x and this gives

a aft

the function

i / / , \ v’' (B, Tfi) xmyn

(y, m + n) m ! n !

Taking next Appell’s series F2, we apply to it the same process, and
obtain two new functions, the first one by dividing y by ft', and making
ft' infinite ; and the other one by dividing x by ft, y by ft', and making

75

1920-21.] Hypergeometric Functions of Two Variables.

both /3 and ft tend to infinity. These two functions will be denoted by
the symbol 'F : their expressions are

*i(«; fi;y,yi *, 2/) = ZlVfn"’ V”.

(y> m)(y j w) m ! n !

^o(a ; y» 7 ; x> 2/) = 2Z

From the function

F3(a, a, ft ft; y ; i/)=22

(a, m + n) xmyn
(y, m)(y', 71) m \ n\

(a, m)( a', rc)(ft m)(ft, »)

(y, m + n)

! *, 1

may be obtained in like manner a new function by dividing y by ft, and
making ft-> oo . This is the function *

H,(«, a'-, P;y,x, 2/)=22(“’ ")(A ^ —

(y, m + n) m \ n !

Similarly, replacing y by y/a'ft, and making a and ft infinite, we
obtain a function

b(a> P ; y ; ^ y) = 2 2

(a, m)(ft ra) icw2/r

(y, m -j- w) m ! n !

Chapter II.

VARIOUS EXPANSIONS FOR THE FUNCTIONS; RELATIONS BETWEEN THEM.

The seven confluent functions which we have introduced, and defined by
double power-series, may also be represented by simple power-series in x,
or in y, by performing the process of confluence on the similar expressions
given by Appell for the four F functions. We thus find

, , 0 N xWa, m)(6, m) ,, , x xm

$i(a; Pm> y> x, y) = Zj , , — -$(a,+ ?», y+m, y)

(y, rn) ml

_ ^ (a, m)

3T

2 7 — — ( F(a + m, ft y + m: x)~\

,S(y , w) x r > /

and similar formulae for the other confluent functions.

We shall next consider formulae derived from the definite-integral
values of the F functions, such as

F0 =

r(y)r(y')

- ux - vy)~*dudv.

r(f3)T(B‘)T(y- mv - n

We have

(1 - ux-vy)~a=( - l)"a[l - (1 - ux) - (1 - vy)]~a

= ( - ir“2 - «*)"( i - ^)-

m ! n !

76

Proceedings of tlie Royal Society of Edinburgh. [Sess.

so

F9 =

( - l)-ar(y)r(y) f1 ^ )y^ _ux)mdu

T(P)T(P')T(y-p)T(y'-p)^^ mini J { ' { ’

jfV_1( 1 - 1 - vy)ndv

=(-ir22 <i^brf) F( ~m’ p ’ y ’ *)F( - ». p ; y ; 2/),

a formula to which we can apply the ordinary process of confluence,
obtaining the interesting expansions for the 'VF functions :

*i(<h P ; y> y ; *. y) = ( - F( _ m> P : v> *)$( - *> y’> s')

%(a ; y,Y; a, j /) = ( - l)"‘22l^r ®( “ TO> T> *)*( ~ »> y’< 2/)-

By reasoning of a similar type we find

r.(. : ; ft ft ;r 2 . ! ■ - »* F,(. . - i ft +« ; ft + - ;

y-p' + m, y + m; x , y)
or

F, = y, ( - w) y F2(a+m ; p + m, ft + m ; y + m,y - p + m ; x, y).

" (y - P, m)(y, m) m'.

From these we obtain by confluence

*,(«;ft;y; *, y) - 2 (- 1)” m) s ^

" (y - P, m)(y, m) m !

(ft m) ?/

^(a + m, p + m; y + m, y - p + m; x, y)

Pi=

<f3(A y ; y) = 2 ( - 1)m(y_^’m)(y, m) m T ^ +m’y+m’ “W? ~ P + m> v)>
which may be transformed into

$3(ft y; X , y) = ex^(-l)m7 $(y-a, y + m, -x)B(y- p + m, y) ;

(y — ft m)(y, m) m •

i

lastly, from F3 we obtain in a similar way

Ei(a, a ; P ; y; x, y)|| ^ M 1 )m ^ m^,a ’ f F(a + m, P + m, y - a + m, x)

^ (y,m)(y-a,m) mi

3>(a' +m, y + m, y)

$2(a, a ; y; X, ( “ 1)™ (a> ™)(a » m\ $(a + m, y - a + m, x)

(y, m)(y- a , m) ml

<J>(a +m, y + m, y)

a„(a, ft y, x, y) = 2 ( - 1 )“ 7 TT — 7 -C F(o + m, /? ; y + m ; x)

" (y, m)(y - a, m) ml

B(y — a + m, y).

Another type of expansion may be obtained as follows : in the formula

r(y)

npw

)F(y -ji- W)fofy ~ ^ ~ \ 1 -ty-fi-P-'i 1 -vyP+l - tz-vy + vtx)-‘dtdv

77

1920-21.] Hypergeometric Functions of Two Variables,
take

(1 - tx - vy + vtx)~a*= ( - 1)~“[1 - (1 - tx) - (1 - vy) - vtx\~a

whence

(«, m + n+p)t

m n p 171 \ 71 \ p \

r, = (-i)-222*fl

(a, m + n + p)(p, p)((3', p)_

m\n\p\(y, p)(y - /?', p)

and
3>

F( - m, /3 +p ; y - p' +p ; x)

F (~n, /¥+p, y+p, y)

y-fi + p, y).

All these expansions show the intimate connection between these functions
and the similar one-variable functions.

It is easy to show also that an important relation exists between <i> 1
and and that, in fact, they always reduce to one another. Let us start
from the expansion which we gave for <L1; in ascending powers of x ; then,
using the relation

<I>(a + m, y + m, y) = ey®(y - a, y + m, - y)f

we can write

Z(a,m)(i3,m) x xm

^ -y $(y-a ; y + m, - y)

and, comparing with the expansion for S1?

$i(a ; P ; y ; y) = ey%i(<h y - a ; P ; y ; x% y)>

which is the relation in question.

m !

Chapter III.

DIFFERENTIAL EQUATIONS SATISFIED BY THE FUNCTIONS.

The seven confluent functions satisfy partial differential equations of
rather simple forms, which it is easy to obtain, by confluence, from the
four systems of equations found by Appell for the F functions.

W riting

dz dz d2z

ay -a. S?-r, etc.,

we find that the system for the function flq is

rx( 1 - x)r + 2/(1 - x)s + [y - (a + P+ 1 )x~\p - pyq - apz = 0
l yt + xs + (y - y)q - px - az = 0,

78 Proceedings of the Boyal Society of Edinburgh. [Sess.

that for is

fx( 1 - x)r - xys + [y - (a + /3 + 1 )x\p - (3yq - a/3z - 0

yyt + (y - y)q -vx - ^ = o,

and similarly for the other functions.

Each of the systems is of the type

* fr = axs + a2p + asq + a^z

V= bxs + b2p + b^q + b±z

(the as and b’ s being functions of x and y), of which a general theory has
been given by Appell, with the aid of certain propositions established by
Bouquet. When the expression

1 - alb1

is different from zero (which is the case for the 'VE and 3? systems), the general
solution of the system is a linear function of four independent solutions

and if

z=C1zl + C 2z2 + C3z3 + C4z4,

1 - albl = 0

(which occurs for the systems), it is a linear function of three independent
solutions

2 — CjZj + C 2z2 + C 3z3 .

We may observe that the system satisfied by the function

^i(a ; P ; y ’> x> v)

admits also the independent solutions

x1~y^1(a+ l-y;/3 + l- y;2-y , y ; x, y)
yl~y^1(a+l-y' ; [3 ; y, 2-y ; X, y)
x1~yy1~y'$r1(a +2 -y-y ; fi+l -y ; 2 - 7, 2 - y ; x, y).

A similar result may be obtained for the function so that the general
solution of the two T' systems may readily be expressed in terms of the
\E functions themselves.

Chapter IV.

SOME SPECIAL PROPERTIES OF THE AND H FUNCTIONS.

We shall next give a few formulae illustrative of the properties of the
<f> and H functions : the function which has a special importance, will
be considered in the next chapter.

The dq function admits recurrence formulae analogous to the well-

1920-21.] Hypergeometric Functions of Two Variables.

79

known relations between contiguous hypergeometric functions of one
variable; thus

£?*!(<*+ 1; P+ 1 ; y+l; x,y)+ ^(a + 1; /?; y+1; x, y)

7 7

= + 1 ; /? ; y ; y) - ^i(<* ; P ; y ; ^ y)

$i(a ; /3 + 1 ; y ; x, y) = ^(a '> Pi 7 i y) + — ' $i(a + 1 ; £ + 1 i 7 + 1 i ^ 2/)-

7

The relation

iU-i(a; P; y , x, y) = “£*>,(<* + 1 ; 0 + 1; y+1; *, ?/)

shows that the derivates of the <h1 function are expressible in terms of the
function itself.

Similar formulae may be obtained for d?2.

<3^ may be expressed by a simple definite integral

*i(«J Pi 7; y) - r(a)r((y - «)f ~ “)T'a~1(1 -

while <f>2 may be expressed by the double integral

ri * »> - rmnml-f -<?>// *‘~v "(1 - -

(u^O, v^O, l - u - v^O).

Formulae of the same type may be obtained for the H functions : thus
we have

ft’ “> ^ *’ y> = r(.)r(,Wy- a -,-)//

the field being the same as above.

\y-a — a'-l

dudv .

Chapter V.

THE FUNCTION AND ITS TRANSFORMATIONS.

The function Tg proves to be the most interesting of the seven, as its
properties afford a very direct generalisation of the one- variable confluent
hypergeometric function. To render this fact more conspicuous, we shall
substitute for Ar2 a new function, just as Whittaker * studied, instead of T>,
his functions M or W.

We therefore make the following change of parameters:

a = /x -f v — /*' -f 1
7= 2/x-f 1
y =2v+ 1,

* Bull. Amer. Math. Noc., iv, p. 125.

80

Proceedings of the Eoyal Society of Edinburgh. [Sess.

and we define the function

M kt v{x, y) = L ^2(/x + v-k+l; + 1, 2r + 1 ; x, y).

The development in ascending powers of x and y is then

,, V+1 _*±e y y (fi + v-k+l, m + n) xmyv

2V 2 ““(2/*+ 1, m)(2v+ 1, n) m\ n\ '

We see that this function exists only when /u and v are both different
from the half of a negative integer ; a similar feature occurs with the
one-variable confluent hypergeometric function

M*, „(*) = xT He^ lim F (ix-k + i, P; 2^+1 ; - )

which disappears if 2/ul is a negative integer. If, however, we suppose v,
for instance, to become equal to — J, and simultaneously y to become equal

to zero, with the condition that the fraction 0 ^ — tends to zero, the

l i/+.l

function becomes, as it is easy to verify by considering the above
expansion, equal to

+ k m) ^

" » (v+i, m) m !

or precisely Mfc> ^(x). We then have the most important relation

Mfc, 0) = Mfc, M(z),

provided that lim ^ =0 ; to which can be added the similar one

Mfc,_£>v(0, y) = MktV(y),

. OC

provided that lim — - = 0.

Lfx -f- 1

It is easy to form the system of partial differential equations satisfied
by Mfcf v : it is

x2r - xyq + z(^ - ~ ^ -f kx + \ - /x2^ = 0

yH - xyp + z(^ - 1 ^ + ky + \ - v2^ = 0.

(S)

If in this system we take y = 0 and v=— J, the second equation
vanishes, and the first one becomes

o cPz
dxi

+ kx + \ - /x2 ) = 0,

which is precisely the confluent hypergeometric equation of one variable,
in Whittaker’s form; and we obtain a similar result by taking x = 0 and
U— ~~ 2*

1920-21.] Hypergeometric Functions of Two Variables. 81

We shall, in general, denote by WkjfXiV (x, y) a solution of this system
with the condition that it reduces to WktfJi(x) for y = 2i/ + l = 0, and to
W k,v(y) f°r ^ = 2^ + 1 = 0.

The general solution of the system S is readily found to be of the form
2/) T y) + fx f ~ y) “l- ~fJlj _ v(x, ?/),

the C’s being arbitrary constants.

Numerous recurrence formulas may be written for the M function. We
shall only give the following as an example:

M

& — v'

dx~~K'tx'v V ' * 2/ ‘ 2^+1

The expansions for ”T2 furnish analogous results. W7e thus obtain,
bearing in mind the definition of the one- variable M function and its
relation with <E>,

and

M lx v) f-;ya!"Wi('‘ + l'"i;+1’ m>M /.a

V (2/t+l, m)m! •’fe)

M (a v) - vm+"+i(_t + r ~ k + 1, m)

2d (2v + 1, m) m !

By transforming the formula

^2(a ; y>y*> v) = ( - 1) aX2-a* ?+T^( y, *)$(-», y , 2/)

m ! n !

we obtain

M, „ m y)={-

7« 71 • ''J •

Let us consider the one-variable M functions which occur under the
symbol of summation. The expansion of the first one is

M

( -• m, p)

pto(2/x-+L^!

but, as m is an integer, the product ( — m, p) vanishes whenever p is
greater than m, so that the sum represents not an infinite series, but a
polynomial of degree m in x,

The question is now, what is this polynomial ? Let us write
= ( - rnt ™ - 2)

^(2/x+l, m-q)(m-q) !

q=m Xm~q

= r(2/x + t)m ! — l)w_?— 77 , ; lVO , r

v A ’ f-fp ’ q \ (m - q) \ T(2/jl + m — q)

VOL. XLI.

6

82

Proceedings of the Royal Society of Edinburgh. [Sess.

or

.m— i

P(z) ( l)mm\ r(2/t+l)^0! ml r^2/t + m) 1 I (to-1)! r(2/* + m- 1)

and the expression between brackets is the polynomial of degree m
considered by, Sonine * in his researches on the Bessel functions ; it is
here Tm (x), the definition of the polynomial being the expansion

tx

ew, ',="°

and its expression, as given by Sonine, being precisely

afi-*

T^M- x -i-

a W p\0\T(a + p) (P-I)l 1 ! r(a + /3- 1) (/5-2)! 2! T(a + P~2)

We can then write the following expression :

Mm+M+i,M(^) = (-1)w^! T(2[x+l)x*+h

a result which can be verified by using the expression of the T polynomial
in terms of the Wk m function, as given by Whittaker, j-

We then obtain at once the very simple and remarkable expansion

x+y

Z/) = ^+y+ie 2 r(2/»+ l)r(2v+ 1)22(-

m n

([x, + v—k+ 1, m + n)T™Jjc) T”(y).

Some interesting consequences, concerning certain particular cases of
the M function, can be deduced from this formula.

If we suppose, in the first place, /jl and v to be of the form

Z z

where a and b are integers, we have to consider in the expansion poly-
nomials of the type

Tr+i(*>-

for which we readily find the simple expression

fia+ 1

r:+i(x)=^xr+Xx).

But we can observe with Sonine that, if A is an integer,

Ty*) = lW^)

where U is Hermite’s polynomial,

d?j

* Math. Ann xvi(1880), p. 41.
t Modern Analysis , 3rd edition (1920), p. 352.

1920-21.] Hypergeometric Functions of Two Variables. 83

so that we can write, for an M function of the aforesaid type,

x+y

k-

ct+&+3

mav V2 *e 2 r(fl + })r(& + })22( i)

„a+ i ^ 2(a+m+l)( ^

(a + b + 3 \ d“+1

x\ 9 -k, m + n) x

d6+1

dy

rU,

6+1 ^ «(5+rc+l)

(>/*)•

As any differential coefficient of the U polynomials can be expressed in
terms of the U themselves, we can express any function M where ya and v

are of the type 9 + \-\-\ in terms of Hermite’s polynomials.

£ JL

Let us take, in particular, a = b= — 1 ; we have at once, with a change
of variables,

Mi

-(j, yf) - V? (-■ x 2 Z ( ■ - 1 r+,*(i - *. « + ")u-(^)u«(^>

This formula connects the special M function with the parabolic-cylinder
functions.

Chapter VI.

CONNECTION BETWEEN CERTAIN KNOWN FUNCTIONS AND THE
CONFLUENT HYPERGEOMETRIC FUNCTIONS.

Several functions of two variables introduced by different authors can
be connected with some of the seven confluent functions of two variables.
Of this we shall give three examples.

1. The Two-variable Polynomials Am>n of Appell. — It is a well-known
fact that limiting cases of a great number of one-variable polynomials are
expressible by the W&; m function or by Bessel functions. For instance, as
anyone knows, for Legendre functions we have

J m(x).

We can establish a similar property for certain two- variable polynomials.

Let us consider the two-variable polynomials discussed by Appell,*
and defined by

A m, J x, y) = X1 V y (l - x- y)y+y'

As shown by Appell himself, they can be written under the form

AWt „ = (y, m){ 7, n)( 1 - a - y)m+n F2(y + y - 8 ; - m, - n; y, y';

x + y - 1’ x + y - 1/

Archiv Math. Phys lxvi, 1881, p. 238.

84

Proceedings of the Royal Society of Edinburgh. [Sess.

Let us now divide x by m and y by n, causing m and n to tend
simultaneously to infinity : we observe then that

A (- yA

li m' n\m ’ n )

».»=« (y, m)(y'j n)

e-2^%(y + 7-8; y, y ; a, y),

showing a connection between AWj n and of the same nature as the
connection between Legendre and Bessel functions.

2. The Two-variable Polynomials n of Hermite. — These functions,
introduced by Hermite,* arise from the derivation of an exponential
where the exponent is a quadratic form of x and y ; their definition is

0m+n

- y )

where

dxmdyn
cf>(x, y) — ax 2 + Tbxy + cy1.

It may be shown that this polynomial depends essentially on the function

Wm+n-l

2 » ' ?» ?•

3. The Two-variable Bessel Function of order Zero. — Several results
have been published lately on the subject of new functions of two vari-
ables possessing certain properties analogous to Bessel functions.*)* These
two-variable Bessel functions are defined by the expansion

y)u»

or by the integral

1 fn

Jn(x , y) = - I cos ( nu — x sin u - y sin 2 u)du.

*} o

It may be shown that the simplest of these functions, J0(x, y), satisfies the
same differential equation as our solution

e~iy%(h b - i^2)-

* CEuvres , ii, p. 293.

f Of. a paper by Jekliowsky, with a bibliography of the subject, in Bull. Astron .,
t. xxxv, 1918.

1920-21.] Hypergeometric Functions of Two Variables.

85

PART II.

THE CONFLUENT HYPERGEOMETRIC FUNCTIONS
AND THE POTENTIAL.

Very important connections exist between the confluent hypergeometric
functions of two variables and the theory of potential in hyperspace, a
fact which generalises in an interesting way the well-known relations
between the hypergeometric functions of one variable, or their confluent
forms, and the potential in three-dimensional space. We shall now
develop some of these propositions.

Chapter I.

THE FUNCTIONS OF THE PARABOLIC HYPERCYLINDER.

Let us consider a four-dimensional space, where the Cartesian co-ordinates
will be denoted by x, y, z and t, Laplace’s equation in this System being

AU = — + 05J+!^ + — = 0.
lu'i pf

Let us now make the change of variables

X = UV COS (j)

y.= uv sin <f)

t — t.

The hypersurfaces thus introduced are rather simple ones : it is at once
obvious that t — const, and 0 = const, are hyperplanes; as for u = const., we
obtain the corresponding hypersurface by eliminating v and <p between the
first three equations, obtaining

x2 + y2 = u2(u2-2z) (A)

so that it is an hypercylinder, with its generatrices parallel to the £-axis,
its basis in the xyz space being the quadric (A), which is a paraboloid of
revolution. We shall say, therefore, that this hypersurface u = const, is
a parabolic-hypercylinder. The hypersurface v — const, is of the same
nature.

If now we transform Laplace’s equation, we obtain

86

Proceedings of the Royal Society of Edinburgh. [Sess.

A solution may be obtained by taking

U = U1(«a, v) cos m<f) cos nt ;
the function \J1 verifies then the equation

02lL 02U, 1 0IL 1 0IL 2( 1 1 \TT 2/ 9 2xTT A /m

which we shall name the parabolic hypercylinder equation, the two-variable
function U fu, v) being a function of the parabolic hypercylinder.

It is obvious that equation (B) may be solved by the product of a
function of u alone by a function of v alone : but solutions of that kind we
shall consider as degenerate, and therefore reject them.

A real two-variable solution, however, is easily found by considering
the Wfc ^ v system. If in this general system we take

Jc = 0

and replace x and y by we shall see that this function verifies

p ( n2x2 n2y2 , 1 — m2\ ~

r-t-nyq + ^- r-^ + _j = 0

if)-*-

and that, if zx is a solution of this system, the function

verifies

1 --(*2+2/2)

= — e 4 Zj
xy

r + p( nx + -) - nyq + z( - n2y 2 -

s

r + t +

XJ \ XT

+ q(ny + - nxp + z(^ - n2x2 -~^j = 0,

and therefore the single equation obtained by addition of these, i.e.

- + ?- m2(~ + ^)z - n\x2 + y2)* =

x y \xz yzJ

which is precisely equation (B). We have then this remarkable result:
the function

1 — ~(w2+i?2) / nu 2 nv2\

Vi(u, v) = ~ce VVo, ™ ~2 )

is a function of the parabolic hypercylinder, and Laplace’s product in
parabolic hypercylindrical co-ordinates may be taken equal to

7 T cos md> cos nt -%2+«2)w ( nu 2 nv2\

U= * e 4 W0i« 4— , — J.

uv 2 2 \ l A /

1920-21.] Hypergeometric Functions of Two Variables.

87

Chapter II.

THE FUNCTIONS OF THE HYPERPARABOLOID OF REVOLUTION.

Let us now, in like manner, consider the change of variables

x = uv sin 0 cos 0
y = uv sin 0 sin 0
Z = UV COS 0
u2 — v2
2

The hypersurfaces 0 = const, and 6 = const, are hyperplanes; the equation
of the hypersurface u — const., obtained by elimination of v, <p , and 0, is

x2 + y2 + z2 = u2(u2 — 2 1).

It represents therefore an hypersurface of the second order, obtained by
rotation about the £-axis of the quadric

x2 + y2= u2(u2— 2 t)y

which is, in the xyt space, a paraboloid of revolution about the Laxis. We
shall term this hypersurface an hyper paraboloid of revolution. An hyper-
surface of the same type corresponds to v = const.

Laplace’s equation is now

, „ • , 0U1 .

u2vz sm 9 — +

CU J

dv

' o 2 • , 0U1 0

UlV2 Sill 0 — — I -f-

^ dv J 00

( u 2 + v 2) sin 0

0U

00 .

+

00

U2 + V2 0U
_ sin 0 00

p

We easily get rid of the 6 variable by taking

U = U-^w, v, 0) cos mO,

wLich gives

0 / o 2^l\ . 9 \ . / 2 . 2\

— U2V2— -I + — U2V2—± ) + (u2 + V2)

ou\ ou J ov\ dv

1 0/i ,0UT\ m2 IL

_sin 0 00 \ ^ 00 / sin2 0_

= 0.

But it is also obvious to take

p = P(“> -)P:(cos <£),

where P™ is the associated Legendre function, which satisfies

P»+1)-PL1P = 0>

sin2 0 J

and we obtain an equation in u and v only,

1 d l . ,dP\ ,

— ( sm 0 — +

sm 0 dcf)\ a0/

02tL . 02UO . 2 0UO . 2 0U

+

+ -

(C)

du2 dv2 u du v dv

a solution of which, really depending on two variables, will be a function
of the hyperparaboloid of revolution.

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

Introducing again the W k,^,v function, we shall form the system
satisfied by

There is no need to give the complete calculation : let us say only that,
adding together the equations thus obtained, we find that 0 is a solution of

r + t + -p + ‘1q + z(-+ t)(i- V)|o,
x y \x2 y V

y \x* r

the parameter k having disappeared.

/Yb

If we take therefore 4/x2 — \ = n(n-\-l), or = ^ + we obtain complete

identity with equation (C), so that

U Ju, = W, «+1 n - . ^

2+?> 2it?V2

is a function of the hyperparaboloid of revolution.

We shall now make several remarks touching these functions.

1. The confluent function which appears in the question is of a type
we studied in Part I, Chapter Y, where the two last parameters jx and v

are of the form - + J, a being an integer. Referring to a property estab-

lished there, we can say that the function of the hyperparaboloid of
revolution is expressible in terms of the parabolic-cylinder functions.

2. Let us consider the change of variable

O 9

x = — - — sin (p cos 0
2

oi2

y = - — - — sin <£ sin 0
u2 — v2 ,

Z = COS (f)

t = uv.

The hypersurface u = const.,

i(x2 + y2 + z2) = (u 2

is obtained through rotation about the £-axis of the surface

4(«2 + y2) = («2 — ^)2,

which is of the fourth order in the xyt space, and itself the result of the
rotation about the £-axis of the parabola

89

1920-21.] Hypergeometric Functions of Two Variables.

Laplace’s equation, written in this system, is easily solved by the change
of variables

u + v
u —

V2

u! - v'

V— . ,

x/2

which reduces it to the equation for the hyperparaboloid of revolution. A
solution is then

W

multiplied by a convenient factor, or

Wk "+i[(^ + v)2> ~ (u VY]‘

A similar remark may be made regarding the change of variables

u1 - v1

y = cos 0

j 2 r
z = uv
t = t,

where Laplace’s product is readily reduced to the parabolic hypercylinder
function.

3. We shall show presently that there exists, between the hyperspherical
zonal functions and the functions of the hyperparaboloid of revolution, a
connection similar to that between Legendre polynomials and the parabolic
cylinder functions.

Let us first investigate the relation between the one- variable functions,
and for that purpose give a preliminary definition.

If between two differential, linear and homogeneous, equations, E and
D, there exists a relation such that, deriving equation D n times with
respect to the independent variable x, we obtain equation E, we shall say
that D is the equation of Didon of E for the order n. Similarly, if between
two linear and homogeneous two- variable systems, S and A, there exists a
relation such that, deriving both equations of A m times with respect
to x and n times with respect to y, we find the system S, A will be called
the system of Didon of S for orders m and n. This definition, which we
proposed some time ago,* has its origin in the fact that F. Didon made
an extensive and successful use of the transformation in question to solve
differential equations occurring in the theory of two- variable polynomials.

* Nouv. Ann. de Math., decembre 1919.

90 Proceedings of the Eoyal Society of Edinburgh. [Sess.
Let us consider now the differential equation for Legendre polynomials,
(x2-l)y" + 2xy'-n(n+l)y = 0 .... (E,)

and its equation of Didon for the order n, which is

(x2 - l)z" — 2(n - l)xz — 2nz = 0 .... (D2)

X

In this last equation, let us replace x by -^=, and cause n to tend to infinity.
We obtain

z" + 2xz' + 2z = 0 (D2)

which equation is itself the equation of Didon for

y" + 2xy’ + 2(n + 2)y = 0 ....

But (E2) is verified by

(E2)

-h -*
1 * e

W

n s

9 2~5

where the W function is of the type of the parabolic-cylinder functions.
The connection between it and Legendre function is therefore established,
through their equations of Didon.

Let us come now to the field of two variables, and consider the poly-
nomials Vm, n{x, y ) studied by Hermite, which, as we mentioned in our
Introduction, Appell showed to be hyperspherical zonal functions. The
Ym> n function satisfies the system

(Sj)

^(1 - xl)r - xys - (n + 3 )xp + myq + m(m + n + 2)z — 0
\(1 - y2)t - xys - (m + 3 )yq + nxp + n(m + n + 2) z = 0,

of which the system of Didon for the orders m and n is

(*i)

f( 1 - x2)r - xys + (N - 3 )px + N qy + 2 N* = 0
1(1 - y2)t - xys+ (N - 3 )qy + Rpa? + 2Nz = 0,

y

where N = m + n. Replacing in it x and y by -j == and -y==, and making
then N infinite, we obtain the system

(A2)

itself the system of Didon of
(S2)

fr 4- px + qy + 2z — 0
[t+px + qy+ 2z = 0,

cr + px + qy+(m + n + 2)z = 0
1 1 + px + qy + (m + n + 2)z = 0.

But a solution of (S2) is

~i ~i — i(sc2+2/2) tt-
z — x y 6 m+w+i

-1, -1

91

1920-21.] Hypergeometric Functions of Two Variables.

where W is of the hyperparabolo'id type, the connection between this
function and the hyperspherical polynomials being exactly the same as
that between the two one-variable functions considered.

Chapter III.

HYPERCYLINDRICAL FUNCTIONS.

Another example of the use of one of the confluent hypergeometric
functions for solving Laplace’s equation is given by the introduction of
hypercylindrical co-ordinates. We shall first consider the problem in
four-dimensional space, and afterwards generalise it.

The change of variables

x = p sin # sin </>
y = p sin 0 cos </>
z = p cos 0
t = t

defines what may be called hypercylindrical co-ordinates, the hypersurface
p = const, being an hypercylinder with its generatrices parallel to the /-axis,
and with the sphere

X2 + y2 + Z2 = p2

as a basis in the xyz space. It may therefore be termed a spherical
hypercylinder. Laplace’s equation is then

AU = ^ + 1S +

1

02U + 02U + 2 0U + cot(9 5U_0

0/o2 p 2 dO2 p 2 sin2 0 dcj>2 dt2 p dp

dO

A solution may be obtained by taking

U = ef* cos 0),

the two-variable function Up which we shall call a function of the
spherical hypercylinder, or more briefly hypercylindrical function, being a
solution of

d2u1

dp2 p

2 86>2

2 dl\ cot# 01T1
p dp pz dO

p2 sin2 0

or, by putting cos 0 = go,

(A)

202UXj n 2\02U1 j 0 0Ux 0 0UX , 2 oTT

P2— ^+(1 -o>2)^ + 2p— i- 2w—± + p.2p2XJ1-
op L 0(t)Z op 0(0

Ui = 0;

,U!=0.

Let us denote by U1/(p, w) a solution of the same equation in which we
gave to v the value zero. The product

TJ' = efltJJ1'(pi w) = e^U/(p, 0)

92

Proceedings of the Royal Society of Edinburgh. [Sess.

is a solution, independent of 0, of Laplace’s equation, and therefore a
zonal harmonic function. We shall say therefore that the function U/,
solution of

i&U’ n fell' 0UY 9 SUf 2 2TT ' O

(B) p ap1 +11 )-^ +2p^y “ 2o>-^J- + /xVui

is an hypercylindrical zonal function.

Such a function is readily found by considering our confluent function

Z = E2(a, /?, y, X , y),

which, as we said, satisfies the system

jx(l “ x)r + ys + [y - (a + ft 4- 1 )x\p - afiz = 0
+ xs + yq — z = 0,

and therefore the single equation, obtained through elimination of 6',
x\x - l)r + y2t + yqy - [y - (a + /3 + VfX^px + a/3zx - zy = 0.

Let us now, in this last equation, make the change of variable

x =

y = \yf

and substitute for 0 a new function f defined by

Let us then give to the parameters the special values

We find

a=l, £

= 1

r=|.

(1-«l+^+2^-2f-4^=0’

M2

an equation which becomes identical with (B) if we take A= — ~ ; so that
the function

or

1 „

,2n2

W<* e)=«teuA1’ i; §; 1+tan2e’ _/v

is a zonal hypercylindrical function.

The research of a complete hypercylindrical function is now exceed-
ingly simple, if we make the following remark : if U/ is a solution of (B),
a solution of (A) will be

i

U2(p, ti,) = (l-C02) 0-^U/
mdm

(just as Pn(a?) = (l — x2)- — mPn(cc) is a solution of the associated Legendre

dx

equation, and a complete spherical function, while Pn is a zonal one).

1920-21.] Hypergeometric Functions of Two Variables. 93

Therefore

Uj = sinv 6

dv

0 (cos 0)V -

is a complete hypercylindrical function. But the differential which occurs
in this expression is easily reduced. Let us, for brevity, put

/*V_

We have, considering the expansion of 3?2,

(j, m) 1 un

and

'V ZZ(!

0'TTf / "V (£> m)(2w + 1, v) 1 u

(-§, m + n) ^m+i ^ j

Soj" ~ ^ ^ 22/ + to2m+*'+i w.!’

and a rather simple transformation shows that

(J, m)(2w + l, v) =

+ 1, m )( n +b m

m !

so that we have

0W=(_irAvy

2 + b + i» m) i

do)v

(f-, m + ra)m! o)2m n !

= < - 1 )"d+H2(i + lj i + 1 5 b “}

The function

Ui(P) 6) =

tan,, 0 ^ fv
cos 0

5 + 1, £+1; I; l+tan*«,-££

is therefore an hypercylindrical function, Laplace’s product for hyper-
cylindrical co-ordinates being

u = cos v<y^H2(| + i,|+i; I; i + e, -

The same problem in {n-\- 2)-dimensional space leads us again to the H2
function. If the Cartesian co-ordinates are denoted by xv x2, . . . , xn+2,
hypercylindrical co-ordinates will be defined by

= p sin 0 sin (f)1 sin <jf>2 . . . sin <£n_2 sin ^n-1

x2 = p sin 0 sin ^ sin <j>2 . . . sin <f>n_2 cos ^n-1

xs = p sin 6 sin cf)1 sin cf>2 . . . cos cf>n_2

xn = p sin 0 cos
xn+i = p cos 0

94

Proceedings of the Royal Society of Edinburgh. [Sess.

and Laplace’s equation is

it an; w 92u

^ dxj2 0#22 + ‘ + dxn+22

= Pn sin”"1 0 sin”-2 <^ . . . sin <f>n_2
+ ^[pw“2 sin”-3 6 sin”-2 <£t . . . sin <£n_2
+ ^[pwsin”-1^sm”-2^1 . . . sin <£n_24?J

i=n— 1

Pn 2 sin”-3 0 sin” 4 4>1l . . . sin”-*-2 <^i_1 sin”-*-1 sin”-*-2 <£i+] . . . sin <f>n_2—

i= i 09*L “<ty<

We shall try to solve it by a function of the form

U“/oWi(U • • • /«-i(<*i)ui(p> 0).

We readily observe that we may take

/o = ef

and

/i = cos

where m1 is an arbitrary integer.

The terms containing <^n_2 can then be dissociated from the rest, and
we find for /2 the equation

d%

7 » — 2 + C0t <t>«-2 /£* - mi + *>2 - 0,

d<t>n-22 2 sin- <f>n_2

F being a certain function of (pn~3, . . . , <pv p, 6. We shall therefore
introduce the associated Legendre function and take

f2 = P^(C0S ^n-2)i

m2 being an arbitrary integer, and the equation for /3 will then be

^2 + 2 cot - m'2(TV~ ^/a + F1/3 = 0,

d<f>n— 3 d(f>n— 3 sin (fan — 3

the law of formation of the successive equations appearing clearly enough.

Let us now consider the polynomial C^(2) of Gegenbauer, which is the
coefficient of aA in the expansion, in ascending powers of a, of

(1 — 2aZ + a2)~v,

and let us denote the function

It /7m v

where pt is an integer, by the symbol CT ^(z). This function CT ^ plays

1920-21.] Hypergeometric Functions of Two Variables. 95

with respect to C^the same part as P™ to Pn; and we have in particular

C* = P*.

fJL A

It is easily seen that the function CT (cos <p) satisfies the differential
equation

/72/w rim u( n _L_ O.ir 1 \

= 0,

d2u , 0 , , du

w v

A(X+2,)ij^ + ^-1)

sim (f>

so that there appears a way of solving our above equations by taking,
in general,

i- 1

fii&n-i) = C (COS <frn-i).

v i— 1

The last equation, which contains only 0 and p, is found to be

A 2 02U, , 0IL , 02lL , , 1N , /j 0U-. TT

, 2n2 , %-tK-! + n - 2)
P sin2 0

We can then easily verify, as we did in the case of four dimensions,
that a solution of it is

TT tanmn-i ( mn_x + » + ra - l . w + 1 . , 2 A k2p2\

— 2 — * 1+tan ~~r)’

so that Laplace’s product in hy percy lindrical co-ordinates and (n-\- 2)-
dimensional space is

~ ^ tanmn_1 0

U = COS ^(oos <t>n-2)Gli3, ^(cos <£„_3) . . . C^_tVi(™ 0i) cogn_1

x S2(m-‘ + ”, ro"-1 + m~ A ; 1+1 • 1 + tan2 .

If we seek a solution independent of the 0’s, which will therefore be a
zonal function, we equate all the m’s to zero, and obtain

IV(P, 0) =

1 ^ fn n— 1 7i + l

cos

Z-2n2

; 1 + tan2 0, — — £

2\2’ 2 ' 2

Let us take in particular n= 1 : we are in three-dimensional space, and we
obtain a cylindrical zonal function which is here

U^p, 6) = S2(i, 0; 1 ; l+tan20,-^!);

but this is equal, through the expansion of %2, to

/ &2p2\n

zv V.

w (1, n)n !

which is precisely Bessel function J0(&p) ; an obvious result which, however,
affords a good confirmation of the preceding theories.

96

Proceedings of the Royal Society of Edinburgh. [Sess.

These examples are sufficient to show the importance of the confluent
hypergeometric functions of two variables in four-dimensional potential
theory. We present them together in the following scheme, adding Appell’s
previous results on Hermite’s two- variable polynomials, and the correspond-
ing relations between one- variable functions and the three-dimensional
potential theory : the scheme explains itself.

Solutions of Laplace’s Equation by Hyperueometric Functions.

(a) 3 Dimensions— One Variable.

1. Sphere

2. Parabolic cylinder

3. Circular cylinder

Legendre functions { P^taVfa^on hyperge°'

Weber functions { P^ticular case of the confluent

f hypergeometnc function 4s.

Bessel functions 1 “"fluent hypergeometric function

l -B.

(6) 4 Dimensions — Two* Variables.

1. Hypersphere

2. Parabolic hypercylinder j

3. Hyperparaboloi'd

4. Spherical hypercylinder

Hermite polynomials (Particular case of the hypergeo-
r J ( metric function _r2.

v f particular case of the confluent

Function W k, n.,v \ hypergeometric function ¥2, de-

t duced from F2.

Function s, 1 confluent hypergeometric function,

2 ! deduced from F3.

{Issued separately May 9, 1921.)

INSTRUCTIONS TO AUTHORS.

The ‘ copy ’ should be written on large sheets of paper, on one side only,
and the pages should be clearly numbered.^ The MS. must be easily legible,
preferably typewritten, and must be absolutely in its final form for printing.
All tables of contents, references to plates, or illustrations in the text, etc.,
must be in their proper places, with the page numbers left blank; and
spaces must be indicated for the insertion of illustrations that are to appear
in the text.

Illustrations. — All illustrations must be drawn in a form im-
mediately suitable for reproduction ; and such illustrations as can be
reproduced by photographic processes should, so far as possible, be
preferred. Drawings to be reproduced as line blocks should be made with
Indian ink (deadened with yellow if of bluish tone), preferably on fine
white bristol board, free from folds or creases ; smooth, clean lines, or
sharp dots, but no washes or colours, should be used. If the drawings are
done on a large scale, to be afterwards reduced by photography, any
lettering or other legend must be on a corresponding scale.

If an author finds it inconvenient to furnish the drawings according to
these regulations, the Society will have the figures re-drawn and the letter-
ing entered at his expense ; but this will cause delay.

When the illustrations are to form plates, a scheme for the arrangement
of the figures (in quarto plates for the Transactions, in octavo for the
Proceedings) must be given, and numbering and lettering indicated.

Proofs. — A first proof and, if desired, a revise of each paper will be
sent to the author, whose address should be indicated on the MS. Expenses
for proof correction should not exceed 10 per cent, of the printers’ charges
on the setting and printing of each paper. Any excess will be charged
against the author.

All proofs must, if possible, be returned within one week, addressed to
The Secretary, Royal Society, 22-24 George Street, Edinburgh, and not to
the printer. To prevent delay, authors residing abroad should appoint
someone residing in this country to correct their proofs.

The author receives fifty of the reprints free, and may have any
reasonable number of additional copies at a fixed scale of prices which
will be furnished by the printer, who will charge him with the cost. To
prevent disappointment, especially if the paper contains plates, the author
should, as soon as possible, notify to the Secretary the number of additional
copies required, and should also repeat the notification on the first proof
returned.

Index Slips. — In order to facilitate the compilation of Subject
Indices, and to secure that due attention to the important points in a
paper shall be given in General Catalogues of Scientific Literature and
in Abstracts by Periodicals, every author is requested to return to the
Secretary, along with the proof of his paper, a brief index (on the model
given below) of the points in it which he considers new or important. These
indices will be edited by the Secretary, and incorporated in Separate Index
Slips, to be issued with each part of the Proceedings and Transactions.

MODEL INDEX.

Schafer, E. A. — On the Existence within the Liver Cells of Channels which can be directly
injected from the Blood-vessels. Proc. Roy. Soc. Edin., vol. 1902, pp.

Cells, Liver, — Intra-cellular Canaliculi in.

E. A. Schafer. Proc. Roy. Soc. Edin., vol.

Liver, — Injection within Cells of.

E. A. Schafer. Proc. R,oy. Soc. Edin., vol.

, 1902, pp.
, 1902, pp.

] V

CONTENTS.

No. PAGE

VII. The Relation of the Soil Colloids to the Thermal Conductivity
of the Soil. By Capt. T. Bedford Franklin, B.A.

(Cantab.), 61

{Issued separately May 9, 1921.) ■

VIII. On a Graphical Method of determining Shear Influence Lines
and Diagrams of Maximum Shearing Force for a Beam
subjected to a Series of Concentrated Rolling Loads. By
Alex. R. Horne, B.Sc. (Lond.), Professor of Engineering,
Robert Gordon’s Technical College, Aberdeen, ... 68

(Issued separately May 9, 1921.)

IX. The Confluent Hypergeometric Functions of Two Variables.

By Pierre Humbert. Communicated by Professor E. T.
Whittaker, F.R.S., 73

(Issued sep>arately May 9, 1921.)

The Papers published in this part of the Proceedings may be
had separately , on application to the Publishers , at the follow-
ing Prices : —

No. I .

. Price 3s. Od.

No. VI .

. Price —

No. II .

. „ Is. Od.

No. VII .

„ Is.

Od.

No. Ill .

,, Is. 4d.

No. VIII

■ „ Is.

Od.

No. IV .

Is. Od.

No. IX .

• i, 2s.

8d.

No. V .

. „ Is. 4d.

PROCEEDINGS

So

OF THE

ROYAL SOCIETY OF EDINBURGH.

SESSION 1920-21

Part II] VOL. XLI. [PP- 97-275

(Contains Title, Contents, and Index.)

CONTENTS.

NO. PAGE

X. An Experimental Analysis of the Losses by Evaporation of
Liquid Air contained in Vacuum Flasks. By Professor
Henry Briggs, D.Sc., Ph.D., A.R.S.M., .... 97

( Issued separately June 20, 1921.)

XI. Note on a Continuant of Cayley’s of the Year 1874. By Sir

Thomas Muir, F.R.S., .111

(. Issued separately August 23, 1921.)

XII. On the Old Red Sandstone Plants showing Structure, from the
Rhynie Chert Bed, Aberdeenshire. Part IV. Restorations
of the Vascular Cryptogams, and discussion of their bear-
ing on the General Morphology of the Pteridophyta and
the Origin of the Organisation of Land-Plants. Part V.

The Thallophyta occurring in the Peat Bed ; the Succes-
sion of the Plants throughout a Vertical Section of the
Bed, and the Conditions of Accumulation and Preservation
of the Deposit. By R. Kidston, LL.D., D.Sc., F.R.S., and
Professor W. H. Lang, D.Sc., F.R.S. [Abstract], . . .117

(. Issued separately August 23, 1921.)

XIII. The Adsorption of Gas under Pressure. By Henry Briggs,

D.Sc., Ph.D., A.R.S.M., and William Cooper, M.A., B.Sc., . 119

(. Issued separately August 23, 1921.)

XIV. Utilisation of Solid Caustic Soda in the Absorption of Carbon
Dioxide. By Elizabeth Gilchrist, ALA., B.Sc., A.I.C.
Communicated by Professor Henry Briggs, D.Sc , Ph.D.,
A.R.S.M., .......... 128

( Issued separately September 5, 1921.)

XV. On the Criterion for Stable Flow of a Fluid in a Uniform
Channel. By H. Levy, M.A., D.Sc., Assistant-Professor of
Mathematics, Imperial College of Science, South Ken-
sington, .......... 136

{Issued separately December 13, 1921.)

XVI. Note on Conditions for Mirage on the Queensferry Road.

By Alex. G. Ramage, 148

{Issued separately December 13, 1921.)

[Continued on

EDINBURGH:

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

Price Eight Shillings.

THE ROYAL SOCIETY OF EDINBURGH.

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

The Council beg to direct the attention of authors of communications to
the Society to the following Regulations, which have been drawn up in
order to accelerate the publication of the Proceedings and Transactions,
and to utilise as widely and as fairly as possible the funds which the
Society devotes to the publication of Scientific and Literary Researches.

1. Manuscript of Papers. — As soon as any paper has been passed
for publication, either in its original or in any altered form, and has been
made ready for publication by the author, it is sent to the printer.

2. Method of Publication. — As soon as the final revise of a Trans-
actions paper has been returned, or as soon as the sheet in which the last
part of a Proceedings paper appears is ready for press, a certain number
•of separate copies or reprints, in covers bearing the title of the paper and
the name of the author, are printed off and placed on sale. The date of
such separate publication will be printed on each paper.

3. Additions to a Paper after it has been finally handed in for
publication, if accepted by the Council, will be treated and dated as
separate communications, and may, or may not, be printed immediately
after the original paper,

4. Brief Abstracts of Transactions Papers will be published in
the Proceedings, provided they are sent along with the original paper.

5. Special Discussion of Papers accepted for Publication. —
Where a paper has been accepted for publication, the Council may, with
the consent of the author, select this paper for Special Discussion. In the
case of such papers advanced proofs will be sent to the members of the
Society desiring copies, and copies will be supplied to the author for dis-
tribution. A paper selected for Special Discussion will be marked with an
asterisk (*) and placed first on the Billet for the day of reading. Any
following papers for that day may be adjourned or held as read if the
discussion prevents their being read.

6. Communications not submitted for Publication, such as
Demonstrations of Experiments, Statement of Scientific Problems, etc.,
may be received by the Council, and may also be selected for Special
Discussion. The Council does not undertake to publish any notice of such
communications in the Proceedings or Transactions of the Society.

[Continued on next page.

Errata in the Abstract of Sir J. A. Ewing’s Address on Molecular Energy
in Gases, Proc. R.S.E., vol. xl, pp. 102-111, for May 3, 1920.

Page 105, line 20, for f read f (bis), and for read
Page 106, line 28, for 10“23 read 1028

1920-21.] Evaporation of Liquid Air in Vacuum Flasks. 97

ft

X. — An Experimental Analysis of the Losses by Evaporation
of Liquid Air contained in Vacuum Flasks. By Professor
Henry Briggs, D.Sc.

(MS. received March. 1, 1921. Read March 21, 1921.)

The experiments here described were made on behalf of the Oxygen
Research Committee of the Scientific and Industrial Research Department,
and the paper is given by permission of the Department. The fullest
acknowledgment is due to Dr J. A. Harker, F.R.S., and to his co-workers,
Professor G. W. Todd and Mr S. H. Groom, who have, in a series of able
memoirs presented to the Oxygen Committee, analysed the nature of the
heat-transfer from the outer atmosphere to the interior of metal vacuum
bottles; but for their memoirs the writer’s experiments would not have
suggested themselves.

The Dewar Vacuum Vessel.

The Dewar vacuum flask, which enables low boiling-point liquids to
be stored and transported, has been the principal means of rendering
possible the great expansion now proceeding in the scientific and com-
mercial uses of liquid air and liquid oxygen. These liquids are being
increasingly employed as laboratory reagents, and are being put to service
in mine rescue apparatus, for blasting, in aviation and therapeutics, and
in evacuation plant.

Vacuum vessels are made in glass, silica ware, porcelain, and metal;
but for carrying and handling the liquids in bulk, only the last kind is
at present of much value. The glass vessels devised by Dewar in the
course of his researches on liquefied gases, and made by him in many forms,
are too well known to need description.*

Dewar described the metallic vacuum vessel in 1906, f and not long
after that date its manufacture was taken up in Germany, whence, before
the war, all the flasks required at British mine rescue stations were
obtained. During the latter part of the war these bottles became necessary
for the Services, and as a result of the exertions of makers and of the

* Sir James Dewar, “Liquid Atmospheric Air,” Proc. Roy. Inst. , xiv (1893), p. 1;
“The Coming of Age of the Vacuum Flask,” ibid., xxi, p. 240.
t Ibid., “ Studies on Charcoal and Liquid Air,” xviii, p. 439.

VOL. XLI.

to

98

Proceedings of the Royal Society of Edinburgh. [Sess.

guidance of Government research officers they are being successfully
produced in this country.

The most convenient size of liquid air or liquid oxygen container, or
storage and transport flask, is designed to carry 50 lbs. of the fluid.
A metal container of this capacity and of proportions usual at the present
time is shown in sectional elevation in fig. 1. It consists of inner and
outer spheres, A and B, respectively 14 and 15 ins. in diameter, the inner

one being suspended by a thin, narrow
neck, C, of low-conductivity alloy which
is soldered at its upper end into a metal
plug, E. The space between the globes
is evacuated through a lead pipe, G,
which, when the operation is complete,
is squeezed flat and sealed off by means
of a flame ; the pipe is finally protected
(as is shown) by a metal cap containing
bitumen or wax in which the end of the
tube is embedded. The care needed
in making these bottles will to some
extent be realised from the fact that a
high vacuum requires to be maintained
through the agency of seven soldered
joints. A dish-shaped metal spinning,
F, is attached to the lower half of
the inner globe, and holds activated
charcoal. This important addition is
due to Dewar ; without it, even a well-
made and well-evacuated metal flask
would not long hold a high vacuum.
In the container illustrated, the charcoal
is connected to the vacuum space by means of one or more openings
in the dish, the openings being covered by fine gauze. At liquid-air
temperature the charcoals power of adsorption is very strong; it draws
into and retains in its own capillaries and inter-molecular passages most of
the residual gas in the vacuum space, and therefore automatically preserves
the high degree of vacuum needed.

The inner surface of the outer globe and the outer surfaces of the inner
globe and charcoal dish are highly polished, to reduce as far as possible the
heat transferred across the vacuum space by radiation.

Most of the containers made in this country are constructed of copper —

1920-21.] Evaporation of Liquid Air in Vacuum Flasks. 99

the metal which, with the sole exception of silver, has the lowest emissivity.
The German-built vessels now in this country are of brass, in the manu-
facture of which alloy, in its finest grade, the Germans are unrivalled.
Dewar, before the war, built satisfactory vacuum flasks of nickel.

A first-class 50-lb. container loses, by tranquil evaporation, about
2‘5 lbs. of liquid air per day. The average loss of these vessels is probably
about 3*5 lbs. per day.

Causes of Evaporative Loss.

Leaving out of account certain minor and negligible causes of heat-
transfer, there may be said to be three ways by which heat from the
outside atmosphere may reach liquid air stored in a
vacuum flask. Stated in their order of importance
for a good flask, these are :

(1) By radiation from the relatively warm outer

vessel to the cold inner vessel ;

(2) By conduction across the vacuum space ; and

(3) By conduction down the neck of the flask.

When the vacuum is failing, conduction across

the vacuum becomes responsible for a greater heat
transfer than radiation.

Let be the absolute temperature of the hotter

outer globe, and 02 that of the colder inner globe.

Let us deal with the three processes of heat-transfer in the order

given above.

©

(1) Radiation. — We are here concerned with heat passing from a
relatively hot spherical surface (whose temperature was caused to assume
different values in the course of the experiments) to a similar cold surface
whose temperature remains constant, the latter being the boiling-point of
the liquid the vessel contains. Variation in the temperature of the hotter
surface involves variation in the dominant wave-length of the radiation,
and it is necessary to inquire whether this does not, in its turn, involve
a change in emissivity.

The dominant wave-length, in microns, \m, and the absolute temperature
of the hotter surface, 0V are connected by the expression \mQ1 = 2950. In
the case of the three-litre gilding-metal flask (fig. 2), whose evaporation
rates were determined (see below) at external temperatures of 10°, 44°, 70°,
and 100°C., \m assumes the values 10*4, 9*4, 8-6, and 7‘9 respectively. The
gilding metal contained 95 per cent, of copper; and although it will
eventually be seen that its emissivity is considerably higher than that of

100

Proceedings of the Royal Society of Edinburgh. [Sess.

the polished pure metal, it is justifiable to assume that the variation in
emissivity, over the range of Xm in question, will be similar to that of
copper. The data available indicate that the emissivity of copper is very
nearly constant between Aw = 10 4/x and Am = 7'9/x ; and that, if it be taken
as 0 016, it will be correct over the whole range to the third place of
decimals. The emissivity of gilding metal has accordingly been regarded
as constant for the temperatures used in the tests described below.

The first of the analyses here attempted is based upon figures given by
Dewar for a glass flask in which the inner vessel was “ silvered ” with
mercury, the outer one being untreated. The evaporation loss of the flask
was ascertained over a temperature-range (of extending between 158° abs.
and 338° abs. Information does not appear to be available regarding the
change of emissivity of glass and mercury surfaces over such a wide range
of Xm as is here involved, and it has been necessary to assume the emissivity
of these surfaces to be constant between the stated extremes of temperature.
Owing to the uncertainty resulting from the incompleteness of the physical
data, the results obtained for the glass flask must be regarded as rough
approximations. When emissivity is constant, the heat radiation may
be expressed as

Ls^W-9/) (1)

in which a is a coefficient depending upon the emissivity of the surfaces
and upon their dimensions. The unit may be calories per second, or, as is
here more convenient, grams of liquid air evaporated per hour.

(2) Conduction across the Vacuum Space. — With the highly refined
vacua with which we are concerned, the mean free path of the gas
molecules is greater than the distance (about 1 cm.) between the hot and
cold surfaces ; hence, if conductivity had been independent of temperature,
the heat carried by conduction across the vacuum would be proportional to
($i — 02)- In a gas, however, the conductivity varies as the square root of
the absolute temperature, and, as the mean temperature across the vacuum
space is 0-5(d1 + 02), the expression representing the evaporation loss due
to this cause is, in grams of liquid air evaporated per hour :

• • • • (2)

where b is constant for a given bottle.

(3) Neck Conduction. — The amount of liquid evaporated because of heat
conducted along the inner neck, C, of the flask cannot be evaluated even
roughly by direct computation based upon the dimensions of the neck and
the conductivity of the metal, owing to the fact that the tube forms the

1920-21.] Evaporation of Liquid Air in Vacuum Flasks. 101

channel of discharge of the cold gas leaving the vessel. Much of, and in
many cases all of, the heat flowing down the neck-tnbe enters the uprising
current of air in that tube, and never reaches the liquid in the flask. The
evaporation loss due to neck conduction thus depends upon the rate of
discharge of gas from the flask as well as upon the dimensions of the neck,
and in a poor flask with a high total evaporation loss the neck-loss will
be actually as well as relatively less than in a good flask of the same
dimensions.

Other things being equal, the evaporation rate of a large vessel, though
proportionately less, is, in grams per hour, actually more than in a small
vessel It therefore follows that as the size of the flask is increased the
neck may be shortened, or alternatively, made stouter, without the evapora-
tion rate due to neck conduction being affected. Heat-transfer along the
neck is studied experimentally in a later part of the paper.

In the cases examined, the temperature of the gas issuing from the
mouths of metal vacuum flasks containing liquid air lay between —4° C.
and —30° C. As the inner globe is made of so good a conductor as copper,
gilding metal, or brass, its temperature may be regarded as uniform at all
points of the sphere, that temperature being the boiling-point of the liquid.
It is therefore apparent that the heat transferred to the inner globe by
radiation and conduction across the vacuum space is all absorbed in giving
latent heat to the gas boiled off, and that the neck alone is responsible for
heating the evaporated gas from the boiling temperature to that at which
it discharges into the outer air.

Evaluation of the Effects of Radiation and Conduction
for a Glass Flask.

The writer’s method of analysing the tranquil evaporation-rate of a
vessel holding liquid air or oxygen, so as to apportion the amount of loss
due to the three several causes set forth above, is indicated by the present
example, which consists of a simplification of the general problem in
that the transference of heat down the glass neck, and in opposition
to the upward flow of cold gaseous oxygen, must have been altogether
negligible.

Dewar filled a glass vacuum flask with liquid oxygen (boiling-point,
— 185° C.) and measured its evaporation rate when the flask was immersed
in liquids maintained at different temperatures, with the results stated in
Table I.* At that time (1893) the vacuum was obtained by washing out

* Sir James Dewar, “Liquid Atmospheric Air,” Proc. Roy. Inst., xiv (1893), p. 1.

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

the space between the inner and outer vessels with mercury vapour, and
then exhausting. Some condensation of the residual vapour took place
when liquid oxygen was introduced, causing the formation of a mercury
mirror on the surface of the inner vessel.

Table I. — Glass Flask : Evaporation Losses at Different External

Temperatures.

Temperature of
Outer Vessel.

Absolute
Temperature of
Outer Vessel.

Absolute
Temperature of
Inner Vessel.

6. 2-

Evaporation, c.cs.
of Gas per minute.
L.

-115° C.

156°

91°

60

- 78° C.

195°

91°

120

+ 6° C.

279°

91°

300

+ 65° C.

338°

91°

600

Neck-loss being inconsiderable, the total evaporation loss, L, is the sum
of the losses due to radiation and conduction across the vacuum ; or, from
equations (1) and (2): —

L==Ct(014 — ^24)'k^(^l — $2) T d2 ■ * • (3)

The values of the table are in reasonable agreement with the equation : —

L = 3-O1(01<-02^)]O-8+O-O41(01-02)x/§H:02 . • (4)

The first term on the right-hand side of the equation expresses the loss
due to radiation, and the second that due to conduction. At 15° C. radiation
was responsible for the evaporation of 236 c.cs., and conduction across the
vacuum for 138 c.cs. of gas per minute. Had the flask held liquid hydrogen
instead of liquid oxygen, the losses at an external temperature of 15° C.
would have been 238 c.cs. and 187 c.cs. per minute respectively.

Estimation of the Three Causes of Evaporation Loss for
a Small Metal Flask.

The vessel is illustrated in fig. 2. It is a vaporiser flask, i.e. one whose
function it is, by the aid of certain fittings, to evaporate liquid air at set
rates. The fittings are not shown ; they were not attached during these
tests. The capacity of the flask is 3 litres (about 7 lbs.) ; it is made of
gilding metal (95 per cent, copper ; 5 per cent, tin), and the inner neck, C,
is of cupronickel, an alloy having one-seventh the conductivity of copper.

1920-21.] Evaporation of Liquid Air in Vacuum Flasks. 103

The charcoal (plumstone) is in this instance held in a copper tube, F, passing
through the inner globe, the ends of the tube being covered with gauzes.
The spheres are respectively 8§ ins. and 7-J ins. in diameter, and their
surfaces are 220 and 177 sq. ins. or 1419 and 1152 sq. cms. in area. The
neck is unusually short and wide in comparison to the size of the
bottle, being 3J ins. long, of which only 2f ins. (6 cms.) are surrounded
by vacuum. The bore of the neck is f- in. and the metal 0*024 in. in
thickness; there is 0047 sq. in. or 0*303 sq. cm. of metal in a cross-section
of the tube.

Before any of the following observations were made, the flask held
liquid air for twelve hours It was never allowed to boil empty during the
fortnight over which the test extended. The same weight of liquid air
(5 lbs.) was put in, and about 2 lbs. of air were allowed to evaporate on
each “ run.” The exact losses were ascertained by weighing. The lowest
of the external temperatures recorded below was obtained by standing the
flask in a cellar, and the others by immersing it, up to the base of the neck-
screw, in a water-bath kept at constant temperature. The average
composition of the liquid air was 50 per cent, oxygen, 50 per cent, nitrogen,
and was found from samples of the liquid drawn from the flask at the
beginning and end of a “run.” This mixture boils at —191° C. The
ascertained losses at different external temperatures are given in Table II.

Temperature measurements of the air passing up the neck were made
during the first few tests in order to find out if neck-loss was serious. They
showed that, (a) with the short neck in question, this source of loss could
not be neglected, and ( b ) the neck -loss was proportionately less important
as the outside temperature rose.

Table II. — Metal Flask : Evaporation Losses at Different External

Temperatures.

Period of Test.
Hours.

i

Temperature of
Outer Globe.

Absolute
Temperature,
Outer Globe, j

0i.

Absolute
Temperature,
Inner Globe.
02.

Evaporation
Loss, grams
per hour.

(a) 21 )

( b ) 161 (

(c) 14 A

10° C.

283°

82°

42*5

(d) 111)

(a) 131 1

(b) 131 }
13

44° C.

317°

82°

l

61*3

70° C.

343°

82°

72-0

91

100° c.

373°

82°

97*6

104

Proceedings of the Royal Society of Edinburgh. [Sess.

To enable neck-loss to be evaluated independently of the other modes
of heat- transfer, an inner tube of cupronickel of the same length as the
neck was slipped inside the latter, and the evaporation rates were again
determined at the selected temperatures.* By inserting this extra tube,
the sectional area was increased from 0*303 sq. cm. to 0*856 sq. cm. of
metal. The enhanced rates of evaporation resulting therefrom are set
forth in Table III.

Table III. — Metal Flask : Evaporation Losses when Additional Tube

WAS INSERTED IN NECK.

Period of Test.
Hours.

Absolute
Temperature of
Outer Globe.

0i.

Absolute
Temperature of
Inner Globe.
02.

Evaporation Loss,
grams per hour.

14

283°

82°

62-5

10

317°

82°

89-4

8±

343°

82°

99*7

j 7

373°

82°

124T

It will be observed that when the . outside temperature was 10° C.
(283° abs.) the extra tube added 20 grams per hour to the rate of
evaporation. By simple proportion, the neck-loss at this temperature when
the additional tube was absent was 11 grams per hour. The equivalent
losses at the other stated temperatures (Table IY) were obtained in the
same manner.

To make sure that the flask was not deteriorating under the treatment
it was receiving, frequent check determinations were made of the normal
evaporation rate at 10° C. There was no sign of deterioration.

Table IY. — Metal Flask : Neck Losses Calculated from Foregoing Tables.

Absolute

Temperature,

Outer

Globe.

^1-

Increase of Evaporation
due to insertion of
Extra Tube, 0-553 sq. cm.
section ; grams per hour.

Evaporation per
sq. cm. of Neck
Section ; grams
per hour.

Actual
Neck-Loss,
grams per
hour.

283°

20*0

36-2

11-0

285° (25° C.)

11-9 t

317°

28 T

50-9

15*4

343°

27-7

50T

15-2

373°

26*5

48-0

14-6

t Interpolated.

* This method of determining neck-loss is described in “ Grundlagen zum Bau von
Transportgefassen fur verfliissigte Gase,” by F. Banneitz, G. Rhein, and B. Kurze, Annalen
der Physik, vol. lxi (1920), p. 113.

1920-21.] Evaporation of Liquid Air in Vacuum Flasks. 105

The last table shows that as 01 increased, the neck-loss rose to a
maximum and then fell. The fall was due to the fact that the stream of
cold air passing up the neck increased at a more rapid rate than did the
passage of heat down the metal of the neck.

By subtracting the ascertained neck-losses (Table IV) from the total
losses (Table II) the . rates of evaporation (L) due to radiation plus con-
duction across the vacuum were obtained (Table V) : —

Table V. — Metal Flask : Losses due to Conduction plus Radiation across
the Vacuum ; Neck-Losses Eliminated.

Absolute Temperature,
Outer Globe.
dv

Absolute Temperature,
Inner Globe.

0o-

Radiation, plus Con-
duction, grams per hour.
L.

283°

82°

3L5

317°

82°

45*9

343°

82°

56-8

373°

82°

83-0

With these values equation (3) takes the form : —

L = 8,228(d14 — (924)10 ~9 + 0*00284(0! — 02) J^T~02 • • (5)

Since, as before, the first term of the right-hand side of this equation
determines radiation and the second term determines conduction, the
complete analysis of the loss by evaporation is now possible. It is given
in Table VI, the values for neck-conduction being copied from Table IV.
The degree of agreement between the results derived from equation (5)
and those obtained by experiment may be gathered by comparing the last
columns of Tables II and VI.

Table VI. — Metal Flask : Losses due to Conduction, Radiation and Neck,

Severally Stated.

Temperature,
Outer Globe.

Conduction
across Vacuum,
grams per hour.

Radiation,
grams per
hour.

Neck Conduction,
grams per hour.

Total Loss,
grams per
hour.

10° C.

10-9

20-6

11-0

42 5

15°

11-3

22T

11-9

45-3

44°

13*3

32 5

15-4

61-2

70°

15-3

44*5

15-2

75*0

100°

17-6

62-4

14-6

94-6

The radiation loss at ordinary external temperatures is thus, in this
flask, about twice that due to conduction of heat across the vacuous space.

106

Proceedings of the Royal Society of Edinburgh. [Sess.

Pressure in the Vacuum Space of the 3-Litre Flask, and
Emissiyity of the Metal Surfaces.

The results stated in Table VI allow the emissivity of the reflecting
surfaces of the flask and the degree of tenuity of the vacuum to be
obtained.

Before emissivity can be calculated it is necessary to inquire into the
manner of heat-exchange, by radiation, of two reflecting surfaces facing
each other. The following demonstration is due to J. A. Harker : —

Let the emissivity of either of the two similar surfaces be E. Suppose
E units of heat to be emitted by the hotter surface ; of these E2 will be
absorbed and E(1 — E) will be reflected by the second or cooler surface.
The first surface will then reflect E(1 — E)2 units, of which the second
surface will absorb E2(l — E)2. Proceeding thus, it appears that when the
hotter surface emits E units the cooler surface gains an amount which is
the sum of an infinite G.P. whose first term is E2 and whose common ratio

is (1 — E)2, and that summation is

E

2 - E'

Applying Barker’s result to Stefan’s Law ; taking the constant of that
law as L385 x 1CT12 (calorie units) ; taking the latent heat of a half-and-half
mixture of liquid nitrogen and liquid oxygen as 502 cals, per grm. ; and
making use of the dimensions of the flask, the emissivity of the gilding-
metal surfaces was found to be O’OSO. That for pure copper polished to the
highest degree is 0016. The fact that the makers of the flask have only
succeeded in getting an emissivity amounting to thrice that of copper is
important. In studying to reduce the tranquil evaporation rate in these
particular flasks it is evidently on the radiation loss that most attention
should be focussed. A small increase upon the value for the emissivity of
copper might have been expected owing to the gilding metal containing
tin, and a further slight increase is no doubt due to the smear of solder
running equatorially round the inner sphere ; but the main reason for the
enhanced radiation is probably that water vapour condensed on the inner
sphere and spoilt the surface. It is a most difficult matter, with the
method of evacuation used at present for soft-soldered metal flasks, to rid
the charcoal and vacuum space entirely of water vapour.

With pressures as low as those in the vacuum spaces of liquid-air
bottles, the heat-transfer by conduction across such a space is proportional
to the difference of temperature, (dx — d2)> to the pressure, y>, and to the area
of the surface, A, and is independent of the distance.

That is to say : —

Heat transferred by conduction across the vacuum = c(61 — 02)p A . (6)

1920-21.] Evaporation of Liquid Air in Vacuum Flasks. 107

It is also known, when p is measured in mms. of mercury and A in
sq. cms., that c takes a value for air of approximately 2 x 10~5 at 30° C.
To apply equation (6), this figure has first to be adjusted to the average
temperature of 0’5 ( 9 3 +d2) ; Table VI has to be consulted for the conduction-
loss at any given value of 61 ; and the latent heat of the liquid mixture in
the flask and the dimensions of the flask have to be taken into account.
The pressure in the vacuum space, p, can then be computed. It was found
in this case to be 0'00038 mm. mercury. Considering that the flask had
been evacuated twenty months when the tests were made, this degree of
tenuity may be regarded as satisfactory.

Effect of Surrounding the 3-Litre Flask by an Insulating

Medium.

As radiation proved to be the most important cause of evaporation, and
as, in radiation between two given surfaces, the temperature of the hotter
surface is the all-important factor, it appeared probable that evaporation
would be appreciably reduced by insulating the flask. The neck was
extended by soldering to it a length of brass tube, and the whole of the
flask, excepting a short part of that tube, was encased in slag-wool in a
sheet-metal canister. The immediate effect was an increase in the rate of
evaporation ; but after the slag- wool had been given time to cool down, its
influence became beneficial. Eventually the rate of evaporation settled to
a value thafi was 82*5 per cent, of the rate given at the same external
temperature (8° C.), when the flask was uninsulated. The increased bulk
and clumsiness of the insulated flask outweighed, from the practical point
of view, any advantage gained.

The Neck-Loss of Liquid- Air Containers.

Measurements were made to ascertain the temperature-gradients along
the necks of four containers for the purpose of finding whether the
relatively great length of the necks (see fig. 1) was necessary. Tempera-
tures were taken by means of a Foster pyrometer designed for low-
temperature observation. The wires of the thermo-element were 1*5 mm.
in diameter. The thermometric scale of the galvanometer was tested at
room temperature, and at that of boiling liquid air, to ascertain the
proportional correction to apply to readings. In taking a reading the
thermo-junction was lowered to the desired point in the neck and allowed
to stay there until the galvanometer needle became stationary. Inasmuch
as the thermo-couple was in the up-flowing current of cold air, and not

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

necessarily in effectual contact with the neck-tube at the point, the
temperatures obtained were not strictly those of the metal ; the difference,
however, was probably not more than a few degrees, and was greatest
where it mattered least — namely, near the mouths of the flasks.

The results are set forth graphically in fig. 3.

Three of the bottles were 50-lb. containers of dimensions substantially
those indicated by fig. 1. The fourth was a German-built vessel — the
largest vacuum flask in the country — capable of holding over 300 lbs. of
liquid air.

The first container examined (see curve labelled “ German 50-lbs.,” fig. 3)

TEMPERATURE IN CONTAINER NECKS

was a brass vessel built and evacuated
in Germany before the war. After many
years of continuous service at the New-
castle mine rescue station its vacuum
was showing signs of breakdown ; its
evaporation rate at the time of the test
was 1*85 litres of gas per minute at
18° C., which is equivalent to a daily
loss of over 7 lbs. The top of the
outer neck was thickly coated with ice.
The inner neck was of German silver,
f-in. bore, the thickness of the metal
being 0 02 in. As fig. 3 indicates, the
neck enters the vacuum space 3T9-g- ins.
from the mouth of the flask. The
temperature T7-g- in. below that point was
as low as — 172° C., and at all parts
below 4^ ins. from that point the temperature was the same as that
of the liquid in the flask. Under the conditions then obtaining, therefore,
the loss due to neck-conduction was nil, and if the neck had been shorter
by 5 ins. it would still have been nil.

The second and third containers examined were made in this country,
and were in satisfactory condition. They were of copper, with German-
silver necks 13^- ins. long and J-in. bore. Their rates of gaseous discharge
(measured at 16° C.) were respectively 1T5 and T03 litres per minute at the
time of the tests. The curve labelled “ L. 12 and L. 13,” fig. 3, expressed the
fall of temperature down the neck for both these flasks. The temperatures
at the bottom of the necks were, in these cases, appreciably above the
temperature of the liquid, a fact which seems to indicate that the evaporated
gas gained a little heat from the upper part of the inner globe before it

1920-21.] Evaporation of Liquid Air in Vacuum Flasks. 109

reached the neck in its upward path. With these flasks the gradient near
the base of the neck, though slow, was not zero ; a certain amount of heat,
therefore, reached the inner sphere by the neck. The graph indicates,
however, that the transference of heat due to this cause was here equivalent
to that which would have been yielded by a neck of the same sectional
dimensions about 64 ins. long in which the gradient was uniform from
top to bottom.

The fourth container, as already stated, was a very large German vessel ;
at the time of testing, it was found to be discharging gas at the rate of 3 *3
litres per minute, measured at 18° C. It was constructed of brass, with a
German-silver neck 24f ins. long and xV-in. bore. The thickness of the
metal of the neck could not be determined ; the plug (E, fig. 1 ) probably
extended to a depth of about 3-J ins. from the mouth of the bottle. The
measurements (see fig. 3, curve marked “ German 300-lbs.”) show that the
passage of heat to the liquid via the neck was zero, and that the rate of
evaporation would not have been affected in the least had the neck been
half the length.

In general, the results indicate that container necks may be con-
siderably shortened, or both shortened and thickened, without appreciably
increasing the rate of loss of the flasks. Such an alteration in construction
will strengthen the flask and save weight, and, while preserving sufficient
flexibility in the neck to allow of the spheres touching during the act of
pouring, the excess loss during transportation — which is principally due
to the continual bumping together of the cold and hot globes — will
be lessened. Underground transport (a matter that the present writer
has especially in view) will be facilitated by the reduced height of
the bottle.

Results obtained with Short-necked Containers.

Believing at that time that container necks could be shortened and
strengthened without any serious effect upon the evaporation rate, the
writer designed, in 1918, a 50-lb. container of which twelve were made and
ten proved sound. Though there were in these bottles a number of
variations upon the standard design illustrated by fig. 1, only two of
them could have any influence upon the rate of evaporation. The first of
these — namely, the provision of a loose, insulated cap to fit over the mouth
of the bottle — was found to have only a slight effect ; the cap, when in place,
only reduced the loss by a few ounces per diem, a fact which itself
demonstrated the relatively small heat-inflow by the neck. The second
variation was in the size of the neck, which in each of these special

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

containers was of cupronickel (an alloy having about thrice the con-
ductivity of German silver;; the bore was J in., the thickness of the metal
XV in., and the length 9J ins. Had it been possible to disregard the
influence of the up-flowing stream of cold air along the neck— that is to
say, had neck-loss been merely a question of the conductivity, sectional area,
and length of the tube for a given temperature difference — the neck-loss
of each of these modified containers would have been 17 5 times that of
the German 50-lbs. container referred to above. Actually the rates of
evaporation of these more robust flasks showed little if any increase upon
those of an equal number of containers of the usual design, selected at
random. Their daily evaporation losses proved to be respectively 3*43,
3-75, 4 00, 2*75, 3*31, 3*31, 3*62, 3*69, 3*75, and 4*00 lbs.

Acknowledgment is due to Messrs J. Mallinson, B.Sc., W. Cooper, M.A.,
B.Sc., and J. J. Brodie, Government research workers, for their help in the
experiments here discussed. In the tests upon the 3-litre flask, weighings
and temperature observations had to be taken at all hours of the night and
day for a fortnight.

Summary.

(1) J. A. Harker and his co-workers having shown that of all the
possible causes of heat-inflow to liquid air in a vacuum flask only three,
viz. radiation, conduction across the vacuum space, and conduction along
the neck of the flask, are of importance, the writer illustrates by two
instances an experimental method enabling these sources of heat-transfer
to be separately assessed.

(2) In the two selected instances radiation proves to be the main
method of heat-transfer.

(3) In the second example (a 3-litre metal flask) the analysis is carried
further, and the emissivity of the surfaces and pressure in the vacuous
space are determined. The reasons for the relatively high emissivity are
discussed.

(4) Pyrometer measurements in the necks of long-necked, large metal
storage flasks (containers) show the loss due to neck-conduction to be
either zero or entirely negligible. The results indicate that the necks of
such vessels may be shortened with advantage.

(5) The tranquil evaporation rates are given of ten metal containers
having relatively short, stout necks, in proof of the foregoing conclusion.

(Issued separately June 20, 1921.)

1920-21.] A Continuant of Cayley’s of the Year 1874.

Ill

XI. — Note on a Continuant of Cayleys of the Year 1874.

By Sir Thomas Muir, F.R.S.

(MS. received March 8, 1921. Read March 21, 1921.)

(1) In a ‘‘Note sur une formule d’integration indefinie” of the year 1874,*
Cayley has occasion to use a determinant of a very peculiar structure,
whose value when of the (^ + l)th order is

{[a]#2 * + [&]z/2}n,

[a]r in the development of this standing for

a(a— 1) . . . . ( a — r+ 1).

The first three instances are

1 (a— \)x— by

2y (a - l)(x2 Pxy)

V 2

1

y

ax — by
a(x 2 + xy)

= ax 2 + by2,

1

(a + \ )x— (b - 1 )y
a(x2 + xy)

= a(a — l)#4 + 2 abx2y2 + b(b— l)y\

1 ( a—2)x—by 1

3 y (a—2)(x2 + xy) ax-(b—\)y 2

3 y2 . (a - \){x2 + xy) (a + 2)x - (b - 2)y

I yB . . a(x2 + xy)

= a(a-l)(a-2)xG + 3a(a-l)bxY + 3ab(b-l)x2y 4 + b(b - l)(b - 2)y\

where, it is as well to note, the coefficients of x2-\ -xy in the main diagonal
increase by 1 at each step, and the coefficients of x in the adjacent
minor diagonal increase by 2. Viewed as an equivalent for a power of
\_a\x1 + [b~]y2 the form of the determinant is far from attractive, its order
being higher than seems natural, and there being nothing in it to show
that it is unaltered by the change of x into — x, of y into — y, or by the
simultaneous interchange of a with b and x with y.

(2) Resembling it, but more pleasing in form, is another determinant,
also noted by Cayley the first three instances of which are

* Comptes rendus . . . Acad, des Sci. (Paris), lxxviii, pp. 1624-1629 : or Coll. Math .
Papers, ix, pp. 500-503.

t The reference for this I cannot at present find.

112

Proceedings of the Boyal Society of Edinburgh. [Sess.

j ( a - \)x + by 1

\ (a - l)(x2 - xy) (a + l)x + (b — l)y

(cl — 2)x + by 1

(a-2)(x2-xy) ax + (b-l)y 2

( a-l)(x2-xy ) (a + 2)x + (b - 2)y

{[«>+[%} 2

{[a]x + [b]yY

(i a—3)x + by 1

(a-3)(x?-xy) (a — \)x + (b— \)y 2

. (a-2)(x2-xy) (a + l)x + (b — 2)y

(a — l)(x2 — xy)

= {[a> + [%}4.

(a + 3 )x + (b — 3)y

Here the determinant is a pure continuant, and its order seems natural,
so that the only one of our critical queries remaining is that in regard
to the interchange of a , x with b , y.

(3) Writing x 2 for x and y 2 for y in the second series of deter-
minants we obtain equivalents for the determinants of the first series,
for example,

1

(i a - l)a? — by

1

2 y

(a- 1 )(x2 + xy)

(cl + \)x — (b — 1)?/

=

y 2

a(x 2 + xy)

(a- \)x2 + by2 1

(a - l)(a?4 - x2y2) (a + l)x2 + (b - l)y2 }

so that we have two different determinant expressions for

{[< <x\x2 + [b]y2}n ,

and a not very simple-looking problem facing us in transformation.

(4) Further, the member of the second series with the sign of y
changed is the cofactor of the element yn in the (?i+l)th member of the
first series ; and, following this up, we obtain the curious expansion-
theorem

(-1 )n{[a]x2 + [b\y2}n = yn{[a\x-[b]y}n

- (w)1yn_1{[a]aJ - \p\y}n~l . a(x2 + xy)

+ 0)2; yw_2{[a> - [%}w“2 • [a\2(x2 + xy)2

- (n)^yn~^{[a\x - [&]y}”~3 . [af(x2 + xy)3

(5) Before referring further to these forms of Cayley’s it is desired
to draw attention to a new form, which, besides being interesting in itself,
adds considerably to the interest of the others. It arises as follows: —
Putting

j31 for ax + by and 7rl for \a\x + \b]yi
/3 2 for ax2 + by2 2!tt2 for { [ci\x + [&]y}' 2,

jS8 for ax^ + by 3 3!tt3 for {[cl]x + [5]?/}3,

113

1920-21.] A Continuant of Cayley’s of the Year 1874.
we find that

fti ~ *1 - 0
ft 2 _ ftl^l + 27T2 = 0

ft 3 ~ ft 2^1 + ftl^ ~ 3?r3 = 0

fti ~ fts77! + ft 2^ 2 ~ ftl^S + 4tt4 = 0

and on solving for the 7r’s there is readily obtained

whence

02 ftl 2 •

A P2 ftl 3
A ft 3 A A

{[>> + [%}*•=

ax + fyy 1

ax2 + by 2 ax + by 2

ax3 + by 3 ax2 + by 2 ax + by 3
ax4 + by 4 ax3 -f 6?/3 ax2 + &?/2 ax + by

T

— the new result referred to.

(6) The most interesting point about this is that the relation on which
it depends,

ftr — ftr—i^i + ftr~27r2 ~ • • • + ( - 1 )rr7rr = 0,

is exactly Newton’s relation between the s’s and the cs of a number of
quantities, that is to say, where sr is the sum of the rth powers of the
quantities and cr the sum of the rth combinations of them.

(7) Turning now to Cayley’s second form we shall first show how there
may be derived from it a better, especially as regards the interchange of
a, as with b ,y. Using the fact that any factor of an element of a con-
tinuant may be removed and attached to the conjugate element, we obtain
in the case of the fourth order

(a -3)x-\-by x

(a-3)(x — ■*/) (a— l)x + (b - \)y 2x

. (a — 2)(x - y) (a+ l)x+ (Z> - 2)y 3x

(a - l)(x - y) (a + 3)x + (b — 3)y ,

which for shortness’ sake we may denote by

K4(a — 3 , x , b,y),

the a — 3 under the functional symbol being written instead of a to recall
the element in the (1 , l)th place. If in this we diminish the second row

by the first, the third by the new second, and so on, we obtain
VOL. XLI.

8

114 Proceedings of the Koyal Society of Edinburgh. [Sess.

(a - 3)x + by x

(3 -a-b)y (a-2)x + (b-l)y 2x

-(3-a-b)y (3 — a — b)y (a — \)x + (b — 2)y 3x

(3 -a—b)y —(3 — a—b)y (3 — a—b)y ax + (b—3)y ,

where now the diagonal term is invariant to the interchange of a , x with
b , y, and so likewise the coefficient of y in the elements outside the
diagonal. The latter coefficient in the case of the nth order is n—l — (a + b),
and may be conveniently replaced by a single letter.

(8) If we try to simplify the form of § 7 by increasing the first column
by the second, the second by the third, and so on, the diagonal elements
return to their original awkward law of formation, the result being

(a—2)x + by x

(a-2)(x-y) ax + (b-\)y 2x

. (a— \){x-y) (a + 2)x+(b — 2)y 3x

a(x — y ) ax + (b—3)y .

This, however, is not valueless, when we observe that it would be
K4(a— 2 , x,b , y) save for the occurrence of ax in its last element instead
0f Changing therefore ax into (a + 4<)x — 4x, we have the quasi

recurrence-formula

K4(a-3,x,b,y) = K4(a - 2 , x , b , y) - 4zK3(a- 2 , x , b , y),

and generally

Kn(a-n+l,x,b,y) = Kn(ct -n + 2 ,x,b ,y) - nxK^a - n + 2 , x , 6 , y).

As it is only the first of the four variables that changes in it, the
equality may be viewed as giving the increment of Kn due to a receiving
the increment 1.

(9) There is a generalisation of the foregoing which, merely for its
own sake, deserves to be noted in passing. If the n-line continuant
whose diagonals are

b 2b 3b ....

a ct-\-b-\-z cl + 2b + 2z ct-\-3b-\-3z ....

c c + z c + 2z ....

be denoted by

then

H Ja

b b

c z.

„ / b b
Hn ft
\ c z

b b

Hn( a + b J ^ — rcfrHn-, (a-vb
\ c + z zj \

b b
c + z z,

The mode of proof is quite similar to that of § 8.

115

1920-21.] A Continuant of Cayley’s of the Year 1874.

(10) Following on § 8 we now show that the “recurrence-formula” of
{[a]x-\-[b]y}n is the same as the corresponding recurrence-formula found
for the continuant. The increment of the former expression, due to a
becoming a + 1, is

r=n r=n

2(»)r[a+ l]n-rbrxn~ryr - ^(n)r[a]n-rbrxn- y,

r= 0 r- 0

and this

r—n

= 2 (”)<• • {[“ + 1]n_r - [«]B'r} • brxn~ryr

r= 0
r—n

= • (n - r)[a]n~r~1 . brxn~ryr

r-0

r—n

= 2(w " *)»•» • [a]n~r~l • brxn~rif

r= 0

= '^(nx . (n - 1 )r[a]n-r-1brxn~r-1yr

r= 0

= nx . {\a]x + \b]y}n~l,

as desired. The proof, however, for the case where n is 4 would probably
be very little less convincing.

(11) And now looking closer into Cayley’s continuant, and examining
specially the recurrence-formula of it as got by expanding in terms of the
elements of the last column and their complementaries, namely, the formula

Kn+l(a-n,x,b,y) = {{a + n)x+ (b - «)?/}.Kn(a - n,x,b,y) - n(a - l)(x2 - xy) .Kn^a- n,x,h,y),

we see that the algebraical equality which we have got to verify in order
to establish the truth of Cayley’s result is

{[a\x + [6]?/}n+1 = {(a + n)x + (b - n)y}{[a - Y\x + \b~]y}n - n{a - \)(x2 - xy){[a-^x+\b]y}n~1.

This can of course be done, by proving that the coefficient of xr on the left
is identical with the coefficient on the right ; but the doing of it forces on
our attention how complexity has been unnecessarily introduced into the
affair. The evil centres in the fact that each determinant of the series is
not the first primary minor of the next determinant ; or — confining our-
selves to a portion of this — that while the (1 , l)th element of the 1-line
continuant is of necessity ax + by , the corresponding element of the 2-line
continuant is (a— 1 )x + by, of the 3-line continuant (a — 2 )x + by, and so on.

The above algebraical equality is thus an equality connecting

{[a> + [%}n+1, {[a- l]x + [b]y}n, {[a - 2 ]x + [b]y}n~\

whereas what is wanted is an equality connecting

{[a]x + [%}n+1, {[a]x + [b]y}n, {[a]x + [b]y}n~l.

116

Proceedings of the Koyal Society of Edinburgh. [Sess.

(12) This desired equality I have found to be
{[a\x+ \J)]y}n+l — {{a - n)x + {b - n)y}{\a\x + [b]y}n - nxy{a + b - n + l){[«]a? + [b]y}n~1

so that if we put Fn for {[ct]x-\-[b]y}n we have

F ^{ax + by} =0

F2— {(a — V)x + (b— l)?/}F1 + ^(a + 6) =0

F3— { {a — 2 )x + ( b — 2 )y }Fg 4- 2 xy{a -\-b — 1)11 = 0
F4— {(a — S)x+ ( b - 3)//}F3 + 3 xy(a + b— 2)F2 = 0

and thence

{[«> + [%}“ =

ax + by xy . . ...

a + b {a— V)x + (b— l)y 2 xy . . .

a + b — 1 (a- 2)x+ (b— 2)y 3 xy . . .

a + b — 2 {a — 3)« + (6 — 3)y . . .

which, besides being ideally simple in its law of formation, remains
invariable to any and all of the above-mentioned changes in a , x , b , y .

Rondebosch, S.A.,

1 6th February 1921.

{Issued separately August 23, 1921.)

1920-21.] On the Old Red Sandstone Plants.

117

XII. — On the Old Red Sandstone Plants showing Structure, from
the Rhynie Ohert Bed, Aberdeenshire. Part IV. Restora-
tions of the Vascular Cryptogams, and discussion of their
bearing on the General Morphology of the Pteridophyta and
the Origin of the Organisation of Land-Plants. Part V. The
Thallophyta occurring in the Peat Bed; the Succession of
the Plants throughout a Vertical Section of the Bed, and
the Conditions of Accumulation and Preservation of the
Deposit. By Dr R. Kidston, LL.D., D.Sc., F.R.S., and Professor
W. H. Lang, D.Sc., F.R.S.

(Read May 2, 1921. MS. of Part IV received May 2, 1921, and Part V June 28, 1921.)

(Abstract. Papers published in full in Transactions , VoL LII.)

Part IV. — This paper concludes the authors’ account of the Vascular
Cryptogams found in the Rhynie deposit. Restorations of the four plants,
Rhynia Gwynne-Vaughani, R. major , Hornea Lignieri, and Asteroxylon
Mackiei, are given. A few additional features, supplementary to the
descriptions of these plants in the preceding papers of the series, are
described and illustrated. The hemispherical projections of Rhynia
Gwynne-Vaughani are shown to have originated underneath stomata.
A comparison is made between them and certain intumescences in existing
plants. Areas of necrosis and marked wound-reactions of the tissues
around them are described for both species of Rhynia. The apex of a
stem of R. major is figured. For Asteroxylon additional figures are given
of a large rhizome, of the leaf-arrangement and immature structure of the
stem in the region of a shoot-apex, and of the longitudinal markings on
the epidermal cells resembling those found in Rhynia Gwynne-Vaughani.
The discussion summarises the authors’ views on the main bearings of the
facts described in Parts 1-4 on various problems in plant morphology.

Part V. — The Thallophyta occurring in the peat bed ; the succession of
the plants throughout a vertical section of the bed, and the conditions of
accumulation and preservation of the deposit.

In this concluding part of this series of papers the Thallophyta found
in the silicified peat are described. The most abundant are Fungi, repre-
sented by hyphse of the mycelium and vesicles or resting-spores borne on
this. With the exception of one specimen, the hyphse were non-septate and

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

the fungi are regarded as belonging to the Phycomycetes. A number of
form-types are described and illustrated by photographs. Some of the
most distinct of these forms are given specific names in the comprehensive
genus Palceomyces. The species distinguished are Palceomyces Gordoni ,
P. Gordoni var. major , P. Aster oxyli, P. Hornece, P. vestita, P. Simpsoni,
P. agglomerata. The possibility of there being a symbiotic (mycorrhizal)
relation between certain fungi and the Vascular Cryptogams is discussed ;
there is no conclusive evidence in favour of this, but the question is left to
some extent open. The majority of the fungi in the Rhynie peat were
certainly living as saprophytes.

Bacteria were doubtless present in abundance, but are difficult to
distinguish in the granular matrix. The most remarkable representative
of the Schizophyta is a filamentous organism with the small protoplasts
preserved. It is named Archceothrix oscillator if or mis and is compared
with Beggiatoa and Oscillatoria among existing plants.

Scattered remains of a remarkable Alga, the vegetative structure of
which presents a number of resemblances to existing Characeee, are
described under the name Algites ( Palceonitella ) Granii. Two frag-
ments belonging to an organism with the characteristic structure of
Nematophyton are described as N. Taiti. The occurrence of this plant
in such a deposit is noteworthy, and the small specimens are of importance
in showing the structure of the peripheral region that has not been
preserved in specimens previously described.

The succession of the plants throughout a section of the Chert Bed as
exposed in situ is followed, and the conditions of formation of the Rhynie
deposit discussed. On grounds mainly of resemblances presented by
Asteroxylon to Thursophyton ( Lycopodites ) Milleri, the view is expressed
that the Rhynie Chert band is probably of Middle Old Red Sandstone age.

(. Issued separately August 23, 1921.)

1920-21.] The Adsorption of Gas under Pressure.

119

XIII. — The Adsorption of Gas under Pressure. By Henry Briggs,
D.Sc., Ph.D., A.R.S.M., and William Cooper, M.A., B.Sc.

(MS. received June 15, 1921. Read July 4, 1921.)

I. Introduction.

In 1917 Messrs F. C. Short, B.Sc., and F. W. Moore, of Walsall, applied for
a patent for a method of storing gas, under compression, in cylinders or
containers filled with charcoal which had been impregnated with a metal
(e.g. iron, nickel, palladium) in a very fine state of division. The immediate
intention of the inventors was to provide a compact method of storage of
coal-gas serving as fuel for internal combustion engines. They realised
that by filling a cylinder with impregnated charcoal its gas-capacity would
be augmented. Independently, in 1919, one of us began experiments to
ascertain if it were feasible to increase the capacity of a nitrogen cylinder,
without increasing the pressure, by loading the cylinder with an un-
impregnated activated charcoal before compressing the gas into it, and
the results given below indicate that such an increase is in some degree
possible. It is unfortunate that experiments with the gas in which we
were principally interested, namely, oxygen, had to be limited to colloidal
silica, this being the only non-inflammable adsorbent available ; for had
oxygen been compressed into charcoal there would have been grave risk of
explosion. We have recently learnt that similar experiments have been
carried out on coal by Mr J. I. Graham at the Doncaster Coalowners’
Research Laboratory, though at the time of writing his results have not
been published. The only published investigation known to us on the
effect upon gaseous adsorption of pressures higher than atmospheric
is that of Sir James Dewar,* who ascertained the volume of hydrogen
taken in by a mass of 6’7 grams of cocoanut charcoal at — 185° C. He
found that the charcoal adsorbed a volume which increased from 620 c.c.
at atmospheric pressure to 1050 c.c. at 10 atmospheres, and that between
10 and 25 atmospheres no further gas was taken up.

The use of a porous medium, such as kieselguhr or asbestos wool, in
acetylene cylinders is well known. Its function is to absorb the acetone
which, in those cylinders, is used to dissolve the gas. The solution of
acetylene in acetone is, however, a phenomenon of an entirely different
kind to the adsorption of, say, nitrogen by charcoal.

* “ Studies on Charcoal and Liquid Air,” Proc. Roy. Inst ., xviii (1906), p. 433.

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

II. Method of Experiment.

Measurements were carried out at 15° C. and at pressures sometimes
reaching 100 atmospheres. The gases mainly used were nitrogen,
hydrogen, and oxygen ; a few special tests were carried out with firedamp
and carbon dioxide. The nitrogen and oxygen employed were the com-
mercial gases supplied by the British Oxygen Company; they usually
contained about 2 per cent, of impurity. Hydrogen and, on some occa-
sions, C02 were made in the laboratory. The firedamp was obtained in
compressed form from South Wales, and contained about 98 per cent. CH4.
Tests were carried out with (a) activated cocoanut charcoal, ( b ) activated
birch charcoal, (c) German impregnated charcoal, (d) common wood charcoal,
and ( e ) activated colloidal silica made in the laboratory from the hydrogel
by the method described in a paper recently given before the Royal Society,
London.* In addition, a few special tests, dealt with in the next section,
were made upon anthracite.

The method consisted in filling a small steel cylinder with the substance
to be tested, the material being well shaken down within. Before loading
the cylinder the charcoal or silica was dried in thin layers in a gas furnace ;
it was inserted hot. The cylinder was fitted with a gas-cock screwed and
soldered into place. After it had cooled it was charged with dry gas
to the desired pressure, and a sufficient time allowed to elapse to allow the
heat of adsorption to dissipate and the pressure to stabilise. The cylinder
was then provided with a throttle-valve and pressure-gauge and placed in
a water-bath. The volume contained by it was determined by allowing
the gas to flow out very slowly through a meter. After the discharge of
1 litre, or, in some cases, 5 litres of gas, the throttle was closed, and a
pressure-reading taken after stability had again been attained. The opera-
tion was repeated until no more gas was discharged. The pressure-gauges
were tested from time to time against a large gauge which had been
calibrated at the National Physical Laboratory. The meter was tested
against displacement.

III. General Results.

The experimental method described ascertained the volume, at 15° C.,
discharged between any given pressure and atmospheric pressure. When
constructing the graphs it was necessary to add to that volume the amount
of gas retained by the adsorbent at atmospheric pressure and 15° C. This

* H. Briggs, “The Adsorption of Gas by Charcoal, Silica, and other Substances,”
Proc. Roy. Soc., A, 1921 (in course of publication).

121

1920-21.] The Adsorption of Gas under Pressure.

additional quantity was separately determined for nitrogen and cocoanut
charcoal and nitrogen and silica by methods which have previously been
described (Briggs, loc. cit.). For each of the other gases and substances
employed the addition in question was made by extrapolation from the
graph itself.

Fig. 1 records the results obtained with activated cocoanut charcoal,
which, of all the substances tried, gave the greatest adsorption under
pressure. Curves A and B respectively indicate for various absolute

Fig. 1.

A, Adsorption isotherm for nitrogen.

B, Adsorption isotherm for hydrogen.

C, Adsorption isotherm for nitrogen with damp charcoal.

D, Simple compression according to Boyle’s law.

E , Simple compression for hydrogen.

pressures (abscissae) the total volumes (ordinates) of nitrogen and hydrogen
contained by a gross volume * of 1 litre of charcoal. Gas volumes are
expressed at N.P. and 15° C. To show the great influence of damp, a test
was carried out on nitrogen, using cocoanut charcoal which had been for
many months exposed to the air and which was found to hold 25 per cent,
by weight of moisture. The results of that experiment are set forth by
curve G. The straight lines D and E are included for the sake of com-
parison ; the former expresses for 1 litre of open space the pv relation
according to Boyle’s law, and the latter expresses that relation for
hydrogen.

* Gross volume includes the interstitial spaces, or voids, between the granules.

122

Proceedings of the Royal Society of Edinburgh. [Sess.

It is clear from fig. 1 that the gas-capacity of a cylinder intended to
hold nitrogen under compression may be increased by filling the cylinder
with dry cocoanut charcoal. The advantage gained from the charcoal is
especially marked for pressures below 50 atmospheres. When blown off
from 35 atmos. abs. to 1 atmos. abs., for example, a cylinder containing
cocoanut charcoal would discharge 66 per cent, more nitrogen than the
same cylinder containing no adsorbent. Put in another way, the results
indicate that a cylinder of 1 cubic foot water-capacity filled with dry
cocoanut charcoal and charged with nitrogen at 21 atmospheres would hold

Fig. 2.

A , Oxygen in colloidal silica.

B, Nitrogen in common wood charcoal.

C , Nitrogen in birch charcoal.

D, Hydrogen in colloidal silica.

F, Hydrogen in German impregnated charcoal.

F, Nitrogen in German impregnated charcoal.

a total volume of 50 cubic feet of gas, of which 43'5 cubic feet would be
discharged on the pressure being released to atmospheric. Had the cylinder
not held charcoal it would require to have been charged to 44*5 atmos. abs.
to yield the same volume. The increase of available volume could probably
be raised from 66 to about 80 per cent, at 35 atmospheres by ramming the
charcoal forcibly into the cylinder. A similar but smaller difference is
observable for hydrogen (compare curves B and E , fig. 1).

As gaseous adsorption is much improved by cold, it follows that a
cylinder containing charcoal could be charged with a given mass of gas at
low temperature (obtained, say, from a Claude or Linde plant) with a less
expenditure of energy than if charged at ordinary temperature.

The influence of moisture (compare curves A and G, fig. 1) points to the
need for dryness in both adsorbent and gas if this method of gas storage
be adopted.

123

1920-21.] The Adsorption of Gas under Pressure.

Most commercial gas-cylinders are charged to 120 atmospheres; at that
pressure the advantage to be gained by the charcoal is small.

In fig. 2 a number of other pressure-volume isotherms are given, the
ordinates in each case being the volumes (at N.P. and 15° C.) taken up by
1 litre of the granules at 15° C. These, with the exception of B (nitrogen
and common wood charcoal), are straight lines having much the same slope.
The slope, moreover, is not far from 45°, which is that of the pv relation
according to Boyle’s law. In some of the cases illustrated, for example

Fig. 3.

A , Including the gas compressed in the interstitial spaces.

B, Corrected for the gas in the interstitial spaces.

C, Simple compression according to Boyle’s law.

A (oxygen and colloidal silica), the cylinder held slightly more than it
would hold without adsorbent; while in other cases, such as C (nitrogen
and birch charcoal), it held slightly less. In all these instances, then, the
adsorption has been considerable ; in some it obeys Henry’s law, while in
others it departs from that law. Curve A, fig. 3 (colloidal silica and
nitrogen), expresses a relationship differing from Henry’s law ; it is
analysed below.

Tests made with firedamp compressed into anthracite threw fresh light
upon the problem of sudden outbursts of gas in collieries, and that subject
has been dealt with recently by one of us in a paper read before the
Institution of Mining Engineers.* These outbursts, which occasionally

* H. Briggs, “ Characteristics of Sudden Outbursts of Gas in Mines,” Trans. Inst . Min.
Engs ., vol. lxi.

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

happen in this country, are characterised by the almost instantaneous
discharge into the mine workings of thousands, and in some cases millions,
of cubic feet of firedamp, and along with the gas hundreds of tons of coal
are displaced. The coal associated with an outburst is soft, sooty, and
disintegrated. By taking some anthracite ejected at an outburst in South
Wales, drying it, filling it into a gas-cylinder, and pumping in pit
firedamp, it was found that 1 cubic foot of the coal was able to take
up at 6 or 8 atmospheres pressure, and hold in a condition ready for
almost instantaneous release, a quantity of firedamp considerably greater
than could be contained in 1 cubic foot of open space charged with gas
at the same pressure. The sudden outburst of gas constitutes, in fact,
a problem in gaseous adsorption ; the gas is held in the coal in a state
available for discharge when the pressure is released.

IV. Theoretical Considerations.

Dr A. M. Williams has shown by an able theoretical analysis * that the
most probable form for an adsorption isotherm at low concentrations is

logeg) = A0-All; (1)

where p is the absolute pressure and v the mass of gas adsorbed at that
pressure by a given mass of the substance. At present it is convenient to
express v in litres of gas expanded to N.P. and 15° C. A0 and A1 are
coefficients. Williams found the above equation to represent very closely
the connection between v and p as observed by several previous workers
who had experimentally determined that connection for various gases at
pressures below atmospheric. Our own results go to show that the
equation (with one correcting factor) also holds at high pressure for, at
any rate, gases above their critical temperatures, though, at those pressures,
the degree of concentration is considerable.

To enable this matter to be studied, it was necessary to eliminate the
effect of the interstitial spaces between the granules. We had previously
found the interstitial space of cocoanut charcoal (well shaken down) to be
40 per cent., and that of silica to be 43 per cent, of the gross volume (Briggs,
loc. cit.), and these values were used in making the correction in question.
In fig. 3, A is the original curve plotted from the experimental data and
B is the curve resulting after the volumes compressed into the inter-
stitial space had been deducted. Now it will be seen that B has a double
flexure, the gradient first decreasing as pressure rises and then, at the high
* Proc. Roy. Soc. Edin ., xxxix (1918-19), p. 48 ; Proc. Roy. Soc ., A, xcvi (1919), p. 287.

125

1920-21.] The Adsorption of Gas under Pressure.

pressures, slightly increasing again. If the pressure is carried high enough,
this effect is found to be common to all the pressure-volume relations we
have examined, provided the relationship is of the non-linear type. At
15° C. and with the gases concerned the possibility of a change of phase
at the higher pressures is nil, and another explanation has to be sought
for the effect.

The internal gaseous volume of an adsorbent granule is made up partly
of openings of molar dimensions and partly of much larger canals or
capillaries, some of which may be visible under the microscope. With
these gases of low critical temperature, even under pressures of about
100 atmospheres, the adsorbed film cannot occupy the whole of the internal
gaseous volume, some of which must therefore be occupied by gas, not
adsorbed, but approximately obeying Boyle’s law. Thus it appears neces-
sary to modify equation (1) so as to include a term to cover the effect
of compression upon unadsorbed gas existing in the capillaries. Let v be
the volume (expressed at N.P. and 15° C.) taken up by a gross litre of the
granules, the volume compressed in the interstitial spaces not being
included. Let v1 be the volume taken up by true adsorption upon the
solid surfaces, and v2 be the volume contained in the capillaries under
simple compression.

Then from equation (1)

log^-A^V, (2)

and

v = + v2,

but, by Boyle’s law, v2 = kp%, therefore

v = vl + kj) . . . . . (3)

Equation (3) thus expresses the extent of the modification of Williams’
rule needed to take into account the existence, in the granules, of gas
under simple compression.*

The curve for nitrogen in silica (B, fig. 3) was found to agree remark-
ably well with the equations

log* (p) = ~ 092 “ '01552), .... (4)

v = v1 + ‘10p ...... (5)

For cocoanut charcoal with nitrogen the equations are

log, (^) = 2-43 -'045^ (6)

v = v1 + -10p ...... (7)

* Williams lias made use of a similar correction to allow for the volume occupied by
the adsorbed layer, ibid., p. 306.

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

though in this case the agreement is not so good. For hydrogen in
cocoanut charcoal the following equations satisfy the data very exactly : —

log. (|) = 1-92 --076®! (8)

v = vY + *25/> ...... (9)

The argument does not take into account the probable thickening
of the adsorbed layer as the pressure rises; if this effect were allowed
for, k would become a variable depending upon the pressure. With
gases below their critical temperature the effect in question will be
considerable, but for gases such as hydrogen and nitrogen at 15° C.
the proportional influence of such a correction must be small, and it
has been disregarded.

It will be seen (equations (4) to (7)) that the amount of the internal
gaseous volume unoccupied by adsorbed films is, with nitrogen, about
the same for silica and cocoanut charcoal. As the specific attraction
between silica and nitrogen is, according to available evidence, less than
that subsisting between cocoanut charcoal and nitrogen, the thickness
of the adsorbed film will be less with the former than with the latter
substance ; therefore it is probable that the average section of the
internal passages is smaller in our colloidal silica than in the charcoal.
This may in part be due to the absence in the silica of the relatively
very large (microscopic) openings present in charcoal. The higher
value of k in equation (9) points to the conclusion that, with cocoanut
charcoal, the surface film of hydrogen is thinner than that of nitrogen.

The straight-line relationships, exemplified by all but one of the
graphs of fig. 2, should, we think, not be regarded as exceptions to the
general law expressed by equations (2) and (3), but rather as special
cases in which is of negligible influence; for if the term A-^ is
inappreciable, the equations reduce to the straight line

v = p(eA° + k). . . . . (10)

We propose to reserve for the present the consideration of adsorption
under pressure of a gas, such as carbon dioxide, whose critical tempera-
ture is above 15° C. — in this instance the temperature at which the
experiments were carried out. It is sufficient to say that the double
flexure of the curve, referred to above, is much more marked with
such a gas, and, as might be expected, the slope of the curve increases
rapidly as the pressure of liquefaction is approached.

We wish to express our thanks to the Department of Scientific
and Industrial Research for permission to publish this paper.

1920-21.] The Adsorption of Gas under Pressure.

127

Summary.

1. Experiments made at 15° C. with various adsorbents and gases
(chiefly nitrogen and hydrogen) show that a cylinder filled with adsorbent
granules has a capacity for dry gas under a given pressure which is
generally greater than its capacity when containing no adsorbent.
For example, a cylinder charged with nitrogen at 35 atmospheres has
its capacity increased by 66 per cent, by filling it with cocoanut charcoal.

2. Sudden outbursts of firedamp in coal-mines are the result of re-
leasing immense quantities of gas adsorbed under pressure in coal.

3. The logarithmic relation derived by Williams is shown to apply
to the adsorption isotherms of gases above their critical temperature up
to pressures of 100 atmospheres, providing a correction be applied for
the gas in the capillaries which is not adsorbed, but which exists under
simple compression.

(. Issued separately August 23, 1921.)

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

XIV. — Utilisation of Solid Caustic Soda in the Absorption of
Carbon Dioxide. By Elizabeth Gilchrist, M.A., B.Sc., A.I.C.

Communicated by Professor Henry Briggs, D.Sc., Ph.D.

(MS. received June 17, 1921. Read July 4, 1921.)

In the course of research on Mine Rescue Apparatus under the Department
of Scientific and Industrial Research it was found necessary to investigate
the conditions of utilisation of solid caustic soda for absorbing carbon
dioxide, and particularly the effects of variations of temperature and
water vapour upon the reaction.

Though the experiments relate especially to the conditions prevalent
in breathing apparatus, it is believed that they have sufficient general
interest to warrant their description in a separate paper. The tests
were carried out by Mr D. Penman, B.Sc., and the writer, under the
direction of Professor Henry Briggs, and the results are published by
permission of the Research Department.

Preliminary Experiments.

Preliminary comparative experiments were carried out in which air
containing carbon dioxide was passed through U-tubes holding caustic
soda granules. These exploratory tests showed that : —

1. The temperature at which the caustic soda is maintained had a
most important effect on its power of absorption, and that the absorption
fell off almost to zero if that temperature was kept at or below 0° C.

2. The size of particle had a great effect on the absorptive efficiency,
small particles being more effectual than large particles. This result
doubtless follows from the greater area of surface exposed by the small
granules.

3. When the soda particles act efficiently they swell considerably,
and in so doing tend to fill up the interstices between them, thus causing
choking unless measures are taken to prevent it.

Apparatus and Methods.

In view of the results of the preliminary inquiry, it was found to be neces-
sary to carry out all subsequent experiments with granules of caustic soda
which had been sized. The size adopted was that of from J-inch to J-inch
diameter. Thirty grams of granules were employed in each experiment,

1920-21.] Solid Caustic Soda for absorbing Carbon Dioxide. 129

the caustic being weighed out in a weighing-bottle with a variation not
exceeding ±005 gram; the soda was then transferred, immediately before
starting the test, to the apparatus described below, and sealed in. The
air current caused to flow over the caustic granules was made to contain
a uniform 4 per cent, of carbon dioxide ; it thus resembled in composition
the air expired from the lungs of the wearer of a rescue apparatus. Its
rate of flow was 3*5 litres per minute. The supply of air to be purified
was obtained from a Briggs gas-testing tank.*

During any such test as those to be described, the soda becomes
progressively less active as the test proceeds, and towards the end, though
often a considerable percentage of hydrate remains, the caustic has virtu-
ally ceased to extract carbon dioxide from the air. A period of test of
forty minutes was adopted throughout.

A special apparatus was designed for the tests. It consisted of a
strong tin bath (fig. 1) of rectangular shape, supported on wrought-iron
legs high enough to permit of an ordinary gas bunsen being placed under
it. Surrounded by the water in the bath, J, were two air-tight com-
partments, B and E. At one end of the partition separating B and E
was an opening, C, \ inch wide and 2 inches long. The lower compart-
ment, B, was kept either half full of water or empty, as desired, and into
the upper compartment, E, was slipped a tray containing the caustic.
The gas mixture entered the compartment B at the point X ; rose through
the opening C into the upper compartment, and flowed over the surface
of the caustic to an outlet, F, where samples could be taken. The end,
H, of the upper compartment was detachable, and after the tray con-
taining the caustic had been inserted the end was sealed on.

The tray on which the caustic was spread was 11 inches long by 3 inches
wide, and consisted of a tin base on which was fixed wire gauze crimped
to form six Y-shaped troughs. The caustic was spread uniformly over
the surface of the gauze along the troughs. This form of support for
the soda has been found most effectual in rescue apparatus.]* It is to
be noted that all temperatures given are those of the surrounding bath ;
not necessarily of the caustic particles. The caustic, however, rested
on metal, and, as the vessel was entirely of metal, the conduction of
heat was fairly effective. For temperatures between 0° and 100° a bath
of water was used. Below zero a mixture of ice and salt, and above 100°
paraffin wax was employed.

During the experiments samples of the ingoing and outgoing gaseous
* Colliery Guardian, December 15, 1911.

f Second Report , Mine Rescue Apparatus Research Committee , 1920, p. 46.

VOL. XLI. 9

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

Fig.

1920-21.] Solid Caustic Soda for absorbing Carbon Dioxide. 131

mixtures were taken every five minutes and were analysed in a portable
Haldane gas-analysis apparatus.*

Four series of tests were carried out. For the first series the gas
mixture was dried before it entered the caustic soda compartment. In
the second series the gaseous mixture was saturated at room temperature,
12° C., before coming into contact with the caustic; and the third series
was similarly saturated at blood temperature, 37° C. ; while in the fourth
series the mixture was allowed to saturate itself with moisture at the
temperature at which the bath was maintained. In each of the first
three series the weight of moisture carried by the gas was constant
throughout the tests, while in the last it varied in accordance with the
temperature of the test.

I. Gaseous Mixture dried before passing over Caustic Soda.

The 4 per cent, mixture was dried by passing through concentrated
sulphuric acid, and through U-tubes containing calcium chloride; it then
passed over copper sulphate. The absence of a blue tinge in the latter
showed the gas to be dry. It must here be observed that although
precautions were taken to keep the caustic soda dry, doubtless it
contained a proportion of moisture. Commercial caustic soda usually
contains water up to 10 per cent., and in exceptional cases up to 25 per
cent. Analyses were made of the gaseous mixture entering and leaving
the caustic compartment at frequent intervals. Their results enabled an
average to be struck for that period of the percentage of C02 extracted at
each of the temperatures of the tests. When these average extractions
were graphed against temperature, curve A (fig. 2) was obtained. It was
observed, at any given temperature, that the caustic soda became most
effective after a lapse of from ten to twenty minutes, and that after that time
the efficiency of absorption rapidly fell away. The examination of the
material taken from the tray after an experiment showed the granules to be
substantially unaltered in form and to have received only a thin coating of
carbonate. The greater part of each granule was unaltered caustic soda.

II. Gaseous Mixture saturated with Water Vapour at 12° C.

The tests were carried out in the same manner as those just described,
and as a result curve B (fig. 2) was obtained. The efficiency of absorption
is evidently better in this case than in the last. The maximum efficiency
of absorption took place in the circumstances of this test at 70°-90° C.,
where it amounted to a 72 per cent, extraction of the carbon dioxide.

* J. S. Haldane, Methods of Air Analysis , p. 48.

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

Another feature clearly shown by contrasting curves A and B is that while
in the dry condition represented by the former, a temperature over 100° C.
brought about the most marked diminution in efficiency of absorption, such
a temperature in the second series was not so deleterious. In the latter
series, in the circumstances admitting of maximum extraction, the granules

on being taken from the test cartridge were found to have considerably
increased in size and to contain relatively little unused caustic soda.

III. Gaseous Mixture before entering the Caustic Compartment

was saturated at 37° C.

The temperature and hygrometric state of the stream of air and carbon
dioxide were kept under observation. In this series the lower compartment
of the case contained no water. On the results being recorded in graphical
form (curve C, fig. 2), the curve was found considerably to resemble that
of the last series ; at the optimum temperature extraction was again between
70° and 90c C. The maximum extraction was 72 per cent, of the carbon
dioxide. The remarks as to the condition of the caustic soda in the last
series equally apply to this.

IV. Gaseous Mixture saturated at the Temperature at which the

Caustic Soda was maintained.

In each of these experiments the lower compartment E (fig. 1) was half
filled with water, which was then kept at a definite temperature. The
ingoing gaseous mixture flowed over the surface of the water before
entering the caustic compartment. The results of the series are shown in
curve D (fig. 2). The maximum extraction was 65 per cent., and the best

1920-21.] Solid Caustic Soda for absorbing Carbon Dioxide. 133

temperature was 50° C. The maximal extraction in this case being less
than that in the last two cases would indicate that the greater amount of
water held by the ingoing stream of gas in series 4 was detrimental to
absorption. The curve D shows how much efficiency of absorption
depends on the temperature of the containing vessel ; for though the
extraction was 65 per cent, at 50° C., it was only 30 per cent, at 16° C. and
40 per cent, at 90° C.

Discussion of Results.

A conceivable explanation for some part of the difference in efficiency
of absorption is that, owing to variations of temperature and hygrometric
state, the actual rate of flow over the caustic was different in different
experiments. This effect, however, was found to be of negligible moment
by carrying out special tests, in which the same mass of carbon dioxide was
passed over the caustic per second, though contained in air currents which
flowed at greatly different rates. A more serious criticism on the method of
test is that the recorded temperature of the bath surrounding the caustic
compartment was not necessarily the temperature of the caustic granules
themselves. Undoubtedly there would be very considerable local heating,
and the severity of this local heating may be judged when it is stated that
in certain other experiments in which caustic granules were held on
blotting-paper trays the blotting-paper caught fire from the heat of
reaction. The writer has no means of judging of the temperature of
the active surfaces at which the absorption was actually taking place.
The general conduction of heat away from the granules, however, must
have been moderately efficient, owing to the mass of metal with which
they were in contact. It is advisable to state again that the whole set of
experiments was carried out to give information which would be applicable
for rescue apparatus in the cartridges of which the caustic soda is supported
in much the same way as in the experiments. A slight error in the per-
centage of carbon dioxide in the outgoing sample, as given by the results
of the analyses, was due to the condensed moisture in the sampling-bottles
having dissolved some C02 ; but on calculation it was ascertained that this
error was negligible.

Some remarks have already been made as to the appearance of the
caustic soda on removal from the tray. There was a marked differ-
ence in appearance after tests at high, low, and intermediate temperatures.
At the lowest and highest of the temperatures in the series I., II., and III.,
the granules retained much of their original shape ; but at the high tempera-
tures in series IV., where a great deal more moisture was present in the air,

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

the granules coalesced in a sticky state with corresponding reduction in
surface, and therefore in the efficiency of absorption.

In the circumstances giving the best absorption the caustic particles
were found in all cases to have swollen sometimes to three times their
original linear dimensions, and in many cases they were found to be hollovr
inside. This action is of great importance to the designer of mine rescue
apparatus or other appliances in which these granules are used for the
abstraction of carbon dioxide from air. The action appears to be much as
follows : —

A granule begins its active life by taking up a considerable weight of
moisture, and attains a plastic state. The action of carbon dioxide upon
such a body is to coat it with a layer of spongy dry carbonate. The next
effect is a penetration, by capillary attraction, of the soft caustic through
its skin of spongy carbonate and a further attack by the carbon dioxide on
the soda thus brought within its reach. The continuance of such an action
will evidently be to cause the formation of a carbonate shell with a hollow
interior and greatly to increase the apparent bulk of the granule. When
absorption is at its best, this action continues until there is no caustic soda
left behind ; in other cases until a small granule of caustic is left behind,
apparently lying detached inside the shell of carbonate.

Conclusions.

The following conclusions, of value especially to the designer of rescue
apparatus, follow from these tests : —

1. It is evident that too much and too little moisture is detrimental to
the action. The best results are obtained when the proportion of moisture
carried is approximately that carried by air saturated at temperatures
between 60° C. and 90° C.

2. The best results for absorption are obtained when the container is
kept at a temperature of from 60° to 100° C. Provided the moisture
conditions are right, the average proportional absorption is then about 70
per cent., when using the relatively small amount of caustic employed in
the tests. Below and above those temperatures the absorption efficiency
falls off rapidly. Below 10° C. and above 100° C. absorption is extremely
poor. It is worthy of remark that in actual use with rescue apparatus in
France during the war and in certain cold countries it was found by
experience that caustic is inactive at temperatures near freezing-point, and
the practical precaution was taken on cold days of warming the caustic
prior to use by breathing through it.

3. It is evident that measures must be taken to secure good conduction

1920-21.] Solid Caustic Soda for absorbing Carbon Dioxide. 135

of heat, as it is important to keep an equal temperature in all parts. Other-
wise at some parts the action may become violent, with consequent rise of
temperature and stoppage of the reaction, while at others the temperature
may never rise sufficiently high to give the best results.

4. It is important that the particles be of such a size as to give a fair
surface of exposure for absorption. Excessively large particles are for this
reason to be avoided. Provided the conditions as to moisture and tempera-
ture are at their optima, however, there is no need to decrease the size of
the particles unduly in order to increase the surface ; e.g., given such con-
ditions, granules 6 or 7 mm. in diameter will, by the swelling action
described, be entirely or almost entirely used up.

5. The particles must be so spaced as to give sufficient room for swelling.
There should indeed be a greater volume of interstitial space in a canister
fitted for absorption of carbon dioxide than of actual solid caustic soda
itself. A disregard of this requirement leads to the coalescence of the
granules due to swelling, and to the blocking of the air passages. This, in
turn, involves a greatly increased resistance which is highly detrimental
in breathing apparatus, and at the same time decreases the availability of
the caustic to the carbon dioxide.

( Issued separately September 5, 1921.)

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

XV. — On the Criterion for Stable Flow of a Fluid in a Uniform
Channel. By H. Levy, M.A., D.Sc., Assistant-Professor of Mathe-
matics, Imperial College of Science, South Kensington.

(MS. received May 27, 1921. Read June 20, 1921.)

§ 1. The conditions determining the stable flow of a viscous fluid in a
uniform channel and in a uniform circular pipe were investigated experi-
mentally for water by Osborne Reynolds in a searching series of papers.*

For a channel he concluded that so long as the non-dimensional group
U Ijvt where

U = mean velocity in the channel,
l = breadth of the channel,
v — kinematic viscosity of the fluid,

was maintained below a certain value, any slight disturbance imposed on
the steady flow tended to die out, and the steady streaming persisted, but
in the neighbourhood of and above this critical value a condition of
turbulence and eddying set in immediately the steady stream-line motion
was disturbed.

Many theoretical investigations of this problem, having for their object
the mathematical formulation of the conditions determining this critical
state, have been attempted, but no satisfactory analysis has yet been forth-
coming. The mathematical difficulties of a direct attack are so formidable
that simplifications are invariably introduced ; but these, while they may
render the mathematical development amenable to treatment, nevertheless
involve physical assumptions whose interpretation is frequently obscure.
This is amply borne out by the fact that theoretical estimates of the
critical value of U Ijv vary over exceedingly wide ranges. In the present
paper it is proposed to approach this question from a new standpoint.

§ 2. On general grounds of dimensions it is clear that any problem in
the flow of a viscous fluid with given boundary will centre round the
particular value assigned to XJl/v, and the author has indicated how this
fact may be utilised to approach a solution of any such problem in general.f
A full experimental investigation of the question in relation to the critical
flow of air, water, and oil in pipes has been conducted by Stanton and

* Scientific Papers , vol. ii, p. 51 et seq. ; Phil. Trans., 1883.

+ Phil. Mag., xli, April 1921, “ On a Method of Analysis suitable for the Differential
Equations of Mathematical Physics.”

1920-21.] Stable Flow of a Fluid in a Uniform Channel. 137

Pannell,* who have shown that the conclusions arrived at by Osborne
Reynolds as regards water are independent of the state of the fluid — that,
in fact, the critical value of \Jl/v is a universal constant for given geometry
of boundary. From another standpoint, these results have since received
verification in all hydro- and aero-dynamical experiments, where it is found
that the resisting force R of a body of given shape in a viscous fluid of
density p and kinematic viscosity v is always expressible in the form

where l fixes the scale of the body. In effect these experiments may be
regarded as justifying the assumption that the properties of real fluids in
motion should require nothing further for their explanation than the
assumption that the fluid is viscous and dense. It is important in this
connection to note that compressibility plays no part in this question,
and that for the present purpose the air may be justifiably regarded as
inelastic. Examination of the resistance of projectiles indicates that
compression effects do not become apparent until the velocity of sound
is approached, j-

§ 3. Returning to the flow of a fluid in a channel, let it be supposed
that a disturbance is communicated to the fluid, say, by dipping a small
obstacle into the fluid and withdrawing it. For a given shape of obstacle
inserted in any given manner, for a given speed U of the central stream
line of the channel, and for given viscosity and density of the fluid, it is
clear that the vortex distribution immediately resulting from this dis-
turbance will be physically quite determinate. Let the strength of the
vorticity at a geometrically given position be k, then k can only be
dependent on U, l the breadth of the channel, v the kinematic viscosity,
and p the density, and on nothing else.

Hence

K=/(U, Z, V, p).

Now k being an angular velocity distributed over an area has dimensions

XL2.

Assuming

.-. [k] = L2T-1 ; [U] = LT-1 ; [v] = LH-1 ; [p] = ML-3.

* Phil. Trans ., A, 214, pp. 199-224, “ Similarity of Motion, in Relation to the Surface
Friction of Fluids.”

f Rayleigh’s Scientific Papers , vol. v, p. 534 ; Aeronautical Journal , June 1919, “From
Model to Full Scale in Aeronautics,” H. Levy.

138

Proceedings of the Royal Society of Edinburgh. [Sess.

where Ar is a number, and equating the dimensions of each term on the
right to [k], it is easily found that

r = s=l -t ; u = 0.

where r is indeterminable so far. The quantities Ar and r, in fact, must
depend on the shape of the boundaries.

.-. K=vf1(miv) (i)

or

TJZ/k = F(UZ/v) (2)

where the form of the functions depends on the geometry of the problem.

From (1) it follows that for a given value of JJl/v the strength of the
vorticity is directly proportional to the kinematic viscosity. Equation (2)
indicates that the discussion of the stability of flow in a viscous fluid to
a given disturbance, and all the circumstances of the motion generally,
may equally well be centred round the non-dimensional group JJI/k ; that
in fact we may imagine a given disturbance in vorticity, specified by k,
applied to the fluid, and seek to determine the value of JJI/k, which is
critical in the sense that it separates the region of values of this non-
dimensional grouping for which the motion is stable from those for which
the motion is unstable. Having determined this critical value of JJI/k,
how to determine the exact relation (2) from which to evaluate the critical
quantity JJl/v is clearly the next step, and if this can be completely
effected the problem will definitely be solved. For the present I propose
to restrict myself to determining whether such a critical value of JJI/k
exists at all, and if so to evaluating it. It need scarcely be said that the
discussion so far is not limited to the question of flow in a channel,
although that is the case ,we have had in view.

§ 4. It will be presumed that a fluid is moving between and parallel
to the walls of a uniform channel, with the parabolic distribution in
velocity corresponding to the steady motion of a viscous fluid in such a
case, so that in the usual notation

u = JJ(1 - y2/a2) ; v = 0,

where 2a is the breadth of the channel.

Let it be disturbed in such a manner as to give rise to two vortices of
strengths —k and +/c situated at the points (x = 0, y — h), (x = 0, y=—h)
respectively. These may be imagined to have been produced by the
sudden even insertion of a plate of breadth 2 h stemming the fibw
symmetrically about the axis of x. Experiment shows that two vortices

1920-21.] Stable Flow of a Fluid in a Uniform Channel. 139

would immediately be formed at the two edges, of opposite signs, and
from symmetry necessarily of equal strengths. It will be presumed that
the whole disturbance is initially concentrated in these two vortices.

§ 5. Two difficulties immediately present themselves. In the first place,
if the vorticity thus imposed on the fluid be imagined as concentrated at
the two points, the condition that there is no slipping at the boundary, as
will shortly become apparent, is immediately violated. Whether or not this
is a serious deviation from the real physical conditions is not even yet quite
definite. Ample experimental evidence exists to show that for moderately
small speeds — that is to say, for values of U Ijv well below the critical — there
does not exist any appreciable relative motion at the surface between the
body and the moving fluid, and this condition is satisfied by the solution
for steady motion, u — U(1 — y2/a2), which has been presumed. For
velocities in the neighbourhood of and above the critical, however, where
turbulent motion sets in, experimental results are not so conclusive, and
do not appear to provide sufficiently definite evidence beyond the fact that
as the surface is approached the relative velocity does not drop very
rapidly except when a very close approach is made to the surface. It is,
in fact, the extremely short distance from the surface within which all
the fall is to take place that constitutes the real experimental difficulty.
Whether or not the assumption that a small amount of slipping does take
place is a serious cause of discrepancy will, I hope, be discussed in a later
paper, when some of the results of the present discussion will be developed ;
but in any case it will become evident that the slipping that results from
the assumption of concentrated vortices is comparatively small in general,
although in certain circumstances it may be considerable.

§ 6. The second difficulty is of a different nature, and is not vital. A
vortex formed in a viscous fluid will not for long maintain its spin
unimpaired, because of the viscous action of the fluid ; its energy will be
gradually dissipated into heat. A consideration of the rate of decay of a
single vortex, say, along the axis of a circular cylinder filled with a viscous
fluid indicates, in fact, that for a fluid of such small viscosity as water, for
example, or even air, the rate of decay is very small, and that as far as any
consideration of the effects immediately subsequent to the formation of the
vortex is concerned, no serious error will be involved by the assumption
that k remains constant. This may be illustrated in the following manner.

The general equations of motion of a viscous fluid in two dimensions
are known to be

dt „ K

(3)

140

Proceedings of the Royal Society of Edinburgh. [Sess.

where

2£=V2^ = spin .... (4)

using the customary notation. Where the vortex is situated along the axis
of the cylinder, the motion at any point must be purely a function of r,
in which case (3) takes the form

the terms in u and v cancelling out.

Writing £=Ze~a*vt and inserting in (5), assuming that Z is a function
of r only,

d?Z IdZ 2V n /o\

-T~2+-d-+a Z = 0 (6)

drA r dr

This is Bessel’s equation of order zero, the solution which is finite for
r = 0 being J 0(ar).

Hence a solution of (5) is

£=AJ 0(ar)e-^K

If f=0for£ = 0 at r = R, the radius of the cylinder, then J0(aR) = 0,
a transcendental equation determining an infinite series of values of a, Viz.

^? = -7655, 1-7571, 2-746, . . .

7 T

Accordingly we may write for the complete solution of (5)

£=2An'Jo Me-W* (7)

where the coefficients An are to be found by expanding the initial distribu-
tion of £ as a series of Bessel functions, as specified above.

If £ is initially concentrated mostly in the region of r= 0, the first few
terms only of this series will be of consequence, and these decay on
account of the term e~anvt. Now for water i/ = *01 c.g.s. units, and, taking

R = 10 cm., say, a = *76 = *24.

. e— aM __ g--006^

indicating that a relatively considerable time must elapse before £ decays,
as far as this term is concerned. The terms, of course, decay more rapidly
as we proceed further up the series, but they themselves become small.
From the point of view of the present discussion, where we are primarily
concerned with wjiat occurs in an extremely short interval subsequent to
a disturbance to the vortex, it clearly suffices to assume that the strength
of the vortices -f k and — k are sensibly constant.*

* The full justification for this assumption can ultimately only he found by a com-
parison with experiment. The experimental investigation of the rate of decay of eddies is
at present being conducted by the author.

1920-21.] Stable Flow of a Fluid in a Uniform Channel. 141

§ 7. In practice the ideal case where the vortices are formed exactly in
symmetrical positions is, of course, never realised. The question immedi-
ately arises whether, if the exact arrangement is one of equilibrium or
steady motion, it is also one of stability ; or more precisely, under what
conditions is the symmetrical arrangement of two equal and opposite
vortices in a uniform channel along which fluid is moving steadily with
the parabolic distribution in velocity of a viscous fluid across the channel,
one of stability ?

§ 8. Examination of the Stability of the Vortex Pair. — The general
motion in the channel is given by u = U(l — y2/a2). Let the centres of
the two vortices P and Q of strengths —k and -f k respectively be situated
initially at the points (0, a — a) and (0, — a Pa). We may dispense with
the walls and deal with the infinite fluid provided an infinite row of
vortices of equal but alternating strengths +k and — k be placed along
the y- axis at the points whose co-ordinates are given by

+ k; (0, (in ± l)a + a} ; - k ; {0, (in±l)a — a}.

Let P receive small displacements (£, f) and Q (£', f) parallel to the
x and y axes respectively ; then, in virtue of the fact that the walls are rigid
and that the fluid does not leave them, the displacements of the images
are immediately determined.

Regarding the field as a complex plane, the co-ordinates of the system
of vortices now become

+ k ; $+i(in+la, + a- rj), £' + i(in - la + a + rj')}

“->?') J

(8)

— k ; £+i(in + la - a + 77), £' + i(4rc— la

the vortices P and Q corresponding to

£ + i(a — a + f) and £' + i( — a + a + rf) respectively.

If (u, v) and (u' v') are the component velocities of the vortices P and
Q, they will be composed of two types of terms :

(a) the contribution in velocity due to direct effect of the infinite row
of vortices ;

(, b ) the general translational motion in the channel.

Consider first the effect of (a). The contribution to —u + iv is

1

'27rT^{£ + i(a- a + y)} ~ {£ + i(in+la + a-r))}

-{- etc.

(9)

four terms in all, in each of which the first member in double brackets in
the denominator is the same, while the second member is successively each
of the four terms in (8), with the appropriate sign for K in front of the 2.
Expanding each typical term and neglecting quantities of higher order

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

than the first in the small quantities £ and t], it is easily found that (9)
takes the form

IK

+?!,£? 1 ++++) + +? + +) + 1

lai ^^2ai{2n—\) j 4a2('2/4 — l^2 *-*2i(2

4a2(2/4 - l)2

i(2na + a)

+ 2/2(2wa + a)2 2 o,v.

+ 00

1

2(2/ia + a)

i(2n- la + a )

“ 4(2/4- la + a)2

4K

27T

r +°o

2m

2/(/4a + a)

+ (+n ++?++> + « ■ - n + + - v>

^ 4a2(2»i- l)2 ^

4(2/4 - la + a)2
+ 00

+ y P?

9/Qoo/y _i_ „ \2

(10)

2(2 na + a)5

since the first two terms vanish and the fourth and sixth combine together

c>

into one simple series.

In the same way the contribution to —u' + iv' due to (a) is

+ « l

li<

27r^{£' + ^( -a + a + r{)} - {£ + /(4/4 + 1 a + OL-rj)}

+ etc. . . (11)

there being four such terms identical with (9), except that the first member
in the denominator in each case is the expression for the point Q.

Abandoning once more terms of higher order than the first in f ^ +

on expanding (11) becomes

+ccr 1 (^ -•£) + +/-/?) + l

.24(2/4+ la - a) 4(2/4 + la -a)2 2i(2na-a)

W 1 J+ 1 (£'-£) + i(v' + v)

4a2(2/4+l)2

%K

+

• +oo p
4K

2(2ua - a)2 2i(2n+l)a inai

1 (£' ~ i) +i(y +y) _ (£' - i) + i(y - y)

2 i(na - a) 4a2(2/4 + 1 )2

2(2«<l-a)2] ^

4(2/4 + la - a)2

The infinite series in (10) and (12) are all summable as follows:

2?za + a 2^a + a 2

1 1

1 —

na — a a

+ co

^na - a

1 00 1

+ 2“2

7r an r

2„2 _ „2 = „ C°t — (13)

nLa * — a* a

by a well-known expansion.

+ 0° 1 +c° 1 _2

(2 n - l)2“+(2/4+l)2 = T '

1

71 5

= ++'sec'

2(2„-la + a)2 ^{2n + la-af 4«2

+ 00 1 +00 -1 2

J- ^

^(2/4a + a)2 2na-aSl 4a2COS

2a

7T

cosec2

. (14)

. (15)

• (16)

* Omitting the term n = 0.

m

1920-21.] Stable Flow of a Fluid in a Uniform Channel. 143
Expressions (10) and (12) now reduce to

, . ik r

- U + IV= —

JL. cot — - (£-Q + % + F) # + (£~£') + i(v-y) sec2 ™

2ai a

16

a"

16

ciu 2a

, lr]T72 9 7Ta

+ — - — x cosec2 —
8a'2 2a

_ p

ITT

[_2a

cot " + (f - ?)* tan2 ” + tnl( tan2 ” + 2 cosec2 ™
a ' lba2 2a i6a2\ 2a 2a

*S(-E+>)] ■ ™

u + iv — —
2tt

- ^ cot.a7r+^/~^+^ + ^ 7r2_(^-^) + ^(F-^) ^2SPP27ra

16

16

. — sec"

8a2

cosecz

i« f In , air , u 7 r2 , 9 7ra , ^W2/, , 9 7ra\

= 7T ^r-cot— +(£-D__tan; + Ur-(1+sec: 2 —

27r|_2a a 16a2 2a lba2\ 2 a/

— TTT^ f tan2 — + 2 cosec2 — Y
16a2\ 2a 2a) _

(18)

For the contribution to —u + iv due to (b), it is to be noted that since
the vortices move with the fluid, and the total velocity in the undisturbed

channel at a point x + iy is U^l — there must be added to (17) and (18)
the terms

/ 1 _a-a + 7]\

and

- u(

V a2 /

\

a -f a + r\

respectively ; or, retaining terms up to the first order only,

C{!

a - a
a 2

>-)

a2 )

and

Tj/l-a~a

+ 7?(a-a>) ' <19>

If u0 v0, uQ' v0' are the component velocities of P and Q when in the
undisturbed position, these may be derived from (17), (18), and (19) by
making £=y = £/ = r]' = 0, and equating real and imaginaries. Hence

“o=scot¥+u(1_^)=“o'; v°=°=< ■ ■ (20)

indicating that the two vortices in the undisturbed position would move
steadily along the channel with the velocity given by (20). For a given
value of U Qj/k (positive) the vortex will move up channel only if a/a is
greater than some definite number itself greater than J, for only if a/a>^
can the first term in u0 become negative, while the second term is always
positive.

§ 9. Let the axes of co-ordinates be in steady motion with the speed-
given by (20), so that in the undisturbed position the vortices would

144 Proceedings of the Koyad Society of Edinburgh. [Sess.

appear at rest relative to these axes. The component speeds may now be
written when the vortices are disturbed as

dj drj . d%_ drf

dt ’ dt ’ dt ’ dt'

■■■

+ -^v(a-a) ■ (21)

di‘ + iJ4- = (f - O tan2 ™ + 4 1 + sec2 ™) - id tan2 ™ + 2 cosec2 ™Y

2a \ 2a/ \ 2a 2a/_

dt

dt 32a2

2U „ s

From which, by separating real and imaginary terms, it follows that

32a2

dt;

7 TK

~di

32 a2

dr]

7 TK

dt

32 a2

dt'

7 TK

dt

32 a2

drf

7TK

~dt

tan2 ^ + 2 cosec2 — ) - W 1 + sec2 — )

2a

o 7ra\ 64U

2a/ K7T

(a - a)>7

7ra

2a

2 dt; / , 97ra\ 9 7ra , n 9 7ra\ , 64U/ \ /

= w 1 + sec2 — - 7i ( tan2 — + 2 cosec2 — + (a - a)ri

dt \ 2a/ \ 2a 2a/ K7r

This is a system of linear equations with constant coefficients.
The solutions are consequently in general of the form

(£, y, y') =

i

and the equation to determine the X’s is

32a2

A,

X.

tan2—, X,
2 a

0. - Y.

, o 7TCL

tan2 - ,
2a

A,

tan2 — , 0, tan2 - ,

2a 5 2a’

\nt

1

Y

0

X

A

= 0

where

v , 9 7ra , 0 97ra 64U/ \

X = tan2 — + 2 cosec2 — (a — a)

2a 2a kit

(22)

(23,

(24)

(25)

(26)

(27)

Y-t , o 7 rot

= 1 + sec2 — .

2 a

On expanding (27), it follows that

A2[~A2 + 2tan2™ (Y-X)
L 2a

or

A2 = 0, and A2 = 4 — ^ L--— (a - a) tan2 ~
K7r 2a

(28)

1920-21.] Stable Flow of a Fluid in a Uniform Channel. 145
Equations (24) and (26) indicate that if the initial displacement is

dr\ , dii1

dt andw

yj yi

purely in rj and rj', then -U and -A. are both zero. Similarly (23) and (25)

show that if the initial disturbance is purely in £ and then ^ and (~~

are both zero. In each of these cases the system is neutral to the dis-
turbance in question. This corresponds, of course, to the two zero values
for X.

The other expressions for X2 being real, it follows that the arrangement
is stable or unstable according as

A 128U/ > , 27ra^-f,

4 ( a — a) tan2 — ^0,

K7T 2 a

%.e. as

XJ (a -- a) ^ 7 r 7ra

— v ’ ^ — cot2

<32

(29)

If 2 h is the distance apart of the two vortices, h = a — a, and the criterion
(29) takes the form

UA •> 71 ■ , 97rh /OAN

V<32tan 2^ (30)

according as there is stability or instability.

§ 10. The inequalities (29) and (30) provide the criterion sought for,
and furnish the analogue of the experimentally known critical value for
TJa/v already referred to. At first sight there appears a serious dis-
similarity between the two critical conditions; whereas Reynolds has
found that for Ua/v less than a definite number stability existed, the
analysis of the present paper shows that for U ol/k (or what is in effect the
same, TJh/ic) greater than a definite quantity a stable state of affairs would
exist. The inconsistency is, however, only apparent. For a legitimate
comparison of the two conditions, equations (1) or (2) expressing k in terms
of v and TJajp are required; k/v may be a comparatively complicated
function of JJa/p, and the inequalities (29) and (30) would require to be
transformed accordingly. If, for example, it were found that under certain
circumstances k oc p(Ulfp2), the inequalities in question would immediately
revert to the Reynolds form. How to establish the appropriate relation
of the form (1) or (2) is, however, a question for a future paper. For the
moment it suffices to state that the criterion (29) or (30) determines the
maximum intensity permissible for the two eddies, that they may stably
maintain their arrangement for a given forward velocity of fluid. It should
be noted that where TJh/ic is already above the critical, and therefore stability

already exists, the gradual decay of the vortex strengths due to the
VOL. xli. 10

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

viscosity will tend to force up the value of U Ji/k further into the region of
stability, and to maintain the vortices in their equilibrium positions. No
such corresponding assertion can, however, be made when U h/ic is initially
below the critical, and the vortices move off along paths determined by
their initial displacements.

§ 11. For the evaluation of the velocities in the fluid when the vortices
are in their undisturbed position, we may most conveniently specify the
positions of the latter thus : —

+ k; (2n+ la + a)i. - k ; (2n+ la — a)i.

Hence for the effect of the vortices alone

10

= {l°g [} — (2w + la + a)z] - log [z - (2 n + 1 a - a)?!]}

Ik ,

= 2^°S

v K i

=? — lot

+,oo

z - (2n + la + a)i
-z— (2/z + la — a)i
(z — ai)2

1 +

o 1 +

lK -I

= o' loS

2tt

\2n + l)2a2
(z + ai)2
(2n + l)2a2

cosh ~(z — ai)

2 a> ’

cosh Z-(z + ai)
2 a

. dw ii<

— U + IV = - —

dz 4 a

tanh — (z — ai) - tanh ^-(z + ai)
2a 2 a

. ira
sm —
k a

2 a i 7 tZ , 7ra

cosh — + cos —
a a

To this must be added at every point the motion due to the steady stream-
ing in the channel ; thus

— u + iv =

. tv a
sm —
k a

2 a i 7rZ 7r a
cosh — + cos —

a a

§ 12. The motion in the channel at great distances from the vortices
approaches the steady undisturbed motion of the fluid. Along the walls

y =

-ua + iva =

K

. rra

sin —
a

cosh ( —

\ a

+ l7r) + COS

1920-21.] Stable Flow of a Fluid in a Uniform Channel. 147

. TTOL

Sill —
K (l

2 CL , 7 TX TTOL

cosh — — cos —

= 0.

The slip at the boundary therefore attains a maximum value of ^ cot ^

when x = 0 and falls off exponentially as x increases, becoming zero as
| x | ->oo . The maximum velocity of slip may likewise be written, of

course, ~~ tan Associating this with the conditions for stability and

ZCt ZC6

instability (30) in the form

=— UAcot2J^, it follows that for a stable
7 r 2a

16/?/ It

system the maximum velocity of slip is always less than U cot , and

7 r a 2a

for an unstable system the slip is always greater than this quantity. The
fact that as the passage is made from the stable to the unstable region the
tendency to slip increases, should be associated with the remarks in § 5 of
this paper relative to the insufficiency of experimental evidence on the
question of slip at the boundary when turbulent flow has set in.

{Issued separately December 13, 1921.)

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

XVI. — Note on Conditions for Mirage on the Queensferry Road.

By Alex. G. Ramage.

(Read July 4, 1921. MS. received September 21, 1921.)

The surface of the Queensferry Road, from about the bend above
Blackhall, past Marchfield, and on towards Cramond Bridge, was remade
in the spring 1919.

It was made in the modern fashion for a motoring road, with road
metal and liberal supplies of bitumen, and small pieces of quartz scattered
on top of the bitumen, the whole being rolled by steam roller.

After this had been done, although I watched carefully throughout
the summer, no signs of the mirage, so common on this road during the
previous summer, made their appearance until August, and then but
faintly. This in my opinion points to a triturated condition of the quartz
under road traffic, as being an essential factor in the phenomenon. During
the summers of 1920 and 1921, on bright days, mirage was much in
evidence on this road at the places described in my paper, and at other
parts in the vicinity.

The following observations made during August 1921 may be of
interest.

I have had occasion to use the Craigleith Road (which branches off
from the Queensferry Road near Craigleith Station and joins the Comely
Bank Road) frequently this year, and have carefully looked for mirage,
but saw none. The surface is “old” and not to be distinguished from
that of the Queensferry Road when mirage was observable, It is smooth,
with the small stones well embedded in the bitumen. On the south
side there are open railings, so that the sun reaches it without obstruc-
tion. Compared with the Queensferry Road there is little traffic.

Recently the Queensferry Road between Lord Salvesen’s house and
Craigleith Station has been resurfaced, and considerable traffic has been
diverted round the Craigleith Road. On the 15th August 1921, weather
hot and sunny, I walked from the bus terminus at Comely Bank along
the Craigleith Road and saw an isolated spot of water on this road, but
no reflection. Walking on through Blackhall on Queensferry Road, I
found the two yellow advertisement boards clearly reflected from the
road, and some children’s coloured clothes were well reflected just at the

149

1920-21.] Mirage on the Queensferry Road.

bend of the road from Blackhall towards Marchfield. This is the first
reflection of coloured garments I have seen on the Queensferry Road
since the surface was remade in early summer, although some days earlier
I observed the two yellow advertisement boards reflected, but not so
distinctly as on the 15th August.

The surface of the Queensferry Road where the garments were seen
to be reflected is not yet smooth, the stones are still protruding through
the bitumen in places. The traffic has been very great.

I have just returned from an extensive motoring tour in England,
taking in both main highways and byways. Only on the highways
where there was great traffic did I see mirage on the road. On the
byways I looked for it in vain.

{Issued separately December 13, 1921.)

150

Proceedings of the Royal Society of Edinburgh. [Sess.

XVII. — The Annual Incidence of Intelligence, and its Measurement
by the American Army Tests. By M. M ‘Galium Fairgrieve,
M.A.

(MS. received May 4, 1921. Read June 20, 1921.)

(1) The following investigation was undertaken to verify by the American
Army Tests a result previously obtained by the use of Mr Cyril Burt’s
tests of intelligence (< Journal of Experimental Pedagogy, vol. vi, No. 1),
i.e. that there appears to be some likelihood that boys born in the spring
months are slightly less intelligent on the average than those born in other
months. Of these American tests (see Mental Tests in the American
Army , C. S. Yoakum and R. M. Yerkes, pp. 220-230) the groups of tests
marked “ form 6 ” were used ; but “ test 8 ” was modified to suit British
conditions by using test 8 of group 9 (p. 274, loc. cit.) as a basis, and
replacing tests 1, 3, 7, 8, 9, 11, 13, 19, 35, 36, 38 by 8, 1 ; 6, 3 ; 7, 39 ; 8, 39 ;
6, 35 ; 7, 36 ; 7, 38 ; 6, 39, and by three others of local interest.

(2) The tests were applied in the manner directed to 368 boys — nearly
the whole of the upper school ; whereas the previous Burt, test had been
applied to 192 boys only. But it should be noted that

(a) the tests could not be given to all classes simultaneously ;

( b ) different classes were examined at different times ;

(c) all forms of test 1 were used to minimise possible coaching ;

(d) the test took about a month to complete, but

* (e) a partial repetition of the test, using “ form 7,” showed that this
extension of time was probably immaterial.

(3) The total marks gained by boys of the same age in months was

then added to the marks gained by those a month younger and a month

older, and the average mark obtained. The method and result are given in
Table I. Ages date from October 1.

(4) These average marks are plotted in fig. 1, and show clearly minima

in the late spring or early summer months at 12 years 5 months ; 14 years
6 months: 15 years 4 months; 16 years 3 months; and maxima in the
late autumn months at 11 years 11 months ; 12 years 10 months (or

13 years 0 months) ; 13 years 10 months ; and 14 years 10 months, and

perhaps 16 years 0 months.

m-M

1920-21.] The Annual Incidence of Intelligence.

151

(5) (a) Table II. gives the average mark obtained in three different
ways of boys born in each month.

( b ) The result marked B is the most reliable average for the usual

reasons, the boys aged eleven being rather a clever sample.

(c) The result of the Burt test is added for comparison.

(6) Both diagram and table thus give clear indication that, from some
cause, boys born in the late spring months — say March to July — are in
danger of developing less intelligence than those born about October to
December. But

(a) many of the cleverest boys in the school have birthdays in the

less intelligent period ;

(b) some of the duller boys are brilliant enough athletically ; hence

(c) some effect of environment may possibly be indicated ;

(d) the experiment requires to be repeated in other localities.

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

Table I. — Average Mark gained by a Boy aged x Years and y Months

at October 1, 1920.

The marks have been smoothed in sets of three months. Column 3 gives the number
of boys of each age, and column 4 the number in each set of three months.

(1)

Age.

(2)

S

rce

-4-3

c

EH

(3)

to

O

PQ

~o

6

£

No in Group.

Average Mark. ^

(1)

Age.

(2)

M

fH

03

IS

O

EH

(3)

CO

O

PQ

'o

o’

No. in Group

Average Mark. ^

(1)

Age.

(2).

fH

o3

S

-1-3

O

EH

(3)

02

>*

O

PQ

O

6

£

(4)

o

u

0

o

Average Mark. ^

x y

X

V

X

y

10 5

171

3

...

12

10

403

5

12

93

15

3

904

8

16

112

6

275

4

9

62

11

548

5

16

91

4

588

5

20

110

7

115

2

7

63

13

0

500

6

16

96

5

713

7

18

114

8

52

1

3

57

1

487

5

12

90

6

765

6

17

118

9

4

57

2

93

1

18

93

7

521

4

13

125

10

175

3

8

56

3

1094

12

20

93

8

337

3

9

116

11

285

5

10

54

4

670

7

24

94

9

197

2

11

109

11 0

78

2

9

56

5

499

5

15

96

10

661

6

10

110

1

147

2

8

61

6

275

3

13

95

11

243

2

10

113

2

262

4

8

64

7

457

5

14

95

16

0

228

2

13

136

3

111

2

12

66

8

605

6

19

103

1

1293

9

14

131

4

423

6

10

76

9

899

8

18

112

2

320

3

15

131

5

228

2

15

74

10

519

4

16

116

3

350

3

9

110

6

444

7

13

70

11

440

4

15

116

4

316

3

10

119

7

240

4

14

66

14

0

784

7

19

110

5

522

4

13

130

8

246

3

11

74

1

865

8

19

110

6

853

6

14

138

9

321

4

11

81

2

447

4

16

106

7

551

4

11

133

10

324

4

14

77

3

389

4

12

100

8

81

1

7

128

11

438

6

17

88

4

368

4

10

96

9

266

2

3

122

12 0

625

7

14

88

5

202

2

11

96

10

4

147

1

78

1

14

77

6

388

5

12

93

11

321

*2

5

134

2

380

6

14

73

7

534

5

16

104

17

0

350

3

12

129

3

568

7

21

76

8

722

6

17

118

1

880

7

14

126

4

640

8

19

75

9

743

6

13

122

2

547

4

13

128

5

217

4

20

69

10

118

1

9

123

3

244

2

8

134

6

520

8

18

74

11

251

2

11

113

4

282

2

6

139

7

595

6

18

81

15

0

874

8

16

118

5

311

2

6

157

8

337

4

12

92

1

768

6

17

114

6

348

2

4

162

9

169

2

11

83

2

295

3

17

116

(7) At the right hand of Table II. is also given the average mark of
boys of a definite yearly age and the number of boys in each yearly group.

(a) Marks for ages 12, 13, 14, and 15 may be taken as fairly reliable.

( b ) The differences between these suggest a parabolic form as very

suitable for the normal curve.

(c) The highest mark (140) on this supposition would correspond well

with many of the averages of Yoakum and Yerkes. In par-
ticular, it is nearly identical with that given for the 15,385
cases of the “ White Officers’ Principal Sampling ” (139).

1920-21.] The Annual Incidence of Intelligence. 153

(d) Hence Table III. is suggested as giving a suitable normal mark for
boys of these ages, the figures in brackets being calculated
from the parabola of best fit.

Table II.— Average Score of Boys born in Different Months.

(A) is average score of all years available (10‘6-17‘6).

(B) is score for best years available (1D6-16'6).

(C) is score for best years available (lD6-16-6), unsmoothed figures.

Birth \
month J

x years + .

1 >
6.

-3

■6

7.

,

-1 H

8.

A

i

9.

1

V

P)

10.

>

o

5 C

11.

WGU.

O

Sept.

A ~

bp

*3 r

2.

K* O) K

^ rj k

gj c

1

3. 4.

5.

05

Mar.

ve rage Age.

Average

Mark.

m

> >
o

o

6

1

<

!Z5

yrs.

10 .

62

63

57

57

56

54

56

61

64

66

76

74

70

11

63

43

11 .

70

66

74

81

77

88

88

77

73

76

75

69

74

12

76J

62

12 .

74

81

92

83

93

91

96

90

93

93

94

96

95

13

9H

61

13 .

95

95

103

112

116

116

110

110

106

100

96

96

93

14

1041

61

14 .

93

104

118

122

123

113

118

114

116

112

110

114

118

15

115

63

15 .

118

125

116

109

110

113

136

131

131

110

119

130

138

16

122

47

16 .

138

133

128

122

147

134

129

126

128

134

139

157

162

17

137

31

Totals .

650

'667

688

686

722

709

733

709

711

691

709

736

750

Levelling

correction

50

i 42

34

25

17

9

0

-9

-17

-25

-34

-42

-50

Average (A)

100

101

103

102

105

103

105

100

99

95

96

99

100

„ (B)

97

100

105

105

106

105

109

104

101

94

95

95

97

» (C)

'94

104

103

104

106

108

101

109

93

96

93

92

94

Burt aver-

age mark

n\

13\

n\

17-

17-

17 +

17 +

17-

17-

17

16\

m\

14\

Table III. — Age Norms for American Army Tests.

Age .

Differences of aver-
age mark
Normal mark

8. 9.

10. 11.

12.

13. 14.

15. I 16.

17.

18.

19.

20.

(21) (19) (17) 15 13 11 9 (7) (5) (3) (1)

(19)

(40)

(59) 76

91

104

115

124 (131) (136)

(139)

(140)

{Issued separately December 13, 1921.)

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

XVIII. — Experiments with an Electrified Pith Ball in an Ionised
Atmosphere. By Dr Dawson Turner and Mr D. M. R. Crombie.

(Bead May 2, 1921. MS. received June 16, 1921.)

A pith ball suspended from the centre rod of a charged Leyden jar
provides us with an interesting and very delicate method of demonstrating
the ionised atmosphere surrounding flames and incandescent bodies. In
an ionised atmosphere of sufficient intensity the ball, provided that the
suspending fibre is of high insulating quality, rapidly loses its charge and
falls back toward the centre rod of the jar, from which it receives a fresh
charge and is violently repelled, only to repeat the performance; thus an
oscillation is set up the rapidity of which is governed chiefly by the
length of the suspending fibre.

A screen of any material, even wire gauze, interposed between the
ionising source and the ball, and not too near the latter, at once stops the
oscillation.

The violence of the oscillations seems from the experiments performed
to depend upon the following factors : —

(1) The distance of the source of ionisation. The nearer the source
is to the ball, the more violent are the oscillations.

(2) The nature of the source of ionisation. Thus the bulk of experiments
showed that a bunsen burner was the most effective in producing oscilla-
tions. Less effective sources included a naked Nernst filament, a glowing
platinum wire, a candle flame, and a spirit-lamp flame. An electric arc
gave comparatively poor results. This was somewhat surprising, but may
be due to the powerful electric field between the carbons preventing the
escape of ions to the surrounding atmosphere. To test if the effect had any
relation to the actinic quality of the light, a piece of burning magnesium
ribbon was tried, but was found to be less effective than a candle flame.

Mere bulk of flame does not make much difference to the oscillations,
since a jet of gas burning from an open pipe, though of large dimensions,
was not so effective as the bunsen.

(3) The third factor influencing the oscillations is the potential of
the jar. Effects can be produced at a greater distance when the jar is
highly charged than when it has only a small charge. This might seem
to show the directive influence of the jar and ball in attracting a stream
of the opposite kind of ions towards themselves.

1920-21.] Experiments with an Electrified Pith Ball. 155

(4) The position of the source of ionisation can be shown to have an
important bearing on the oscillations. Thus a candle held directly
opposite the ball at a distance too great to be effective may be made
so at the same distance if held at a lower level than the ball. From
this we may conclude that the ions formed in the flame are carried
upwards by the convection currents of air, and entirely disposes of any
suspicion of projection of ions from the flame. Also, should the ball
happen to be in any position other than directly between the source of
ionisation and the centre rod of the jar, the source may he approached
very close indeed to the ball without oscillations taking place. This is
in confirmation of the previous deduction arrived at, namely, that the
highly charged centre rod of the jar exerts a directive influence on
the ions.

In addition to the above, the atmospheric condition seems to play an
important part. This appears to be a reasonable explanation of the
varying maximum distance at which effects could be produced on different
days when to all appearance other conditions were identical.

The conclusion drawn from the whole series of experiments was that
the nature of the charge given to the jar had no bearing on the results
obtained, and though there were occasions when this did not seem to be
the case, subsequent experiments showed that the discrepancies were
probably due to variation in some of the factors just mentioned.

In performing the experiments we employed the following method : —

The jar was charged from a Wimshurst machine and placed on a bench
with the pith ball standing out towards the ionising source, which was
placed 30 inches off, with a screen interposed between it and the ball. A
reading telescope was mounted in such a position as to have the ball in
the field of view of its graduated scale. The screen was then removed
and the ball carefully watched for any slight drop. This distance was
invariably too great to show any effect, but on most occasions, when the
distance was decreased to 25 inches, a slight drop could be noticed. As
a rule, at 20 inches the drop of the ball was large enough to he seen easily
with the naked eye, and occasionally oscillations commenced at that
distance. This was when the ionising source was a bunsen burner ; but
as a rule oscillations did not commence until the bunsen was about 18
inches from the ball, though sometimes, under unfavourable conditions,
much shorter distances were necessary before effective oscillations could
be produced. Once oscillations had commenced, it was usually found that
the source could be moved further oft' and the movement maintained at
the increased distance.

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

The introduction of a platinum cup containing a sodium salt into the
bunsen flame did not increase the distance at which oscillations could be
produced, but seemed to have the opposite effect.

As already mentioned, a Nernst filament, a candle flame, and a spirit
flame were all found to be inferior to the bunsen as sources of ionisation ;
but especial mention is required in the case of the electric arc, which
was unable to produce oscillations at a greater distance than 6 inches,
while 2 inches of platinum wire raised to a low white heat by an electric
current were quite effective at 13 inches.

An interesting effect was noticed while working with a glass screen
which was held so near the jar that the pith bail was only a matter of
1J to 2 inches from the screen. When a source of ionisation (in this case
the Nernst) was brought up to the side of the screen remote from the
jar, the ball was visibly attracted toward the screen, and when the Nernst
was brought nearer still the ball jumped to the screen and stuck there.
The effect was more marked if in place of the glass screen a thin insulated
metal screen was used ; but in this latter case the ball, instead of sticking
to the screen, oscillated between it and the centre rod of the jar. As
before, this effect was independent of the nature of the charge in the
jar. If, however, the charged pith ball were detached from the jar and
suspended from a glass rod at a distance of 2 inches, as before, from the
screen, the effect was no longer obtainable, and the approach of the Nernst
to the other side of the screen produced no visible attraction between
the screen and the ball.

A possible explanation of these effects is as follows : — The knob of the
jar being in close proximity to the screen induces on the side next to
it an opposite and repels to the far side a similar charge. These opposite
charges in close proximity to one another can have little influence
on the ball, and the thinner the screen the less will this influence of the
opposite induced charge be in attracting the ball towards it. If, however,
the repelled similar charge be removed by any means, then the opposite
charge is left free to attract the ball. This is what happened when the
Nernst lamp was brought toward the far side of the screen, for then
the ionised atmosphere surrounding it rapidly discharged the repelled
similar charge, leaving the induced opposite charge to attract the pith
ball. The fact that when the ball alone was present no effect was
produced seems to show that it was dependent on the proximity of the
highly charged knob of the Leyden jar.

When X-rays were used as the source of ionisation the oscillation
effects, though in the main similar to those produced by flames, etc., differed

1920-21.] Experiments with an Electrified Pith Ball. 157

in one or two important respects. Firstly, as was to be expected, the
distance at which oscillations could be produced was very much greater ;
secondly, the effect could be produced as a rule at a greater distance when
the potential of the jar was low than when it was high ; also, as the
distance increased the oscillations took longer to commence, during which
period the ball was slowing dropping toward the centre rod. Eventually,
when the extreme limit at which oscillations could be produced was being
approached, an interval of two or three minutes elapsed before oscillations
began. At distances too great for the production of oscillations a dropping
of the ball could be observed each time the X-rays were turned on. The
interposition of an iron screen 035 mm. thick stopped the effect at once.

In all the previous cases the potential of the central rod of the jar
was the active means whereby a stream of ions was drawn from the source
of ionisation so as to pass through the ball, hence when, instead of a single
hall, four balls were attached round the circumference of the rod, one in
each quadrant and equidistant from one another, only the ball in the
direct alignment was affected, but in the case of the X-rays all the balls
were almost equally affected, being all equally immersed in a sea of ions.

Similar results, hut at much shorter distances, were obtained by using
the rays from a 50-mm. capsule of radium bromide. The interposition of
the iron screen did not stop the effect.

Summary of Conclusions.

(1) A pith ball suspended from the centre rod of a charged Leyden jar
will oscillate in an ionised atmosphere and can serve as a very delicate
indicator of the electrical condition of its surroundings.

(2) By its means the ionised atmosphere around flames can be detected
at a considerable distance, and the relative intensities of various sources
of ionisation can be compared.

(3) The ions are concentrated along the line joining the centre rod of
the charged jar and the source of ionisation, for unless the pith ball be
in this line it will be unaffected, except in the case of X-rays and the
rays from radio-active bodies.

(4) The ions tend to be carried upwards by convection currents.

(5) The ionisation of the atmosphere does not depend upon the
luminous or actinic intensity of a flame.

(6) The effect upon the electrified pith ball appears to be independent
of the nature of its charge.

( Issued separately December 13, 1921.)

158

Proceedings of the Royal Society of Edinburgh. [Sess.

OBITUARY NOTICES.

Robert Munro, M.A., M.D., LL.D. By Dr George Macdonald, C.B.

(MS. received July 4, 1921. Read October 24, 1921.)

Robert Munro was born at Assynt, in the Ross-shire parish of Alness,
on 21st July 1835. After spending some years at the Free Church School
of Kiltearn, he was sent to finish his education at the Royal Academy, Tain.
Though he was alert and observant from the first, his intellectual powers
seem to have developed somewhat slowly : it was not until his career at
Tain was drawing to a close that his capacity for University work was
realised. The financial difficulty was serious. But his own mind was
definitely made up, and with characteristic determination he set himself to
overcome all obstacles. As a means to the end, he took to teaching, and in
1860 he found himself a graduate in Arts of the University of Edinburgh.
His original intention had been to proceed to the New College, with a view
to entering the Church. In 1859, however, his whole outlook in life had
been changed by the appearance of Darwin’s Origin of Species, which he
read with avidity, and which made an immediate appeal to his scientific
instincts. In the Free Church of those days there was no room for a
Darwinian, and there was nothing for it but to abandon all thought of
the profession at which he had been aiming.

For two years after obtaining his degree he remained doubtful as to
how he should shape his future. Ultimately, with great courage and also
(as the event proved) with great wisdom, he resolved to face the discipline
of the medical curriculum. In 1862, at the age of twenty-seven, he
matriculated once more at Edinburgh. Even then his course was not
destined to proceed on normal lines. What should have been his third
winter of medical study was spent on the Riviera, in charge of a semi-
invalid. At his time of life the interruption might well have seemed

serious. But he never saw reason to regret it. His receptive mind derived
real profit from his sojourn abroad. The fauna, the flora, and the geology
of the Mediterranean all had an interest for him. And in various other
ways his horizon was appreciably widened. If, however, the interlude was
educationally valuable, it had the incidental effect of postponing for a
whole year the accomplishment of his immediate purpose. He did not

1920-21.] Obituary Notices. 159

finally “qualify” till 1867. He was then thirty-two, and had no resources
behind him save the priceless assets of ability and character.

His first appointment was as assistant to a busy doctor in a colliery
district of Ayrshire. He at once became deeply absorbed in his everyday
duties, utilising to the full the opportunities for instruction which they
offered. His own description may be quoted : “ The sudden transition
from a scholastic atmosphere and the teaching of medical science in
lecture-rooms and well-equipped hospitals to the practice of the healing
art among a mining population was to me like going into a new world.
Therapeutic theories and book-learning had to be tested by action there
and then.” The sound knowledge thus acquired of the origin, progress,
and correct treatment of disease stood him in excellent stead when he
aspired to a position of greater independence. This he did after an
apprenticeship of some two years’ duration. Looking round for an open-
ing, he decided upon a partnership in Kilmarnock. Before settling down,
however, he received an invitation to make an extended tour in the
Near East as companion to the son of a well-known Ayrshire proprietor.
The offer came at an opportune moment, and he gladly availed himself
of it. Doubtless he was ultimately responsible for the comprehensive
itinerary which, beginning with the more important cities of France and
Italy, led through Sicily and Malta to Egypt and the Nile, the Holy Land,
Baalbek, Athens, Constantinople, Rustchuk, Budapest, Vienna, and thence
home by Munich and the Rhine.

There followed sixteen years of arduous general practice, diversified by
short holidays abroad. No figure in Kilmarnock was better known in
those days than Dr Munro’s. His regular patients were as numerous as he
could wish for, and the reputation he had won during his assistantship
brought many miners from Cumnock and its neighbourhood to his
consulting-room. At the same time he was in great demand as a popular
lecturer on scientific and social subjects, invariably speaking his mind with
a singularly refreshing frankness. His influence in the community grew
steadily, and to outsiders it must have seemed as if his highest ambition
had been satisfied. There was, therefore, general surprise and regret when,
in 1885, he announced that he had made up his mind to retire. Friends
came to remonstrate. But he was inflexible : “ I divide my life into three
periods : during the first I struggled hard for my education, during the
second I served the public to the best of my ability, and for the rest of
my life I mean to please myself.” Ten years earlier he had married
Miss Anna Taylor, a lady of singular charm, who was to be his devoted
companion for thirty-two years in all, and in 1879 the death of his

160

Proceedings of the Royal Society of Edinburgh. [Sess.

father-in-law had made him a shareholder in two local engineering
companies, then on the threshold of a prosperous career. In 1880 he
became chairman of one of them, and he was subsequently elected chairman
of a combine that included both. The income from these undertakings,
added to what he had been able to save from his professional earnings, had
put him in possession of a comfortable competency.

His decision to relinquish his practice was more immediately prompted
by a threatened breakdown in health. But there was a larger reason
behind it. “ I began to realise that I was gradually becoming enslaved
to a monotonous existence of mere routine work, with the prospect of
premature decay. My real object in joining the medical profession had no
higher motive than to secure an honourable livelihood, an object which had
now, in a small but efficient way, been attained ; but yet worldly prosperity
did not bring with it the realisation of my earlier ideals of an intelligent
human existence. The preliminary studies on which the laws of organic
development of the human body, both in health and disease, are supposed
to be founded, are most fascinating ; but the art of healing, which in practice
is largely based on empiricism, soon engenders in the mind of the con-
scientious physician doubts as to the efficiency of many so-called remedies.
In many instances of serious illness it is often as clear as noonday to the
skilful physician that palliation of symptoms is all that can be done ; but
yet, if the doctor expressed a hint of this truth, he would in all probability
instantly lose his patient. Here lies a dangerous pitfall which sometimes
leads to quackery and hypocrisy.” This outspoken confession throws a
curious and interesting light on the writer’s own temperament. He can
hardly have been one of those medical men “ whose visits make it a pleasure
to be ill,” as R. L. Stevenson puts it. Rather, he must have resembled
Chaucer’s “ Doctour of Phisyk ” —

“ He was a verrey partit practisour.

The cause y-knowe, and of his harm the rote,

Anon he yaf the seke man his bote.

His studie was but litel on the bible.”

As soon as he was free, he set out for Rome, where he rapidly threw
off the painful illness that had attacked him. His physical vigour restored,
he devoted all his energies to a line of research which he had resolved to,
make his own. In 1877 he had been enrolled as an original member of the
Ayrshire and Galloway Archaeological Association. Hitherto his interest
in antiquities had been very detached, although during a holiday in

1920-21.] Obituary Notices. 161

Switzerland his scientific curiosity had been aroused by the fine series of
objects from lake-dwellings displayed in the museum at Zurich. By a
fortunate chance, the very first piece of work undertaken by the Association
was the excavation of a crannog, or artificial island, whose remains had
been accidentally discovered on the farm of Lochlee, familiar from its
association with Robert Burns. The late Mr Cochran Patrick, who was
the mainspring of the organisation, promptly enlisted Munro as a helper,
and a magnificent recruit he proved. Several other crannogs were explored
during the next two or three years, Munro taking a prominent part in
every case, and ultimately becoming leader. In 1882 the results were
brought before the public in his Scottish Lake-dwellings , a performance
which made it clear that he had laid a firm grasp on the essentials of
the subject.

The writing of the book had, however, convinced him of the importance
of extending the scope of his inquiries by the study of analogous phenomena
on the Continent. The great collection of relics from the lake-dwellings
and terramara settlements of the Po Valley, preserved in the Museo
Preistorico at Rome, was systematically examined as soon as his health
was sufficiently recovered, Mrs Munro lending invaluable assistance through
her deftness in sketching. Then followed a series of visits to public and
private collections elsewhere in Italy, as well as to every locality in which
lake-dwellings or relics of their inhabitants were to be found. On return-
ing to Scotland in the summer of 1886, he received an invitation to deliver
the Rhind Lectures for 1888, the subject suggested being “The Lake-
dwellings of Europe.” These lectures were issued in book form in 1890,
and with their appearance his reputation as an archaeologist was made.
The best testimony to their enduring quality is that they were translated
into French eighteen years after they were originally issued. They have
definitely taken their place as the standard work on the subject. The mass
of material passed in review is so extensive that any serious modification
of the conclusions reached is not likely to be called for.

About 1890 Dr and Mrs Munro had settled in Edinburgh, where their
house in Manor Place speedily became a centre of hospitality for antiquaries
on the one hand, and men of science on the other. Munro had hosts of
friends in both camps, and he liked to stimulate young men of promise by
introducing them to the notice of those who had already achieved distinc-
tion. He had been elected a Fellow of the Society of Antiquaries of Scot-
land in 1879. In 1888 he was appointed Honorary Secretary, a post which
he continued to hold for eleven years. In 1891 he joined the Fellowship of

the Royal Society, where he was speedily at home in most congenial company.

VOL. XLI. 11

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

Honorary and Corresponding Memberships flowed in on him from various
learned bodies in other countries. He delighted to attend archaeological
and scientific congresses, largely because it gave him a colourable excuse
for the travel which he so thoroughly enjoyed. His experiences in Bosnia,
Herzegovina, and Dalmatia are recorded in a volume which has gone
through more than one edition. But his most comprehensive tour was
undertaken in 1897, when he and his wife went to Toronto to attend the
British Association meeting, and made the return journey by Japan, China,
India, and the Mediterranean.

In 1892 he played a prominent part in rousing public interest in the
newly discovered lake- village at Glastonbury. Next year he was President
of the Anthropological Section of the British Association. By this time
he had pushed his researches back from the lake-dwellers to the makers
of palaeolithic implements, and he chose for the subject of his Presidential
address “ The relation between the Erect Posture and the Physical and
Intellectual Development of Man,” maintaining the view that “ man’s mental
superiority over all other animals was primarily due to his attainment of
the erect attitude which, by entirely eliminating the fore-limbs from
participating in the function of locomotion, enabled him to utilise these
limbs exclusively for prehensile and mechanical purposes.” The theory
attracted widespread attention, and the address, which was afterwards
published, was always regarded by its author as one of his most important
contributions to anthropology. Such criticism as it received, he welcomed.
Nothing pleased him better than intelligent discussion. Even controversy
had a certain attraction for him : witness the zest with which he used to
recall the main incidents of the dispute about the great “ Clyde Mystery ”
long after time had justified the attitude he himself had so consistently
adopted. So, too, he thoroughly enjoyed being summoned to give evidence
before Lord- Justice Far well in a lawsuit over certain Irish gold ornaments,
when the point regarding which he had to testify was the date of the last
upheaval of the land that formed the raised beaches along the shores of
the North of Ireland and Scotland. This was in 1903.

The same year was marked by an incident that indicated an impending
change in his way of life. He purchased a house at Largs. He was now
sixty-eight, and he was beginning to feel that the bustle of foreign travel
was something of a strain. He hoped to find in the quieter pursuits of a
country environment a more restful form of the variety that he loved. At
first his new home was a summer residence only. But he gradually became
more and more attached to his garden at Elmbank. The death of his wife
in 1907 was a very heavy blow. Thereafter Edinburgh saw him only at

1920-21.] Obituary Notices. 163

rare intervals. As the list of his contributions to learned periodicals
shows, he continued to work strenuously at his subject, seeking in this
way to gain relief, first from the grievous personal loss that had befallen
him, and afterwards from a painful neuritic affection which laid hold of
him in 1909, and slowly but inexorably tightened its grasp until the end.

The evening of #his life wTas brightened by an interest that sprang
directly from his own liberality. In 1910 he handed over to the University
Court of the University of Edinburgh a substantial capital sum for the
endowment of a permanent lectureship in anthropology and prehistoric
archaeology. By a happy inspiration the Court invited the donor himself
to be the first lecturer under the new foundation, and the vigour and
freshness of the inaugural course which he delivered in 1912 are still vividly
remembered by many. During the next year or two he watched with all
a parent’s solicitude the development of the experiment he had initiated.
It was a matter of peculiar satisfaction to him that his friend Professor
Geikie should have been appointed his immediate successor. Similarly, he
journeyed to Edinburgh in the early months of 1914 to welcome and
entertain Mr D. G. Hogarth, the third Munro Lecturer. Then came the
war, an incidental result of which was to postpone for six years the series
which the Abbe Breuil had promised to deliver. The postponement was
a great disappointment to Munro, who had been looking forward keenly
to the visit of the distinguished French scholar, of whose work he had a
high appreciation.

And, when the Abbe did come to Scotland in 1921, the founder of the
Lectureship was no longer alive to receive him. As early as 1916 his
strength had been so seriously undermined that he took the gloomiest view
of the future. But, despite much suffering, his splendid constitution and
his determined will enabled him to hold out for four years more, and even to
write, to lecture, and to publish in the interval. He died on 18th July 1920.
when he was within three days of attaining the age of eighty-five. The
last piece of work to which he set his hand was a short sketch of his
own life, which was composed for the information of his closest friends,
and which has since been printed for private circulation. From it not a
little of the material for the foregoing notice has been drawn. It is a
plain record of a strenuous and useful career, of real distinction achieved
through native ability and steadfast concentration of purpose. Those who
knew Munro can readily fill in the outline for themselves and colour it by
their recollection of his frank sincerity, his genuine kindliness, his love of
all good fellowship.

164

Proceedings of the Royal Society of Edinburgh. [Sess.

LIST OF WORKS.

1875. Notes of a Tour in the East. Being Lectures delivered by the
author at the Philosophical Institute, Kilmarnock. Kilmar-
nock : T. Stevenson.

1882. Ancient Scottish Lake-dwellings or Gran nogs. With a supplementary
chapter on Lake-dwellings in England. Edinburgh : David
Douglas.

1890. The Lake-dwellings of Europe. Illustrated. London: Cassell & Co.

1895. Rambles and Studies in Bosnia, Herzegovina, and Dalmatia. With
an account of the Proceedings of the Congress of Archaeologists
held in Sarajevo in 1894. Edinburgh : William Blackwood
& Sons.

1900. Second edition, greatly enlarged.

1897. Prehistoric Problems. Containing the author’s address as President
of the Anthropological Section of the British Association for
1893, “ On the Erect Attitude of Man, and its relation to the
Development of the Brain.” William Blackwood & Sons.

1899. Prehistoric Scotland, and its Place in European Civilisation.
William Blackwood & Sons.

1905. Archceology and False Antiquities. One of the “ Antiquary’s Books.”
With numerous illustrations. London : Methuen & Co.

1908. Les stations lacustres d’ Europe aux ages de la pierre et du
bronze. Translated by Dr Paul Rodet. Paris : Librairie
C. Reinwald ; Schliecher Freres, editeurs.

1912. Palaeolithic Man and Terramara Settlements in Europe. Being the
first course of the Munro Lectures in Anthropology and Pre-
historic Archaeology in connection with the University of
Edinburgh. Illustrated. Edinburgh : Oliver & Boyd, Tweed-
dale Court. London : Gurney & Jackson.

1914. Prehistoric Britain. “ Home University Library.” Illustrated.
London : Williams & Norgate.

1919. From Darwinism to Kaiserism. Being a review of the origin,
effects, and collapse of Germany’s attempt at world dominion
by methods of barbarism. Glasgow : R. MacLehose & Sons.

1921. Robert Munro, M.A., M.D., LL.D. Autobiographic Sketch. Glasgow:
MacLehose, Jackson & Co.

1920-21.] Obituary Notices. 165

Selected List of Contributions to Societies and Journals.

1876. “Mental Energy.” A. Lecture delivered at Kilmarnock under the
auspices of the Young Men’s Christian Association. Published
in pamphlet form.

1879. “Notice of Excavation of a Crannog at Lochlee, Ayrshire,” Proc.

Soc. Antiq. Scot., vol. xiii, pp. 175-252, including reports on
the flora and fauna and an analysis of vivianite.

1880. “ Inhalation of Carbolic Acid in Diseases of the Respiratory Organs,”

Glasgow Med. Jour., vol. xiv, p. 291.

“Ayrshire Crannogs,” Collections, Ayrs. and Gallow. Arch. Assoc.,
vol. ii, pp. 17-80.

1882. “Ayrshire Crannogs” (second notice), ibid., vol. iii, pp. 1-49.

“Notes on a Crannog at Friars’ Carse, Dumfriesshire,” Proc. Soc.

Antiq. Scot., vol. xvi, pp. 73-78.

1883. “ Minute Organisms and their relation to Disease,” Glasgow Med.

Jour., May and June 1883.

“ Megalithic Monuments of Holland and their relations to analogous
remains in Northern Europe,” Proc. Soc. Antiq. Scot., vol. xviii,
pp. 19-35.

1884. “ Danish Kjokkenmoddings : their Facts and Inferences,” ibid.,

pp. 216-225.

“ Ayrshire Crannogs ” (third notice), Collections, Ayrs. and Gallow .
Arch. Assoc., vol. iv, pp. 10-16.

“ Notice of the Discovery of Five Bronze Celts and a Bronze
Ring at the 4 Maidens,’ near Culzean Castle,” ibid., vol. iv,

pp. 1-8.

1885. “ The Lake-dwellings of Wigtonshire,” ibid., vol. v, pp. 74-124.

“ Notice of an Artificial Mound or Cairn on the Island of Eriska,
within thirty yards of the Tidal Area,” Proc. Soc. Antiq. Scot.,
vol. xix, pp. 193-202.

“ On the Preservation of National Antiquities in Northern Europe,”
Trans. Glasgow Arch. Soc., 16th April 1885.

“ The Scientific Basis of Medicine ” (being inaugural address as
President of the Glasgow and West of Scotland branch of the
British Medical Association ; read at the annual meeting in
Glasgow, 31st January 1885), Glasgow Med. Jour., vol. xxiii,
pp. 172-256.

1886. “Notes on Lake-dwellings in Lough Mourne, Co. Antrim, Ireland,”

Proc. Soc. Antiq. Scot., vol. xx, pp. 321-330. (An iron-.

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

socketed Celt with a loop was found here, and is figured on
p. 330.)

1886. “ The Arch geological Importance of Ancient British Lake-dwellings
and their relation to analogous remains in Europe,” Anthrop.
Inst. Jour., vol. xv, pp. 453-469.

1889. “Notes of a Visit to a Terp-Mound at Aalzum, Holland,” Proc. Soc.
Antiq. Scot., vol. xxiii, pp. 98-105.

“The Prehistoric Cemetery of Frogg, at Rosegg, Carinthia,” ibid.,
pp. 241-246.

1891. “Notice of Wooden Traps supposed to have been for catching Otters

and Beavers,” ibid., vol. xxv, pp. 73-89.

“ On Prehistoric Trepanning,” ibid., vol. xxvi, pp. 5-33.

Article on “ Prehistoric Saws versus Sickles,” Arch. Jour., vol. xlix,
pp. 53 and 64.

1892. “ The Discovery of an Ancient Lake-Village near Glastonbury, in

Somersetshire,” The Tim.es, 24th October 1892.

1893. “ Notes on Crannogs recently discovered in Argyllshire,” Proc. Soc.

Antiq. Scot., vol. xxvii, pp. 205-222.

Address as President of Section (Anthropology), British Association,
Nottingham, Report, pp. 885-895. Also in Jour, of Roy.
Anthrop. Inst., vol. xxiii, pp. 173-187, and in Prehistoric
Problems, chap. ii. The subject of the address was “The
relation between the Erect Posture and the Physical and
Intellectual Development of Man.”

“ On a remarkable Glacier-Lake formed by a branch of the Hardanger-
Jokul, near Eidford, Norway,” Edin. Roy. Soc. Proc., vol. xx,
pp. 33-62. Reprinted in Norway.

“ Prehistoric Trepanning and Cranial Amulets,” Fortnightly Review,
vol. liii, pp. 208-222.

1894. “ The Rise and Progress of Anthropology” (being an Address

delivered at the request of the Council to the Royal Society
of Edinburgh, 7th May 1894), Edin. Roy. Soc. Proc., vol. xx,
pp. 215-244.

“Notes on Flint, Saws, and Sickles,” IUus. Archceologist, vol. i,
pp. 176-193.

“ Notes on Ancient Bone Skates,” Proc. Soc. Antiq. Scot., vol. xxviii,
pp. 185-197.

“The Structural Features of Lake-dwellings,” Jour. Roy. Soc. Antiq.
Ireland, vol. xxiv, pp. 105-114 and 209-221.

1895. “ On Lake-dwelling Research” (being an address delivered at

1920-21.] Obituary Notices. 167

the request of the Council to the Royal Society of Edin-
burgh, 4th March 1895), Edin. Roy. Soc. Proc., vol. xx,
pp. 385-411.

1896. Report to the Society of Antiquaries of London as Local Secretary

for Scotland, Proceedings , vol. xvi, pp. 178-197 (2nd series).
This communication includes brief descriptions of (1) A Crannog
in Lochan Dughaill ; (2) A Cave at Oban containing Human
Remains and Implements ; (3) The excavation of the Roman
Camp at Birrens.

1897. “ On Intermediary Links between Man and the Lower Animals ”

(published in abstract, but in full in Prehistoric Problems ),
Edin. Roy. Soc. Proc., vol. xxi, pp. 249-250.

1898. “ The Relation between Archaeology, Chronology, and Land Oscilla-

tions in Post-Glacial Times ” (being the opening address to the
Antiquarian Section at the Lancaster meeting of the Roy.
Arch. Institute), Arch. Jour., vol. lv, pp. 259-285.

“ Notes on Prehistoric Trepanning in the Old and New Worlds,”
Proc. Soc. Antiq. Scot., vol. xxxii, pp. 220-235.

1899. “Notes on a Crannog at Hyndford, near Lanark,” Proc. Soc. Antiq.

Scot., voL xxxiii, pp. 373-387.

Controversy as to the genuineness of certain manufactured objects
found in the debris of ancient inhabited sites at Dumbuck and
Dunbuie in the Clyde basin. Dr Munro’s statement questioning
their authenticity appeared in the Glasgow Herald, 7th January
1899. (Subsequent correspondence followed in the same journal
and in other journals).

1901. “Notice of an Ancient Kitchen-Midden near Largo Bay, Fifeshire,”

Proc. Soc. Antiq. Scot., vol. xxxv, pp. 281-300.

“Is the Dumbuck Crannog Neolithic?” Reliquary and Illus.

Archceologist, vol. vii, pp. 107-119.

Report to the Society of Antiquaries of London as Local Secretary
for Scotland, Proceedings, vol. xviii, pp. 370-386. This
communication includes the following notices : (1) Isolated
Finds; (2) The Roman Camp at Ardoch ; (3) The Hill-Fort
near Abernethy ; (4) A Romano-British Crannog at Hyndford ;

(5) The Hill-Fort of Dunbuie and its remarkable remains;

(6) The Dumbuck “ Crannog.”

“ Prehistoric Kitchen-Middens and what they teach us,” Trans. Scot.
Eat. Hist. Soc., 7th November 1901.

1902. “ On the Prehistoric Horses of Europe and their supposed

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

domestication in Palaeolithic Times,” Arch. Journ ., vol. lix,
pp. 109-143 ; also in Edin. Phys. Soc. Proc., vol. xv,
pp. 70-104.

1902. “Stray Thoughts on the Theory of Organic Evolution,” Edin.

Phys. Soc. Proc., vol. xiv, pp. 279-298 (read 15th November
1899).

“Notes on a set of five Jet Buttons found on a hill in Forfarshire,”
Proc. Soc. Antiq. Scot., vol. xxxvi, pp. 464-485.

1903. “ Irish Gold Ornaments of the Late Celtic Period and Raised Beaches

(a case of treasure trove),” Juridical Review, vol. xv, pp. 267-277.

1904. “Man as Artist and Sportsman in the Palaeolithic Period,” Edin.

Roy. Soc. Proc., vol. xxv, pp. 92-128 (being the Friday evening
address at the British Association at Southport in 1 903).

“ On the date of the upheaval which caused the 25-ft. Raised Beaches
in Scotland,” ibid., vol. xxv, pp. 242-272.

“ Notes on Primitive Stone Structures of the beehive type in the
North of Shetland,” Proc. Soc. Antiq. Scot., vol. xxxviii,
pp. 548-553.

1906. “Notes on a Hoard of eleven Stone Knives of a peculiar type found

in the North of Scotland,” Proc. Soc. Antiq. Scot., vol. xl,
pp. 151-164.

“ On Human Skeletons found at Casterton and Largs, with reports
thereon by Prof. Cunningham and the Hon. John Abercromby,”
Edin. Roy. Soc. Proc., vol. xxvi, pp. 279-309.

1907. “ Notes on Ornamental Stone Balls,” Proc. Soc. Antiq. Scot., vol. xli,

pp. 290-300.

1908. “ Anthropology,” Encyclop. of Religion and Ethics, vol. i,

pp. 561-573.

“ On the Transition Period between the Palaeolithic and Neolithic
Civilisations in Europe,” Arch. Jour., vol. lxv, pp. 205-244.

1910. “ On a Bronze Age Cemetery and other antiquities at Largs, Ayr-

shire,” Archceologia, vol. lxii, pp. 239-250.

“ Chronology,” Encyclop. of Religion and Ethics, vol. iii,
pp. 610-614.

1911. “Death and Disposal of the Dead in Prehistoric Times,” ibid., vol. iv,

pp. 464-472.

Glastonbury Lake- Village. Introductory chapter, vol. i, pp. 1-35.
“Stone Monuments (primitive),” Encyclop. Brit., 11th edition,
vol. xxv, pp. 962-966.

“ Stonehenge,” ibid., pp. 961-962.

1920-21.] Obituary Notices. 169

1914. “ Lake-dwellings,” Encyclop. of Religion and Ethics , vol. vii,

pp. 773-784.

1915. “The Royal Commission on the Ancient and Historical Monuments

and Constructions in Scotland,” Scottish Historical Review ,
vol. xiii, pp. 238-246.

1917. “Darwinism and Human Civilisation, with special reference to the

Origin of German Military ‘ Kultur,’ ” Edin. Roy. Soc. Proc.,
vol. xxxvii, pp. 149-160 (read 5th March ; issued separately
30th April).

“ Comparative Archaeology : its Aims and Methods,” Dumf. Gallow.
Soc. Trans., 23rd November 1917.

1918. “Scottish Crannogs: their Structure, Distribution, and Chronological

Range,” Roy. Arch. Inst, of Great Britain and Ireland,
6th February 1918.

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

John George Bartholomew, LL.D. (Edin.), F.R.G.S., Geographer
and Cartographer to the King. By Geo. G. Chisholm, M.A.,
B.Sc., Reader in Geography, Edinburgh University, Secretary
to the Royal Scottish Geographical Society. Communicated by
The General Secretary.

(MS. received October 19, 1921. Read November 7, 1921.)

It was in the latter part of 1883 or early in 1884 that I became acquainted
with the subject of this notice. At that time I was settled in London, and
on the occasion of a short visit to Edinburgh I called on the late Professor
Geikie, who said to me, “ There’s a man I want you to know, who has got
his head screwed on the right way on the subject of maps.” He named
Mr Bartholomew, and recommended me to call on him, which I at once
did. I found him at his office in Chambers Street, engaged on the actual
work of map-drawing, and he straightway proceeded to give me his ideas
on this subject and to indicate the methods which he wished to see
displaced. Twenty-five years or so passed, during which, owing to the
distance between our abodes, our meetings were infrequent ; still there was,
I believe, scarcely a visit of either of us to either end without our meeting
somewhere — mostly at the London end, where the increasing business and
reputation of the firm with which Mr Bartholomew was connected fre-
quently brought him. Naturally, our meetings were more frequent when
Edinburgh once more became my home in 1908, and still more so after my
appointment to the secretaryship of the Royal Scottish Geographical
Society.

Meantime the remark which Professor Geikie had made in first speaking
of him to me had been amply verified. At that time Mr Bartholomew was
a young man, under twenty-four years of age. He was born at Edinburgh
on the 22nd of March 1860. Yet he had already for several years taken
an active share in the work of the cartographical establishment then
belonging to his father. From 1888, when accordingly he was only
twenty-eight, he had the entire management of the business. In 1889
he married ; and in that year, too, the business was transferred from
Chambers Street to Park Road and became known as the Edinburgh Geo-
graphical Institute — a name retained at the new premises in Duncan Street,
to which the business was removed in 1911.

Dr Bartholomew’s management of the business was signalised from an

1920-21.] Obituary Notices. 171

early date by the inception of a number of enterprises of great boldness,
and those which were carried out raised the reputation of the firm to a
high pitch. First came The Survey Atlas of Scotland, in 1895 ; but this,
it should be mentioned, was mainly the uniting in one whole of sectional
sheets on the scale of half an inch to the mile, which had been appearing for
several years and formed the first topographical maps in which the method
of representing the inequalities of the surface by layering, or the distin-
guishing of areas between successive contour lines by different colours and
tints, was applied on a large scale. It had previously been made use of at
Mr J. G. Bartholomew’s suggestion, at least as early as 1880 in maps
prepared for Baddeley’s Guide to the English Lake District. The method
has since been adopted on topographical maps prepared by many other
geographical establishments, including the Ordnance Survey Department
at Southampton, but by none with greater taste and effectiveness than by
the firm which first so used it. The Survey Atlas of England and Wales
followed in 1903. Both atlases have, besides the large-scale sheets, more
comprehensive maps on a smaller scale, showing the geology and climatic
and other features of the geography of the countries represented. In both,
the maps by Bosse showing the density of population are particularly note-
worthy. For Scotland this map was brought up to date in maps prepared
by Mr Bartholomew for publication in The Scottish Geographical
Magazine, in accordance with the censuses of 1901 and 1911, the latter
included also in the 1912 edition of the Atlas of Scotland. The three
together form an interesting conspectus of census results, although of
course they cannot but exhibit the inevitable defects of all density of popu-
lation maps arising from the necessary arbitrariness in the choice of the
limits of density distinguished by different colours or shades, and the mode
in which town populations are allowed to influence the density tint of the
areas to which they belong.

Before the issue of the second of the two atlases mentioned there
appeared, in 1899, the first volume to be issued of the grandest enterprise
of the Institute — a physical atlas designed on a scale of hitherto unparal-
leled magnitude. The prospectus of the whole work was given to the
public along with the Atlas of Meteorology , which was the first published
of the seven volumes of which the whole work was designed to consist,
and of which this volume was to form the third.

The whole work was then planned in all its essential details. The
first volume, besides containing a general introduction dealing with the
Extent of Land and Sea Surveys, was to be devoted to Geology ; the second
to Orography, Hydrography, and Oceanography. The third, as already

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

stated, is an atlas of Meteorology. The fourth was to be devoted to
Botany, the fifth to Zoology, the sixth to Ethnography and Demography,
and the seventh to General Cosmography and Terrestrial Magnetism. It
was to include in all 212 plates, the titles of which are given in the
prospectus. The prospectus states that the other sections will follow that
on Meteorology in rapid succession, and, if the fact that this anticipation
proved too sanguine will surprise no one who has had anything to do with
the preparation of comprehensive works even on a much smaller scale
than this, it may be taken as a typical illustration of the patient tenacity
that characterised Dr Bartholomew in all his work that a second volume of
the series, the Atlas of Zoogeography, was at last published in 1911, as well
as that many other plates belonging to other sections not yet published
were prepared under Dr Bartholomew’s direction.

It will serve to give some idea of the magnitude of the whole under-
taking to compare the two sections of the atlas which have been published
with the corresponding sections of the atlas of Physical Geography that
had the first place at the time when that of the Edinburgh Geographical
Institute began to be published, Berghaus Physikalischer Atlas. To begin
with, the size of the plates in the Edinburgh atlas is considerably larger
than those of Berghaus — measured from the outer limit of the border
(exclusive of margin) 19J"xl5f", as against 16"xl3". The section on
Meteorology in the Edinburgh atlas has 34 plates (35, including the
frontispiece plate showing the distribution of meteorological stations in the
world at the time of publication) as against 12 in Berghaus, and an intro-
ductory text of 40 pages, besides an appendix of 12 pages (4 giving a list
of meteorological stations, 4 a bibliography, 2 a glossary, and 2 tables), as
against 10 in Berghaus; that on Zoogeography has 36 plates as against 9
in Berghaus, together with an introductory text of 56 pages, exclusive of
a bibliography of 11 pages, as against a text of 8 pages in Berghaus.

All those primarily responsible for the Atlas of Meteorology are now
dead. It was prepared by Dr Bartholomew himself in association with
the late Professor Herbertson, under the editorship of the late Alexander
Buchan, LL.D., F.RS. Among its new features may be mentioned several
maps illustrating isanomalies of temperature, maps showing isonephs, or
lines marking the limits of equal degrees of cloudiness, and isohels, or similar
lines marking the limits of equal extent of sunshine, and maps showing the
paths of barometric minima.

It may be mentioned as another characteristic fact that when the
Atlas of Zoogeography did appear it contained even more than was
promised in the prospectus — 36 instead of 35 plates. In this case the long

1920-21.]

Obituary Notices.

173

interval that elapsed between the drawing up of the prospectus and the
appearance of the volume resulted in a great change in the selection and
arrangement of the plates. The scheme as originally prepared was that
of the late Philip Lutley Sclater, but the zoologists under whose care the
volume was actually prepared were W. Eagle Clarke, F.R.S.E., F.L.S.,
Keeper, and Percy H. Grimshaw, F.R.S.E., F.E.S., Assistant Keeper of
the Natural History Department, the Royal Scottish Museum ; and the
classification adopted naturally answered to the state of zoological science
at a later date than that of the prospectus.

Though the other volumes of the atlas have not yet appeared, it may
be taken for granted that some of the work done with a view to their
publication has been utilised in other works. Thus the volume on
Ethnography and Demography was designed to include plates illustrating
the Production of Edible and Drinkable Commodities, International
Commerce at the End of the Nineteenth Century, and others on the
same subjects as some of those in the folio Atlas of the World's
Commerce (176 plates), published by Newnes early in the present century.
Dr Bartholomew was also responsible for the preparation of the atlas
accompanying the Imperial Gazetteer of India (1908). At the time of his
death he had supervised the preparation of nearly all the plates for the
important political atlas recently completed and published under the title
of The “ Times ” Survey Atlas of the World.

Inevitably Dr Bartholomew’s zeal for geography wras manifested in
many ways apart from the work carried out in the Geographical Institute.
Most conspicuously was this the case in connection with the Royal Scottish
Geographical Society. He was one of the most active and enthusiastic
of those who encountered and vanquished all the difficulties that had to be
overcome in getting it founded in 1884. From the beginning till the time
of his death he acted as one of its honorary secretaries. He was the
contributor both of maps and articles to its magazine — the articles on
“ The Mapping of the World,” in vols. vi and vii. He took a special
interest in the preparation of the Edinburgh number issued in 1919, and
for it he presented to the Society the interesting “ Chronological Map of
Edinburgh showing Expansion of the City from the Earliest Times to the
Present” (a “ present,” however, previous to the last extension of the
city boundaries).

He bequeathed to the Society the sum of £500.

He took great interest in the establishment of the lectureship in
Geography in Edinburgh University, and was a generous benefactor to the
department when the lectureship was founded and equipment required.

174 Proceedings of the Koyal Society of Edinburgh. [Sess.

From 1909 to 1912 he was a member of Council of this Society.

Only those who knew Dr Bartholomew personally could be aware
of the extraordinary difficulties under which the above-enumerated series
of persevering labours were carried on, and the extraordinary resolution
revealed in carrying them through, and only those who knew him in
his earlier years could realise the whole nature of the man. For a great
part of his life, and, above all, in his later years, he had to contend against
constant weak and too frequently ill health. Sometimes he was absolutely
laid aside, but, except on those occasions, he went on steadily and calmly
with his work to the limit of his strength, and never lost his interest
in those things which he had at heart. Again and again, before Council
meetings of the Geographical Society, I had interviews with him in bed,
and the advice that he had to give on those occasions was always eagerly
looked for by the other members of Council.

This constant fight with ill-health naturally gave to him in his later
years a somewhat melancholy expression ; but it was always a calm, grave,
and dignified melancholy untouched by any hint of complaint. It was,
however, an expression that made it difficult to realise the buoyant and
exuberant energy which characterised him when young, and brought
out other sides of his character. I remember particularly one occasion in
the early days of our acquaintance when seated on a brake in the island
of Jersey I was hailed by him from another brake which was going on the
same tour. The two brakes stopped at the same place for lunch, and Mr
Bartholomew, as he then was, entered with sympathetic zest into the
enjoyments of the youngest and most frivolous. Then it was quite easy to
picture to oneself the energy which he had shortly before shown at the
foundation of the Geographical Society.

His later years were further saddened for him, as for others, by the
War, but in connection with it also his character was revealed. He took
the War as a call to national and personal duty, but — though he lost a son
in the War and had another maimed — without any admixture of national or
personal hatred, but always regarding it as a great human tragedy. It
may be mentioned here that he was for many years an elder in the
United Free Church of St George’s, Edinburgh.

In the later years of his life he frequently had to leave his home in
search of improved health. It was on one of those occasions that he met
his end. Early in 1920 he went to Esterel in Portugal, accompanied by his
wife and daughters. Having been taken up to Cintra in the hope that
the hill air would benefit him, he died there on the 13th of April in the
same year, and there he is buried. He left a widow, two sons, and two

1920-21.] Obituary Notices. 175

daughters, the elder of the two sons now the managing director of the
firm styled Messrs John Bartholomew & Son, Limited.

Both at home and abroad the value of Dr Bartholomew’s services to
science were recognised in various ways. He was an honorary member
of many foreign geographical societies, including those of Paris, Portugal,
Budapest, and Chicago. In 1905 the Royal Geographical Society awarded
to him the Victoria Medal “ for his successful effort to raise the standard
of cartography.” In 1918 the Geographical Society of Chicago conferred
on him the Helen Culver Gold Medal. In 1909 Edinburgh University, his
Alma Mater , bestowed on him the honorary degree of LL.D.

In spite of the drawback of ill-health the private life of Dr Bartholomew
was singularly, though quietly, happy, a natural result of the qualities in
him which inspired confidence and affection among all those who came
into intimate contact with him. This notice may be concluded by
testimony on this head borne by a Russian admirer, General Jules de
Schokalsky, President of the Russian Geographical Society, in a com-
munication to this Society, dated Petrograd, October 1920, just after he had
heard the news of Dr Bartholomew’s death. After speaking in the highest
terms of the value of Dr Bartholomew’s cartographical wTork, taking as
an illustration the remarkable precision even of his “ ordinary ” work
in the map on Lambert’s equivalent area projection accompanying the
paper by Dr (afterwards Sir John) Murray “ On the Height of the
Land and the Depth of the Ocean ” in The Scottish Geographical Magazine ,
January 1888 — a precision such as to enable General A. Tillo to obtain
valuable results working from a much reduced copy of it, — the writer goes
on to say : —

“ My personal acquaintance with J. G. Bartholomew began by corre-
spondence. Being interested in geographical and cartographical matters, I
was introduced to him by Sir J. Murray, and we remained a long time
only in correspondence. At the opportunity of the Geographical Congress
at Geneva in 1908 I paid a visit to Edinburgh, and was for a fortnight the
guest of Mr and Mrs J. G. Bartholomew ; and later we met at Geneva,
staying in the same hotel and working side by side on the Congress
business, and became true friends. In 1912 I came on a second visit
to Edinburgh, and stayed about ten days at the J. G. Bartholomew’s
home.

“ These opportunities of meeting and talking with J. G. Bartholomew
and observing his system of working, his relation to his aids in the
Institute and surrounding scientists and other people, revealed his true
character as a man. . . . He was the personified truth itself, and at the

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

same time with such unselfishness and goodness as charmed anyone who
approached him.

“ Geographical science lost in him one of its best workers, his nearest
and his friends true support in their hard moments of life.

“ Coming myself not from a cold-blooded origin, I have no shame when
in writing this my eyes are full of tears, and his country can remember
that there rarely lived a greater gentleman.”

1920-21.]

Obituary Notices.

177

John Aitken, LL.D., F.R.S. By C. G. Knott, D.Sc., LL.D., F.R.S.

(Read January 10, 1921.)

John Aitken, born at Falkirk on September 18, 1839, was the fourth son
of Henry Aitken of Darroch, Falkirk, head of a well-known legal firm
in that town. He was educated at the Falkirk Grammar School and the
University of Glasgow, where he studied with a view to a career as an
engineer. Two years of his apprenticeship he served in Dundee, and three
years with Messrs Napier & Sons, shipbuilders, Glasgow. After finishing
his apprenticeship as a marine engineer he broke down in health, and was
compelled to abandon all thought of carrying out his profession. Thence-
forward his interest lay in the line of scientific and especially physical
research, for which he received a great inspiration while attending Lord
Kelvins (then Sir William Thomson’s) classes in natural philosophy.

His early training as an engineer was of incalculable value all through
the long series of physical investigations which made his name famous in
the ranks of experimenters. Most of the apparatus used in his researches
was not only devised by him but constructed with his own hand. The
drawing-room of the house he occupied latterly in Falkirk was transformed
into a laboratory and workshop, with a fine turning-lathe placed in front
of the window and supplied with all kinds of tools of the most approved
pattern. A carpenter’s bench and work-tables laden with glass-work, blow-
pipes, and many odds and ends of apparatus in the course of construction
or of apparatus which had served its purpose, covered the floor space, while
cabinets along the walls contained drawers full of thermometers and other
delicate meteorological instruments.

The earliest line of work which brought out his experimental skill was
a discussion of colour sensations in a paper read before the Royal Scottish
Societ}^ of Arts in 1872. He devised new methods of experimenting, and
elaborated a modified form of Young’s three-colour theory of sensation,
supporting it by means of many ingenious experiments. Another early
line of thought led him to discuss the conditions of boiling of liquids and
condensation of vapours, which he showed to depend on the presence of
free surfaces separating different states ; and it was by following up some
of the ideas suggested by this work that he hit upon what will probably
be regarded as his greatest contribution to physical science. This was the

demonstration that water vapour in the atmosphere will not condense to
VOL. xli. 12

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

form clouds unless it has some solid or liquid nucleus to condense upon.*
Dr Aitken worked out this whole research with unswerving zeal, clearing
away by a magnificent series of control experiments many objections which
seemed at first sight difficult to meet and even inconsistent with the broad
theory. He brought into prominence the vast importance of the dust in
the atmosphere, not only visible dust but the impalpable dust particles
which provide nuclei for the condensation of vapour and the formation of
visible drops of rain or mist. By an interesting process of evolution he
gradually constructed a form of apparatus by which, from the number of
raindrops produced in a closed region of saturated air, he was able to
calculate the number of dust particles in this region. A slight expansion
by means of an air-pump in connection with the closed region produced
a cooling in the saturated air, from which the vapour condensed on the
dust particles and formed tiny drops of water. These, falling on a silvered
surface ruled in small squares, were readily counted. This was the so-called
Dust-counter, the final portable form of which was an instrument of con-
siderable precision in the hands of the skilful meteorologist.

The production of a fog cloud in a receiver from which saturated air
was being extracted was a phenomenon which had often been seen by
experimenters; but it was reserved for John Aitken not only to give a
complete explanation of the phenomenon but to open up an entirely new
line of research.

Aitken s experiments proved that when the saturated air was free of
dust no cloudy condensation took place on slight expansion, for there were
no particles to serve as nuclei. He found, however, that once the air was
cleared of dust by filtration through cotton- wool, a more rapid expansion
sometimes led to cloudy condensation. The explanation of this was
subsequently given by C. T. R. Wilson, who showed that ionised air,
although dust free, produced cloudy condensation when a considerable
expansion with accompanying cooling took place. There has consequently
been a tendency in some quarters to explain condensation of vapour in
terms of the presence of ions, arguing that Aitken’s dust particles were
unnecessary as a factor in the process. But such a view shows an absolute
lack of appreciation of the whole meaning of the phenomenon. The sudden
expansion and cooling required to produce cloudy condensation on ions
are much greater than can ever occur in nature. On the other hand, when
dust particles are present a very slight expansion with accompanying slight

* See “On Dust, Fogs, and Clouds,” Trans. Roy. Soc. Edin., xxx, 1880-1 ; and various
papers on dust particles in the air, Trans. Roy. Soc. Eclin., vols. xxxv to xxxix, 1887-1899 ;
and many papers in the Proceedings.

1920-21.] Obituary Notices. 179

cooling suffices. An experiment often made is to hold a bunsen flame for
a moment within a receiver, set the receiver immediately on the air-pump
plate with a dish of water within it, and then pump some of the air out.
A dense fog cloud is formed, and this is not unfrequently referred simply
to the ionisation due to the flame. But the argument is faulty, for of
course there are numerous dust particles also produced by the flame, and
it is impossible in such an experiment to discriminate between the effect
of the particles as fog producers and the effect of the ions. Moreover,
Aitken himself proved that when dust particles were undoubtedly present
electrification of the air did not increase the cloudy condensation.

When we recognise that dust particles are always present in the
atmosphere, and that a slight cooling of the saturated air is the cause of
the production of raindrops, and when we further bear in mind the
beautiful demonstration given by Aitken that no cloudy condensation is
produced in saturated dustless air on slight cooling, there is no escape from
the conclusion that mist, fog, and cloud require for their formation the
presence of dust particles.

Another important direct result of Aitken’s experiments on cloudy
condensation, and especially of his methods of counting the raindrops
formed, is worthy of mention. Sir J. J. Thomson in his classical experi-
ments on the mass and charge of an electron made use of Aitken’s method
of condensation in obtaining one of the measurements on which the deter-
mination of these two small quantities depended.

Meanwhile, Aitken himself pushed his own investigations in many
directions, such as the meteorological and industrial conditions governing the
production of dust particles in the air, the influence of locality and altitude,
the effect of prevalent winds and of cyclonic and anticyclonic distributions.

Closely connected with this whole research is his important paper on the
formation of dew.* His views, though now generally accepted, were strongly
combated by certain authorities at the time of their first promulgation.
What he showed by skilfully arranged experiments was that the vapour
which condenses as dew on cold surfaces comes mainly, if not entirely, from
the ground below and not from the air above. He also showed that the
so-called dewdrop on leaves of plants was not dew at all, but was exuded
sap. He has also placed on record some interesting observations on hoar
frost; and in a paper published in the Journal of the Scottish Meteorological
Society he has given a remarkably clear description of the formation of
ground ice.

In his presentation of papers before our Society, in whose Transactions
* See “ On Dew,” Trans. Roy. Soc. Edin ., xxxiii, 1885.

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

and Proceedings his most important work is published, Dr Aitken spared
no pains in bringing before his audience the very experiments he had
devised in following out his ideas. Thus he imitated on a large experi-
mental scale the production of cyclones and the manner of their trend over
the earth’s surface.* Whether, in view of the new information we have in
regard to the vertical distribution of temperature in cyclonic and anti-
cyclonic distributions, Aitken’s own views as to the genesis and maintenance
of cyclones will continue to meet with acceptance, it is perhaps too soon to
give a judgment. He himself believed that apparent discrepancies could be
explained, and his latest paper on this subject, published in the Proceedings
of the Royal Society of London, discusses many of the physical relations in
an interesting and profound way. In this kind of work, however, he was
handicapped from lack of mathematical equipment.

With a mind keenly alive to all problems of a meteorological character.
John Aitken entered in 1884 upon a long series of experiments on the
measurement of air temperatures. In the majority of our meteorological
stations the thermometers are placed within what is known as the Stevenson
screen. This form of screen was long ago found to be quite unsuitable for
hot climates, and in India the thermometers are placed under a broad shed
through which the air courses freely. Aitken soon satisfied himself that
in this country also the temperature given by thermometers hung within
the Stevenson screen read several degrees too high when the day was fine
and sunny. After many experiments on various forms of screen, he finally
devised a form free from the defects of the Stevenson screen, and incidentally
made many other interesting and important observations on temperatures
of air and soil and solar radiation. At his death on November 14, 1919,
he left in manuscript what might be called his matured views after
thirty years of experimenting, wherein he lamented that meteorologists
still continued to use a demonstrably inefficient method of screening the
thermometer from the effects of radiation, direct and indirect. This paper
has been published in the Proceedings of the Royal Society of Edinburgh,
and it may well be regarded in the light of a scientific legacy from a great
natural philosopher.

The bulk of his estate Dr Aitken left in the hands of trustees to use
(1) for the benefit of the poor of Falkirk; (2)^to establish a temperance
public-house in Falkirk. He also left a fund of £1000 to the Council of
the Royal Society of Edinburgh to meet the cost of publication of a
collected edition of his more important papers. This is now being prepared.

* See <c Notes on the Dynamics of Cyclones and Anticyclones,” Trans. Roy. Soc. Edin.,
xl, 1900 ; also Proc. Roy. Soc. Edin., xxxvi, 1916.

1920-21.] Obituary Notices. 181

I have touched only on the outstanding problems which Aitken tackled
and solved; but his many papers on physical subjects show that he
possessed in a singular degree the power of clear thinking and a real
intuition for the devising of illustrative experiments. His one aim was to
get at the truth. He was severely critical of his own experiments, making
sure at every step that all precautions had been taken against possible
flaws of adjustment or fallacies of reasoning. He was never satisfied until
a clear issue was established. Thus for many years he was unable to find
a convincing explanation of the great increase in the number of dust
particles at certain times of day at Kingairloch, a small holiday resort
on Loch Linnhe, to the south of Fort William. Time and again he returned
to the inquiry ; and at length he was rewarded by the discovery that the
source of the particles was the foreshore under action of the rays of the sun
at certain conditions of tide.*

After the publication of his great paper on Fogs and Clouds, Aitken
was recognised as one of the original experimenters of his day. In due
course he received honours and medals from various scientific societies,
including the Keith and Gunning Prizes from the Royal Society of
Edinburgh, and a Royal Medal from the Royal Society of London. In
1899 he received the degree of Doctor of Laws from the University of
Glasgow.

Much though his friends desired it of him, Aitken would never accept
office as president or vice-president in the societies to which he brought
credit and renown. To the end he remained the same quiet, modest
investigator, keenly interested in all true scientific progress, and never
accepting any theory which seemed to him insufficiently supported by
physical reasoning. Every problem which presented itself was studied in
his own way and by his own methods, and to him in a peculiar sense we
might well apply the Horatian line from which the Royal Society of
London has taken its motto —

“Nullius addictus jurare in verba magistri.”

Handicapped through his long life by ill-health, but blessed with a
competency which made him independent, John Aitken was fortunate in
being able to cultivate his inborn powers undistracted by official duties.
Still more fortunate the country which could claim him as one of its
distinguished sons.

* See “The Sun as a Fog Producer,” Proc. Roy. Soc. Edin., xxxii, 1912.

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

Yves Delage. By Professor J. H. Ashworth, F.R.S.

(Read January 9, 1922.)

The loss of Professor Yves Delage is deeply felt by a wide circle of friends
and fellow-workers by whom he was held in the highest esteem for his
outstanding merits as an investigator and for his unaffected simplicity.
He was a pupil of Lacaze-Duthiers, and obtained his doctorate in 1881 for
his “ Contribution a l’etude de l’appareil circulatoire des crustaces edrioph-
thalmes marins.” His next important work was his famous memoir (1884)
on Sacculina, in which he described the structure and made known for the
first time the complete life-history of this remarkable parasitic crustacean
and its extraordinary relations to its host (crabs). Succeeding memoirs
dealt with Balaenoptera, the histology of Convoluta, the functions of the
semicircular canals — Delage was not only a first-rate morphologist, but a
keen physiologist, — with the otocysts of invertebrates as organs of orienta-
tion, and with the development of siliceous and fibrous sponges.

In. 1895 appeared his stimulating book on Lheredite et les grands
yproblemes de Biologic generate , an impressive example of the great extent
of his knowledge and the clearness of his outlook. In this volume, Delage
discussed in masterly fashion the structure of protoplasm, development,
heredity, the evolution of species, and the principal theories relative to
these subjects. In his views on evolution he was definitely Lamarckian,
and on many points opposed to Weismannism. By this time he had turned
his attention to the factors — external and internal — which determine the
development of the egg, and he propounded a theory to account for the
activation of the egg which led him to the experiments on artificial
parthenogenesis with which his name (and that of Jacques Loeb) will ever
be associated. He was able, by treating eggs of sea-urchins in hypertonic
sea water alternately with tannin and ammonia, to activate them, and he
succeeded in rearing some of the resulting larvae through their meta-
morphosis. His researches in this domain extended over some ten years.
His last published work (1920) is an important volume on dreams, in which
he discussed the principal theories, psychological and physiological. A
list of his publications shows not only his wonderful output of first-rate
work — for his industry was extraordinary — but also his many-sided
intellect.

Delage rendered notable service to biology by founding in 1895

1920-21.] Obituary Notices. 183

L’Annee biologique, some twenty volumes of which have appeared
giving critical abstracts of memoirs on general biology. Reference should
also be made to the Traite de Zoologie concrete, written in collaboration
with Professor Herouard, the five volumes of which are marked by great
lucidity of exposition.

No account of his services to biological science would be complete which
omitted to record an appreciation of his work for the marine biological
station at Roscoff, first as assistant-director under Lacaze-Duthiers, and,
since 1900, as director. In 1908-9 he reconstructed, extended, and re-
organised the station, and for a generation has been an inspiration to many
grateful workers there.

He succeeded Lacaze-Duthiers twenty years ago in the chair of Zoology
at the Sorbonne, and was in active work there practically to the end of his
life. For several of the last years an affection of the eyes made him almost
blind, so that he was unable to carry on himself researches requiring
delicate technique ; but his intellectual vision remained as keen as ever,
and younger workers continued to receive freely of his encyclopaedic
knowledge and his warm encouragement. He was elected an Honorary
Fellow of the Society on 21st June 1920, and died on 7th October 1920,
aged sixty-six.

184 Proceedings of the Royal Society of Edinburgh.

[Sess.

Edward William Prevost, Ph.D., F.I.C. By Dr Henry Barnes,

O.B.E., M.D.

(Read January 9, 1922.)

By the death of Dr Prevost, which took place at his residence, The Sandi-
way, Ross-on-Wye, on 7th October 1920, the Society loses one of its oldest
Fellows and one keenly interested in its welfare.

Dr Prevost was born at Carlisle in 1851, being the elder son of Colonel
T. W. Prevost, at that time Staff Officer of Pensions in the district. His
early education was under private tutors and at Glenalmond, which school
he left in 1864 for Rugby, where he remained till 1867. After two years
on the science side at Edinburgh University he proceeded to Leipzig and
Heidelberg, where he studied chemistry under Bunsen and graduated Ph.D.
Returning to England, he worked for two and a half years at the Royal
College of Science and Art, South Kensington, undertaking chemical
research for Norman Lockyer. For several years he was a tutor in
chemistry at Oxford, where he was employed under Odling as teacher of
quantitative chemistry. He carried out in Oxford an investigation into
the nutritive value of the turnip grown in (a) unmanured, ( b ) manured,
soil. From May 1879 to the spring of 1881 he was Professor of Chemistry
at the Royal Agricultural College at Cirencester. On leaving in 1881 he
retired into private life and took up farming, first at Elsmere, near Tam-
worth, and afterwards at Elton, Newnham, where in 1890 the first part
of the Cumberland Dialect Glossary was written. In 1882 he received the
Gold Medal of the Royal Highland Agricultural Society for a paper on
the cultivation of potatoes. In 1878 he obtained the Fellowship of the
Institute of Chemistry of Great Britain and Ireland. While living at
Newnham he joined the Gloucester Garrison Volunteers, afterwards attain-
ing the rank of major. He became a Fellow of the Society in 1875, one
of the proposers being Professor Piazzi Smyth, then Astronomer Royal for
Scotland, and a paper by him on “ An Ammonium-Cupric Zinc Chloride ”
appears in our Proceedings, vol. ix, 5th February 1877. It is the analysis
of the substance which grows on the brass binding screws and carbon of a
Leclanche cell.

It is, however, by his Glossary of the dialect of Cumberland that
Dr Prevost will be best remembered. He began his study of this subject
nearly thirty years ago, taking for groundwork the Glossary formed by
the late Mr William Dickinson of Workington, published by the English
Dialect Society (1878-81). The first results of his labours, in which he
received assistance from many correspondents throughout the country, was

1920-21.] Obituary Notices. 185

the publication in 1899 of A Glossary of the Words and Phrases 'pertain-
ing to the Dialect of Cumberland , by W. Dickinson, F.L.S., rearranged,
illustrated, and augmented by E. W. Prevost, Ph.D., F.R.S.E. The ampli-
fications and fresh matter contained in this volume constituted practically
a new work, which would in itself have made Dr Prevost’s reputation as a
painstaking and persevering compiler, but from then to the time of his
death his labours in search of unrecorded words, elucidations of meanings,
and illustrations of dialect usage were unceasing. In 1905 he published
a supplementary volume which, like the earlier volume, contained a com-
prehensive Digest of the Phonology and Grammar of the Dialect, by
Mr S. Dickson Brown, M.A. Lond., F.R.G.S. Continuing his efforts with
undiminished ardour, Dr Prevost has for the last fifteen years been adding
to the stock of information already garnered ; and when he learned how
fragile was his hold upon life, he devoted all his energies to complete
his work while he still had power to do so. The application that this has
involved has been continuous and close. Many pages of correspondence
were devoted to discovering the exact significance of a single word, slight
shades in difference of meaning being cleared up, and illustrative quotations
sought for. New words kept cropping up constantly, for in the compila-
tion of a glossary there is no finality.

Dr Prevost just lived to draw to a close the task he had set for himself
of compiling a second supplement of the Glossary ; and it was his last wish
that, should he himself be prevented from finishing this supplement and
seeing it through the press, the duty should be undertaken by Mr James
Walter Brown of Carlisle, who had been in close collaboration with him
upon dialect work for more than twenty years.

The cost of publishing this supplement has been assured by the
Philological Society of London, and it will be issued at an early date.
Dr Prevost was deeply interested in music, and was a skilful organist.
He had explored and inspected the mechanism and equipments of many
of our cathedral organs, and in a letter to a friend three days before his
death were the words, “ I am off* to Gloucester to see how the reconstruction
of the organ is getting on.”

In December 1918 Dr Prevost was found to have an ailment which
might cause his death at any moment, and from that time he was con-
demned to a life of physical inactivity. For the last few weeks he had
been able to take more exercise, and so recently as last September he was
well enough to go to Devonport to see H.M.S. Hood , in which his younger
son is a midshipman. Soon after his return the threatened seizure occurred,
and ended in his death at the age of sixty-nine years.

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

Sir Thomas R, Fraser. By Harry Rainy, M.A., M.B.,

C.M., F.R.C.P. Ed.

(Read January 23, 1922.)

By the death of Sir Thomas Richard Fraser on 4th January 1920 the
Royal Society and the University of Edinburgh have lost one of their
most distinguished ornaments, who, by the extent and carefulness of his
research work, gained a European reputation, and left behind him an
example that must serve as an inspiration to his successors in the depart-
ment to which he devoted himself. He was born in Calcutta on the 5th
of February 1841, and his education, both at school and at the university,
was Scottish. In the Edinburgh University he had the advantage of
having such men as Sir Lyon Playfair, Hughes Bennett, Sir James
Simpson, and Sir Robert Christison as his teachers, whilst amongst his
fellow-students and colleagues in later life he reckoned men like Professor
Rutherford, Sir Thomas Grainger Stewart, Sir William Turner, Professor
Crum Brown, Professor Sanders, and Lord Lister. Under the stimulus
of such associates it is not surprising to find that he made his mark even
whilst he was a student, and that his graduation thesis in 1862, of which
the subject was “ On the Characters, Actions, and Therapeutic Uses of the
Ordeal Bean of Calabar” ( Physostigma venenosum), embodied a research
of the highest order, which brought him into prominence both at home
and abroad, winning for him, in association with a later paper on the
same subject which appeared in the Transactions of the Royal Society,
the Barbier Prize of the Academy of Sciences of Paris, which he received
in 1868. Shortly after graduation he acted as resident physician in the
Royal Infirmary, and in 1869 he was appointed assistant physician to
the Infirmary. In 1863, largely on the strength of his research work, he
was chosen assistant to the Professor of Materia Medica, a post which he
held until 1870, when he relinquished it in order to become a lecturer on
materia medica and therapeutics in the Extra-Mural School of Medicine.
Four years later he was appointed medical officer of health for Mid-
Cheshire, a district which at that time included a population of over
123,000 persons. In those days the work which fell to be discharged by
a medical officer was less sharply defined than it is at the present time,
and Dr Fraser’s methodical mind and organising capacity led to the
development of his work in a way which can scarcely be appreciated by

1920-21.] Obituary Notices. 187

those who nowadays have their duties much more explicitly laid down.
At this time the Public Health Act had just been placed on the Statute-
Book, and the amount of organising work that fell to Dr Fraser may be
more readily realised when it is observed that not only did the adminis-
trative area extend over fully one half of Cheshire, but that it was divided
into twelve districts under twelve boards of guardians both rural and
urban, and that the medical officer of health had several inspectors and
assistant inspectors under him, whose work was entirely guided by him,
and who constantly reported directly to him on all matters of importance.
His time was thus from the first occupied by the public service, and he
never undertook any private practice in the district. Sir Thomas Fraser
himself always laid stress on the importance of this time, not only because
of its opening up a new field of work to him, but also because the com-
paratively regular duties enabled him to indulge in a certain amount of
open-air recreation, such as working in his garden and even riding to
hounds on occasion. To this he attributed the fact that his health, which
had been considerably strained by the arduous tasks of original research,
was much improved, and the relaxation enabled him on his return to
Edinburgh to undertake further research with a better prospect of being
physically able to stand the strain of the work. Another factor which
greatly assisted him in the discharge of all these duties was the hearty
co-operation of his wife, Lady Fraser, a daughter of the Rev. R. Duncan,
whom he married in 1874, without whose constant care for over forty-five
years he would scarcely have been able to complete the tasks to which he
devoted his life.

On many occasions Sir Thomas Fraser was accustomed to say that he
thought that in all research work there is a very considerable element of
chance in the success of the undertaking. But whether this is so or not,
it is a striking fact that nothing that he touched failed to become interest-
ing and valuable, and, without denying the possibility of a certain degree
of good fortune in the way in which his topics developed, a great deal
more is attributable to the sound judgment with which he selected the
various subjects of his investigations, and the extreme conscientiousness
and ability which he displayed in even the smallest details of the research.

In 1877 the death of Sir Robert Christison made a vacancy in the chair
of Materia Medica, and Dr Fraser at once became an applicant. By that
time his contributions in various branches of research in materia medica
had become extensive, and his application contained the titles of no less
than twenty-one important contributions, as well as references to numerous
papers which were written for the Edinburgh Medical Journal and other

188 Proceedings of the Boyal Society of Edinburgh. [Sess.

scientific publications. Amongst the most important of these contributions,
in addition to researches founded on his thesis on the Calabar bean, were
a series of papers in which he was associated with Professor Crum Brown,
“ On the Connection between Chemical Constitution and Physiological
Action,” which in many respects formed the basis of much of the work
which was done in the production of new drugs in the following fifty
years, and which are still of outstanding importance. They were early
recognised as epoch-making, and received recognition by the award of the
Makdougall Brisbane Prize by the Boyal Society of Edinburgh in 1868.
During the same time he published papers on the “ Antagonism between
the Actions of Physostigma and Belladonna,” thus showing how the
opposing actions of their active principles could be made to fulfil the
century-old desideratum of Goethe for drugs which would precisely neutral-
ise each other’s action. During the same time he also published a short
investigation in the Journal of Anatomy and Physiology on the effects of
rowing on the circulation, which emphasises the fact that he was always
a keen supporter and at one time a member of the Edinburgh University
Boat Club. Although latterly his health prevented his taking any
practical share in the work, he never lost his interest in the club, and
was alwa}^s its loyal supporter in every difficulty.

It was striking to note, in the case of so young a man as Dr Fraser was
when he applied for the chair, how many of the leaders in pharmacology
throughout the whole Continent knew him by his work and were sup-
porters of his candidature. No fewer than five eminent French professors,
including Dujardin-Beaumetz and Paul Bert, were reckoned amongst their
number, whilst eleven German and three American teachers also warmly
supported his claims, giving him strongly worded testimonials. It is only
necessary as an illustration to quote the last paragraph of the testimonial
which he received from Schmiedeberg, who was then the illustrious pro-
fessor of pharmacology in Strasbourg : “ It would be superfluous for me to
enter into further details concerning your successful scientific career ; not
only in your own department, but in still wider circles, it is sufficiently
known and it is valued and esteemed by all. I have thus always been of
the opinion that no one is so worthy of the honour of being Sir Robert
Christison’s successor as you, most honoured colleague, for you are already
his intellectual successor. In the interest of that science which I also have
the honour to represent, it is my sincere wish that you may be successful
in obtaining this chair, so that you may be in a position to enrich, as
heretofore, the sciences of materia medica and toxicology by new observa-
tions and discoveries.” To those who know how careful Schmiedeberg

1920-21.] Obituary Notices. 189

always was in giving testimonials of this nature, such an encomium proves
better than almost any other how greatly Fraser’s work had impressed
the minds of these Continental leaders whose opinions were worth
consideration.

His accession to the chair brought increased responsibilities in con-
nection with his duties at the Royal Infirmary, where, as a clinical
professor, he now took charge of wards with the status of a full physician.
But, in spite of the extra labours thus thrown upon him, we find a
continuous succession of papers on subjects of the utmost scientific and
clinical value rapidly succeeding one another in the following years. The
subjects of some of these researches had already occupied his attention
before he returned as a professor to Edinburgh. Amongst these a series
of papers on Strophanthus and other digitalis bodies was specially note-
worthy, and the subject was only laid aside from time to time with a view
to returning to it later. Thus his paper, published in early days, on the
Kombe arrow poison was followed by a long series of communications on
the various varieties of Strophanthus and their selective actions, many of
which appeared in the Transactions of the Royal Society. This series of
papers was recognised by the awarding to him of the Keith Prize by the
Royal Society of Edinburgh for the period 1891-93. During this time
he also wrote on various other arrow poisons, on snake venom, and the
anti- venomous properties of bile.

Whilst carrying on all this research, as well as the ordinary duties of
lecturing systematically on materia medica, Professor Fraser developed
great powers as a clinical teacher, and many of the students who knew
comparatively little of his laboratory research work felt that his teaching
in the wards, whilst he was still in full vigour, was an inspiration. The
scrupulous care with which he established the clinical facts of each case
he examined, the clear logic of his deductions, and the reasoned lines of
treatment did much to impress upon his hearers the conviction that
clinical medicine could almost be raised to the level of an exact science.
Three qualities he possessed in notable degree : accurate observation, clear-
ness of vision which refused to be drawn away by side issues, and an
indomitable will which triumphed to the end over ill-health and bodily
weakness. His intimate knowledge of materia medica found the fullest
scope in combating disease in the wards under his charge, and whilst, to
the mere research worker, there may have seemed to be a lack of applica-
tion of his researches to clinical uses, those who were privileged to be his
students were able to contradict that impression by their daily experience
in the wards. As a clinical teacher he has left as a legacy to the school

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

that tradition of high ideals and of exacting standards of duty which were
characteristic of all his work.

A break occurred in his teaching in the school during 1898, when he
went to India to act as president of a commission appointed to inquire
into the whole question of bubonic plague, its origin, transmission, and
treatment. His capacity and accuracy in detail made itself manifest at
once, and a voluminous report was issued in 1901 which threw considerable
light on the subject of inquiry.

In addition to his academic work, Professor Fraser filled many important
positions in the scientific world, and even before he received his commission
to the Edinburgh chair he was engaged, at the request of the Admiralty,
as a member of the committee to inquire into and report on the causes
of scurvy which broke out in Sir G. Nares’ Arctic expedition. On a
subsequent occasion he acted as president of the section of materia medica
and pharmacology at the London meeting of the International Congress.

It was natural that a man of Sir Thomas Fraser’s clear thinking and
business capacity should become interested in professional matters outside
the duties of his chair, and we find that he occupied many responsible
positions where his powers in this direction could find scope. For twenty
years, from 1880 onwards, he acted as Dean of the Medical Faculty in
Edinburgh University. He was also a member of the University Court
from 1904 to 1913, and in 1905 he became University representative on the
General Medical Council, of which body he remained a member for ten
years ; and during that time, amongst other tasks, he took an active part
in the 1914 issue of the British Pharmacopoeia. For many years he was
the valued principal medical adviser of the Standard Life Assurance
Company, and in that capacity his sound judgment and keen critical
instincts made him a more than usually competent guide in the difficult
problems which constantly emerge in such work. He also discharged for
nearly twenty-four years the duties of consulting medical adviser to the
Prison Commissioners for Scotland, in which capacity his tact and judgment
repeatedly proved of great service.

His distinguished career as a research worker also brought him many
well-earned honours. At an early age, even before he had obtained a
chair in Edinburgh, he had been elected a member of the Royal Societies
of Edinburgh and London, and had been laureated by the Institute of
France. At subsequent dates he received the recognition of the Turin
Academy of Medicine and of the College of Physicians of Philadelphia.
He was created an Honorary M.D. of Dublin, an Honorary Sc.D. of
Cambridge, and received the degree of LL.D. from the Aberdeen and

1920-21.] Obituary Notices. 191

Glasgow Universities. On the death of Sir William Gairdner in 1907,
Sir Thomas Fraser succeeded him as Honorary Physician to His Majesty
the King in Scotland, the honour of knighthood having previously been
conferred on him in 1902. During the years 1900 to 1902 he filled the
Presidential chair at the Royal College of Physicians of Edinburgh, and
discharged its duties with great efficiency. In 1913 he was elected a
member of the Athenaeum Club under the special rule authorising the
committee to elect nine members in each year because of their distinguished
eminence in Science, Literature, or the Arts, or for public services. This
distinction Sir Thomas Fraser highly appreciated.

On retiring from his Professorship in 1919 he was laureated LL.D. of
the Edinburgh University, and his portrait, painted by Mr Robert Home,
was presented to him by a large number of his former students, colleagues,
and professional friends.

During his earlier years, Professor Fraser, though never very robust,
was of a wiry constitution, and took great pleasure in many forms ’of
outdoor exercise. But, as the years passed on, he suffered from repeated
attacks of bronchitis which sapped his vitality, and rendered strenuous
efforts difficult or impossible, and at the age of seventy he fractured his
femur, thus rendering himself still less fit for physical exercise. For many
years he spent his summer holidays at Druimbeg, a small country property
which he purchased for himself on the shores of Loch Shiel in Argyllshire,
where he delighted in showing hospitality to his friends, and where his
garden, stocked with numerous plants of therapeutic interest and of beauty
of foliage, gave him constant interest and pleasure. Whilst his strength
enabled him, he also enjoyed the sports of trout-fishing, shooting, and hill-
climbing, though he gradually had to abandon these amusements as his
health became less satisfactory. To the end, however, his mind was as
clear as ever, and when overtaken by his last illness he was busily engaged
in working up the material which he had accumulated in the course of his
long life of clinical and laboratory research.

In many respects Sir Thomas Fraser’s position in the school was unique.
He formed a link between the older ideals represented in Sir Robert
Christison and the newer methods of separating the laboratory worker
much more completely from the physician in charge of patients, and this
change, though probably inevitable, is not without great drawbacks, for
it eliminates much of the human element from the life-work of those who
now guide the profession in therapeutic matters ; and although this permits
of a higher degree of specialisation, it certainly debars the worker from
that close contact with the problems confronting the practising physician

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

which so often in former days opened up new lines of thought and action,
and led to some of the most important advances in the region of thera-
peutics.

In Sir Thomas Fraser the two outlooks were harmoniously combined,
with the result that he was not only respected as a research worker, but
loved and trusted as a physician.

1920-21.]

Obituary Notices.

193

T. Lindsay Galloway, M.A., F.G.S., A.M.Inst.C.E., M.Inst.M.E.

By Professor W. P. Ker, F.B.A., M.A.

(Read January 9, 1922.)

The following lines are written not as part of a biography but in order
to bring out what Lindsay Galloway’s contemporaries recognised in him,
his combination of scientific attainments and ability with practical good
sense and very wide interests in literature and philosophy, and to pay
honour to a man whose friends found him always unfailing in honour
and goodwill.

Lindsay Galloway distinguished himself at Glasgow University in
mathematics and natural philosophy. Sir William Thomson (not yet
Lord Kelvin) regarded him as one of his most brilliant students, and
entrusted him, when he was not much more than twenty, with the task
of testing the new piano- wire invention for deep-sea soundings in a voyage
to Brazil. Galloway was so successful that the Brazilian Government
asked him to do the soundings for them along their coast from Para to
Pernambuco. He might have found a career there, but he had determined
to work as a mining engineer, and it was with the experience that he had
acquired on the Tyne that he settled down in Kintyre at the Drumlemble
coal-pit.

Lindsay Galloway had sat under both William Thomson and Edward
Caird, and he followed all his life the studies of science and philosophy

which he began under these masters. His work in mathematics and

physics gave him a great advantage over most moral philosophers, while
his philosophy made him sceptical about the more positive and dogmatic
theories of Nature which were popular fifty years ago. He was also a
good scholar and a lover of poetry. Indeed, very few men of his time
have come nearer to the old ideal of the humanities ; there was no province
of knowledge in which he could not find his way. He shared with
Mr Macdonald of Largie in the foundation of the Archaeological Society
of Kintyre, and was ready to give his time and energy to an adventure
which would have been profitable in results for the history of Scotland
— which yet may be successful in spite of the sudden loss of two of the
leaders.

Within the last few years Galloway gave some attention to the im-
provement of a method of determining “the relative directions of two

VOL. xli. 13

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

reference lines or bases for mining surveys ” which he had imagined, and
was engaged in making observations with the magnetometer or magnetic
reflector he had invented for this purpose up to the very day of his death.
He described the magnetic reflector and the method of employing it in
conjunction with a theodolite in a paper read before the Institution of
Mining Engineers in 1918 {Trans. Inst. M.E., vol. lvi, p. 222), and a method
of employing two magnetic reflectors when greater precision is required
in a second paper read before the same institution in 1920 (vol. lx, p. 235).
His other papers include the following : “ On the Present Condition of
Mining in some of the Principal Coal-producing Districts of the Continent,”
Proc. N. of E. Inst, of Mining and Mech. Engineers , vol. xxvii, 1878; and
one on “ James Watt,” Proc. Roy. Phil. Soc. Glasgow , 1920.

He was elected a Fellow of the Royal Society of Edinburgh in 1918,
and died on 22nd September 1921 at Kilchrist, near Campbeltown.

1920-21.]

Obituary Notices.

195

Henry Barnes, O.B.E., M.D., LL.D. Contributed by his daughter,

Miss E. Barnes.

(Read January 9, 1922.)

Henry Barnes, O.B.E., M.D., LL.D., was the third son of Mr Joseph
Barnes, yeoman, and was born at Aikton, Cumberland, on 20th July
1842. He was educated at St Bees Grammar School, and afterwards at
Edinburgh University. He graduated M.D. with honours in 1864, and
in the same year he became a member of the Royal College of Surgeons
(England). He settled in Carlisle in 1866, and in 1873 he was appointed
honorary physician to the Cumberland Infirmary, which position he held
till 1903. He was then appointed consulting physician, in which office
he remained up to the time of his death. From 1904 to 1910 he was
chairman of the committee of management. In 1906 he was elected
one of the vice-presidents, and in November 1920 he accepted the office
of president. It will thus be seen that his labours for the Cumberland
Infirmary extended over nearly half a century. Large extensions were
made to the institution in 1908. A new Nurses’ Home was built, a new
ophthalmic and X-ray department were provided, and additional wards
added. An inscription over the door of the Nurses’ Home states that it
was named “ the Barnes Wing in recognition of the services rendered by
Henry Barnes, M.D., in the enlargement of the Infirmary.” It was also
mainly due to his efforts that the Infirmary received a grant of £30,000
from the British Red Cross Society at the end of the war.

Dr Barnes was keenly interested in the work of the British Medical
Association. It was through him that the Cumberland and Westmorland
Branch was formed. Later on the area was extended and the title was
changed to the Border Counties Branch, and in 1876 he was elected
president. In 1896 the annual meeting of the British Medical Association
was held in Carlisle under Dr Barnes’ presidency. Two years later, when
the annual meeting was held in Canada, the degree of LL.D. from the
M‘Gill University was conferred upon him. He was also a Fellow of
the Royal Society of Edinburgh (1882), a Fellow of the Royal Society
of Medicine, and a Fellow of the Botanical Society of Edinburgh.

In addition to his professional work for the Cumberland Infirmary,
Dr Barnes was physician to the Carlisle Dispensary, the Carlisle Fever
Hospital, the Border Counties Home for Incurables, and consulting
physician to the Silloth Convalescent Institution. In 1907 he helped

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

to found the Cumberland Branch of the British Red Cross Society, and
acted as honorary secretary from the time it was founded to 1918.
During the war his work was most strenuous, and in recognition of his
services he received from the King the O.B.E.

Dr Barnes was made a Justice in 1887, a county magistrate in 1889,
and in 1904 he was appointed chairman of the Cumberland Ward Justices.
He was also intensely interested in antiquarian and archseological research,
and papers by him have appeared in the British Medical Journal , the
Lojncet , the Edinburgh Medical Journal , and the medical journals of New
York, Philadelphia, St Louis, and Toronto. He also contributed papers on
the historical side of medicine to the Transactions of the Cumberland
and Westmorland Antiquarian Society.

Dr Barnes founded and was president of the Carlisle Branch of the
Medical Mission Auxiliary of the Church Missionary Society, and was
deeply interested in its welfare.

Dr Barnes was able to work, as he would have wished, to the end,
passing away on 12th April 1921 after only a week’s illness, from heart
failure following bronchitis. His kindness of heart, courtesy of manner,
social disposition, and well-stored mind endeared him to all classes of
the community.

1920-21.]

Obituaries.

197

The following Notices have been prepared by the Assistant
Secretary, Mr George A. Stewart.

(Read January 9, 1922.)

Alford, Robert Gervase, M.Inst.C.E., son of the late Rt. Rev. Bishop
Alford, died at his residence “ Three Gables,” Tunbridge Wells, on the
10th May 1921, aged 72 years. He was elected a Fellow of this Society
in 1895.

Anderson, Sir Row and, LL.D. (born 1834), the son of Mr James
Anderson, an Edinburgh solicitor, was educated at George Watson’s Old
Hospital School, which occupied part of the site of the Edinburgh Royal
Infirmary. He was for a time in the office of Messrs Keegan & Welsh,
solicitors. His bent, however, was in another direction. From early years
he had shown a fondness for drawing. He studied for a time at the
Trustees’ Academy, Royal Institution, under the late Mr Christie, a con-
temporary of Dick Lauder. Afterwards he entered the office of Mr John
Lessels, one of the leading Edinburgh architects of the day ; and to his
young assistant was entrusted in 1857 the work of superintending the
restoration of the roof of Greyfriars Church, which had been destroyed
by fire. Subsequently he made a tour on the Continent, and for a time
worked in the office of Cuypers, Amsterdam, then in great repute. He
also served for a period in the London office of Sir Gilbert Scott, the great
Gothic architect, who had a high idea of the abilities of the young Scots-
man. On returning to Edinburgh he was employed in the architectural
branch of the Royal Engineers ; then as partner to the distinguished
Scottish architect, David Bryce. In the sixties he settled down to business
on his own account in an office in Dundonald Street.

From the outset Sir Rowand was looked upon as a rising man, and
was kept busily employed in the designing of churches, especially
Episcopal churches, of which denomination he was a member. Sir
Rowand Anderson’s designs were accepted for the following buildings : —
Fountainbridge, Stockbridge, and Causewayside Board Schools, the stately
New Medical School of the University, and the M‘Ewan Hall. It was in
connection with the completion of the New Medical School that at the
memorable celebration of the Tercentenary of the University of Edinburgh
in 1884, he received the honorary degree of LL.D. To him was also
entrusted the task of completing Adams’ design of the Old University by

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

crowning it with a dome. His name is also identified in the public mind
as the designer of the Scottish National Portrait Gallery and Museum of
Antiquities, Queen Street. The palace reared by the late Marquis of Bute
at Mountstuart may be cited as the most important example of the
abilities of the architect in this branch of his art Other architectural works
of note were executed by Sir Rowand during his long professional career.

In connection with church architecture, Sir Rowand Anderson was
frequently consulted regarding schemes for the restoration of ancient
buildings ; and it was he who carried out the restoration of Dunblane
Cathedral, the Chapel of King’s College, Aberdeen, Borthwick Parish
Church, and Culross Abbey. He was employed by the late Marquis of
Lothian to devise measures for the preservation of Jedburgh Abbey, and
these were renewed previous to this ancient religious house being handed
over to the Ancient Monuments Commission.

A scheme with which he was intimately associated, and in connection
with which he did lasting work for his profession and for the arts and
crafts of the city, was the founding of the College of Applied Art, which
had its headquarters in the Royal Institution, Mound, and was under the
aegis of the Board of Manufactures. In the formation of the Edinburgh
College of Art Sir Rowand also took much interest. He was elected an
Associate of the Royal Scottish Academy in 1876, but resigned in 1883 on
a question as to the architectural status of Members of the Academy.
During the Presidentship of Sir George Reid, Sir Rowand Anderson in
1896 was elected an Honorary Member of the Academy, and the feud was
in that way peacefully ended. In 1902 he received the honour of knight-
hood. It may be mentioned that he rendered good service to this Society
during the transference from the Royal Institution to our present building.
He was a man of wide sympathies, and despite a certain reserve in
temperament, had a large circle of friends. He was elected a Fellow of
the Society in 1883, and died at his residence in Colinton on the 1st June
1921, at the age of 87.

Beck, Hon. Sir J. Henrxcus Meiring, Kt., M.D., J.P., M.R.C.P.E., M.L.A.,
son of the late C. Beck, J.P. of Worcester (Cape), was born at Worcester
(Cape Province) in 1855. He was educated at Worcester Public School.
South African College, University of Edinburgh, Berlin, and Vienna;
was one of the delegates from the Cape of Good Hope to the South
African National Convention, and was a Member of Council of the Univer-
sity of the Cape of Good Hope from 1888-1912. For a period he filled the
position of President of the Cape Medical Council. From 1916 he was

Obituaries.

199

1920-21.]

Minister of Posts and Telegraphs, Union of South Africa, was a Senator
from 1910, and Chairman of Committees of Senate.

He was elected a Fellow of the Society in 1892, and died in 1919.

Bridger, Adolphus Edward, B.Sc. (Paris), B.A., M.D. (Edin.), F.R.C.P.E.,
held the following posts : — Senior Physician, St Pancras Dispensary ; Con-
sulting Physician in Tuberculosis, Borough of St Pancras ; Physician
Superintendent, London Hospital for Women; Physician, Chest Hospital,
Margaret Street ; and Anaesthetist, Royal Dental and National Dental
Hospitals. He was a member of the Society of Authors, and published
the following : — Digestion , Perfect and Imperfect ; Depression ; Biliousness ;
Man and his Maladies, 1889; The Treatment of Consumption, 1891;
Minds in Distress, 1913 ; The Function of the Sympathetic Nervous System
in Psychic Phenomena, 1913.

Dr Bridger was elected a Fellow of the Society in 1912, and died in
London on 2nd February 1920.

Brown, David, F.C.S., Manufacturing Chemist, was born in Edinburgh
in 1840. He succeeded his father, Mr D. R. Brown, as senior partner of
the firm of J. F. Maefarlan & Co. He was educated at the Royal High
School, and studied Chemistry at the University of Edinburgh. For some
time he assisted Professor George Wilson in Edinburgh, and afterwards
Professor Anderson in Glasgow. At a later period he joined the staff of
the Apothecaries’ Hall in London, thus gaining a knowledge of applied
pharmacy. Thereafter he was engaged in the manufacture of chemical
substances used in medicine.

Though engrossed in the management of the business, Mr Brown was
the author of several valuable papers on chemical subjects published in
the Pharmaceutical Journal and elsewhere. Notes on Chloroform and
on the location of Salicin in Willow Bark are among his published papers.
Though he refrained from publishing anything on the opium alkaloids, he
recognised oxy narcotine as an undescribed substance, and handed it over
to Dr Wright, who made an analysis and gave the results to the Chemical
Society.

The preparation of salicin from willow bark was begun in Mr Brown’s
time. He was a Justice of the Peace and a member of the Merchant
Company in Edinburgh.

Mr Brown was elected to the Fellowship of this Society in 1893, and
died on 21st June 1921 at his residence, Willowbrae House, Edinburgh.
His son, Mr Rainy Brown, died a few months earlier.

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

Brown, David Rainy, was educated at the Edinburgh Institution,
under Dr Ferguson, and at Edinburgh University. He also studied in
Germany. Entering the firm of J. F. Macfarlan & Co., Manufacturing
Chemists, Edinburgh, as a young man, he later succeeded his father,
Mr David Brown, the subject of the immediately preceding notice. Mr
Brown accomplished a considerable amount of research work on Opium
and Chloroform and published papers in the Pharmaceutical Journal.
An old member of the Queen’s Edinburgh Volunteers, he served during the
war in connection with Coast Defence Work.

He was elected a Fellow of the Society in 1911, and died at Edinburgh
on 9th January 1921, at the age of 50.

Carter, William Allan, O.B.E., J.P., M.Inst.C.E., was a son of Mr
Frederick Hayne Carter, C.A., and was born in Edinburgh in 1847. He
received his early education at the Edinburgh Academy, and was after-
wards trained as a Civil and Consulting Engineer. For a long period Mr
Carter was a member of the Dean of Guild Court of Edinburgh, and from
1909 to 1913 he served as Lord Dean of Guild — an office which gave him
a seat as a Member of the Town Council of Edinburgh. He acted also for
some time as Engineer to the Convention of Royal Burghs, was Secretary
to the Royal Scottish Society of Arts, and Hon. President of the East of
Scotland Engineers’ Association.

Mr Carter started his professional career in paper engineering, and
specialised in the recovery of soda in that connection. He was engaged
later in the construction of bridges, water supplies, and drainage schemes,
etc., for County Councils and Burghs. Appearing often in the Court of
Session as an expert witness, he was greatly respected for his broad and
moderate views and courteous manner. Mr Carter frequently acted as
Examiner for the degree of D.Sc. in the University of Edinburgh. He
was known to a wide circle of acquaintances as a man of outstanding
ability and high professional skill, a capable administrator, and also a
gentleman of wide culture.

Mr Carter was elected to the Fellowship of the Society in 1898, served
on the Council from 1911-1914, and represented the Society on George
Heriot’s Trust from 1911-1918. He died at his residence at Gullane on
7th September 1921.

Dundas, William John, W.S., LL.D., was the son of the late Lord
Manor, and an elder brother of Lord Dundas. Born in 1849, he was
educated at the Edinburgh Academy 'under Mr James Carmichael, and, on

Obituaries.

201

1920-21.]

leaving school, entered the writing chambers of Messrs Dundas & Wilson,
as an apprentice. He was admitted a Writer to the Signet in 1871, and
a few years later became a partner. In 1913 he retired from business.
On the formation of the present Government he returned for two years
to the post of Crown Agent, which he had held from 1895-1905. Dr
Dundas was for many years a Director of the Standard Life Assurance
Company, and was also on the Board of the Edinburgh Academy. In recent
years he rendered admirable service as one of the Carnegie Trustees, and
in 1914 received the degree of LL.D., from the University of Edinburgh.
He stood in the direct line of the best Scottish legal traditions, and his
place will be difficult to fill.

Dr Dundas, who was interested in the study of the higher mathematics,
was elected a Fellow of the Society in 1919, and died at Edinburgh on 9th
July 1921.

Gatehouse, Tom Ernest, A.M.Inst.C.E., MJ.Mech.E., M.I.E.E., was
born in 1854 at Norwich, in Norfolk. He was the son of Mr Tom
Gatehouse, a mechanical engineer ; naturally, therefore, he had a bent
towards engineering as a profession, and about 1870 he became a pupil
of Robert Sabine, one of the most eminent and able pioneers in the
electrical industry. Later he was associated with Sir Charles Wheatstone
and Sir Samuel Canning, foremost exponents of the art of telegraphy on
land and by submarine cable. Amongst the various undertakings with
which he was closely connected were the first electric lighting of Aldgate
Station with Lontin arc lamps, and the development of the Werdermann
arc lamp and the Gramme dynamo; in regard to the Lontin lamp he
patented an improvement. He was also interested in the development
of the telephone and experimented with a view to its improvement. The
introduction of the incandescent lamp, however, indirectly proved to be
a turning point in the career of Mr Gatehouse, who invented a device
(afterwards re-invented in connection with the Nernst lamp) for the
patent rights of which he received a substantial sum. About this time
his fellow-pupil under Sabine, Mr H. R. Kempe (subsequently Electrician
to the Post Office), had become associated with Mr H. Alabaster, proprietor
of the Telegraphic Journal and Electrical Review, and invited Mr
Gatehouse to throw in his lot with them. Mr Gatehouse assumed the
office of editor in 1881. In recent years, owing to failing health, he has
not taken a very active part in the production of the Electrical Review.

Mr Gatehouse was elected to the Fellowship of the Society in 1899,
and died in London on Thursday 31st March 1921.

202

Proceedings of the Eoyal Society of Edinburgh. [Sess.

Gilruth, Geo. Ritchie, L.R.C.P., L.R.C.S.Edin. 1865, held the following
appointments : — Surg. Lt.-Col. (V.D.) 1st. Edin. (City) Y. Artillery ; Asst.
Demonstrator of Anatomy R.C.S. Edin. ; Res. Surgeon Consett Infirmary ;
and was the author of Physiological Effects of Injuries of the Spinal
Cord in the Lower Animals, and papers to the Lancet and Edinburgh
Medical Journal.

He was elected a Fellow of the Society in 1880, and died at Allan ton,
Bridge of Allan, on 15th August 1921.

Helme, Thomas Arthur, M.D. Edin. (Gold Medal) 1889, M.B.,
C.M. (Hon.) 1885, M. R.C.S. Eng. 1894, M.R.C.P. Lond. 1894, was educated
at Edinburgh University, University College, London, and the University
of Strasburg. He was Freeland-Barbour Research Scholar R.C.P. Edin.
in 1890; Leckie-Mactier Fellow 1886; Buchanan Scholar 1885, Univer-
sity, Edinburgh ; Exhib. Univ. Lond. 1884 ; Hon. Phys. Northern Hosp.
Women and Children, Manchester ; V.P. N. of England Obstetrical Society ;
and President Lancs, and Ches. Branch B.M.A. He held the following
appointments : — Physician, Women’s Dispensary, Edin. ; Res. Surg. Roy.
Maternity Hosp. Edin. ; Res. Obst. St Mary’s Hosp. Women and Children,
Manchester; and communicated a paper to the Transactions of this
Society (vol. xxxv) on “ Histological Observations on the Muscular
Fibre and Connective Tissue of the Uterus during Pregnancy and the
Puerperium.” He was author of the Anatomy and Physiology of the
Uterus, 1889, and published papers in the Medical Chronicle, 1893, and
in the British Medical Journal, 1907.

Dr Helme was elected to the Fellowship of this Society in 1890, and
died on 5th September 1921.

Hunter, James, F.R.C.S.E., F.R.A.S., was one of the oldest Fellows of
the Royal College of Surgeons, Edinburgh, and was well known in medical
circles. For a number of years he was Lecturer in Physiology to the
School of Medicine of the Royal Colleges, and latterly he acted as Examiner
in Biology and Physiology for the Royal College of Surgeons in the triple
qualification. He was a keen amateur astronomer, interested in optics,
and published several papers in the Scottish Microscopical Society’s
Transactions and Proceedings, and a joint paper with Mr E. Sang in the
Proceedings of this Society, vol. viii, 1873, p. 126: “Observations and
Experiments on the Fluid in the Cavities of Calcareous Spar.”

Dr Hunter was elected a Fellow of the Society in 1887, and for many
years regularly attended its meetings. He died at Edinburgh on 15th
February 1921.

Obituaries.

203

1920-21.]

Martin, Sir Thomas Carla w, LL.D., J.P., was born on 10th April 1850
near Linlithgow, of farming stock. He was trained in the country schools,
until, in early manhood, he attended the Watt (now the Heriot-Watt)
College and Edinburgh University, in which institution he was Gold
Medallist in the class of Political Economy. After some years spent in
the Post Office, he became associated with journalistic work, and eventually
made it his profession. Sir Thomas was the first and only editor of TJte
Leader, which continued for some years as a GladstOnian-Liberal paper in
Edinburgh. As editor of the Dundee Advertiser for eighteen years he
became a prominent figure in Scottish journalism. St Andrews University
conferred on him the LL.D. degree. While essentially a student and
reflective observer of public affairs, he was especially interested in agricul-
culture and economics. In 1904 he was a member of the Scottish Agri-
cultural Commission to Denmark, and the report of that commission
contains many suggestive and readable pages from his pen. In 1908 he
was Chairman of the Scottish Agricultural Commission in Canada, and in
the same year received the honour of knighthood. In 1910-1911 he was
Chairman of the Australian Agricultural Commission, and in 1911 was
appointed Director of the Royal Scottish Museum. An able administrator,
he did much to improve the working conditions there, and developed its
educational possibilities, keeping in view not only the needs of the student
but of the large number of casual visitors and children from the schools.
For these he wrought out schemes, and with the introduction of guides
and lectures brought the wealth of the Museum before a growing public.
After his retiral from the Directorship of the Museum he acted as
Chairman of the Transport Committee, and contributed largely to its
report. At the time of his death he was Chairman of the local Employment
Committee under the Ministry of Labour.

Sir Thomas was elected a Fellow of the Society in 1912, and died at
Edinburgh on 26th October 1920.

Mylne, Rev. Robert Scott, M.A., B.C.L., Oriel College, Oxon.,
F.S.A. L. and E., Rector of Furthoe, Northants, died at his residence
Great Amwell, Ware, Herts., on 23rd November 1920, in his 67th year.

He was elected to the Fellowship of the Society in 1902.

Oliphant, James, M.A., formerly Headmaster of Charlotte Square
Institution, Edinburgh, died at his residence, 11 Heathfield Park, London,
N.W. 2, on 19th February 1921, in his 67th year.

He was elected a Fellow of the Society in 1888.

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

Roberts, David Lloyd, M.D. St And. 1859, F.R.C.P. Lond. 1878,
M.R.C.S. Eng., and L.S.A. 1857. Held the following appointments : — Cons.
Obst. Phys., Manch. Roy. Infirmary : Phys. St Mary’s Hospital, Manch. ; Lect.
on Clin. Midwf. and Dis. of Women, Owens Coll., Manch. He was a Fell. Med.
Soc. Lond. ; Mem. Lit. and Philos. Soc. Manch. ; late Pres. N. of Eng. Obst.
and Gynsecol. Soc. ; Yice-Pres. Obst. Sect. Brit. Med. Assoc., and Pres. Manch.
Med. Soc., and was the author of the following books : — The Scientific
Knowledge of Dante, 1914 ; The Practice of Midwifery ; Cases of Ovario-
tomy ; Clinical Papers ; The Various Methods of Treating the Pedicle in
Ovariotomy ; Edr. Sir Thomas Browne’s Religio Medici, etc. He also
published papers in the Obstetrical Transactions, and in the Transactions
St. And. Med. Grad. Assoc.

Dr Roberts was elected to the Fellowship of this Society in 1880, and
died on 20th September 1920.

Sprague, Thomas Bond, M.A. Camb., LL.D. St Andrews, F.I.A.,
Hon. F.F.A., was born on 29th March 1830, and was the eldest son of
Thomas Sprague of London, Wholesale Stationer. He was educated at
Tarvin Hall, a private school near Chester, under the Headmastership of
Dr John Brindley. While at school he distinguished himself so much in
mathematics that Dr Brindley advised his father to send him to Cambridge,
and he accordingly entered St John’s College as a Sizar. At the end of his
first year he became a Proper Sizar, and in consequence of the excellent
places he took in the College examinations, he became in due course a
Scholar. In 1853 he was Senior Wrangler and First Smith’s Prizeman,
and was elected a Fellow of St John’s College, and appointed one of the
College Lecturers. About this time he qualified in law and was called to
the Bar, having in view the law as his future profession. Progress, how-
ever, being slow, he sought a career which would be more immediately
remunerative, and entered the Eagle Insurance Company in 1855 as a pupil
of the late Charles Jellicoe.

After holding some minor appointments, Dr Sprague was, for a short
time, Actuary of the then Liverpool and London Assurance Company, until
in 1861 he was appointed, at the age of 31, Actuary and Secretary of the
Equity and Law Life Assurance Society, wuth which Society he remained
for twelve years. In 1873 he became Manager of the Scottish Equitable
Life Office. This involved his removal to Edinburgh. In 1900, after being
twenty-seven years Manager of the Scottish Equitable, he retired from
active business life. In 1893 the University of Aberdeen conferred on him
the degree of LL.D.

Obituaries.

205

1920-21.]

Dr Sprague was elected Associate of the Institute of Actuaries in 1856.
His first paper is to be found in the Institute Journal, vol. vi, on a certain
method of distributing surplus. He was elected a Fellow of the Institute
in 1857, and was elected to the Council in 1863. He remained a member
until his retirement from business in 1900, a period of thirty-eight years,
which is a record. He edited the Journal of the Institute from 1867 to
1883, and the volumes published during his editorship bear witness to
his skill and zeal. Elected President of the Institute in 1882, he occupied
the Presidential Chair for four years. During his Presidency the Institute
received its Charter. In 1874 he was elected a Fellow of the Faculty
of Actuaries in Scotland, and was President from 1894-1896. No one
else has occupied the Presidential Chairs of both the Institute and the
Faculty. He was also President of the Actuarial Society of Edinburgh on
three occasions, 1874, 1882, and 1891.

Besides being an Actuary of unusual erudition, Dr Sprague was a first-
class business man. The business of life assurance, using the words “ life
assurance ” in their broadest sense, was the business of his life, and in all
his investigations he kept in view their immediate practical application, and
refrained from acting on any theories he might have formed until he had
put them to practical test. His writings all bear witness to this ; and one
would like to refer to them in some detail, but in this short notice it is
impossible. The communications to the Journal of the Institute alone
occupy nearly five and a half pages of the index. Of other actuarial
publications special mention may be made of his volume on Life Insurance
Accounts (1874); his contributions to the 9th Edition of the Encyclopaedia
Britannica, particularly an exhaustive article on “Annuities,” in some parts
highly mathematical, which superseded the article by Joshua Milne written
many years before ; and sundry contributions to the Transactions of the
Actuarial Society of Edinburgh. The construction and use of his monu-
mental Select Tables were fully explained in two elaborate papers to the
Journal of the Institute of Actuaries, vol. xxi, p. 229, 1878, and vol. xxii,
p. 391, 1881, and in 1896 they were published separately in book form,
with extensive monetary tables at four rates of interest. He also took a
great part in the preparation of what are now known as the Institute of
Actuaries’ Life Tables.

Dr Sprague’s energies were not confined to matters actuarial. He
published various mathematical papers in the Transactions and Proceedings
of the Royal Society of Edinburgh and of the Edinburgh Mathematical
Society ; and was besides an active member of the Edinburgh Field
Naturalists and Microscopical Society, to the publications of which he

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

made several contributions. A list of these and other papers is given
below : —

“ Note on the Probability that a Marriage entered into by a Man above the
Age of 40 will be fruitful,” Proc. Roy. Soc. Edin., vol. x, 1880, p. 202.

“ On the Nature of the Curves whose Intersections give the Imaginary
Roots of an Algebraic Equation,” Trans. Roy. Soc. Edin., vol. xxx,
1883, p. 467.

“ On a New Algebra by means of which Permutations can be transformed
in a Variety of Ways and their Properties investigated,” Trans. Roy
Soc. Edin., vol. xxxvii, 1893, p. 399.

“ On the Adjustment of Numerical Results derived from Observation,” Brit.
Assoc. Report, 1883, p. 446.

“Note on the Evaluation of Functions of the Form 0°,” Proc. Edin. Math.
Soc., 1884-85.

“ On the Different Possible Non-linear Arrangements of Eight Men on a
Chess Board,” Proc.. Edin. Math. Soc., 1889-90.

“ On the Transformation and Classification of Permutations,” Proc. Edin.
Math. Soc., 1890-91.

“ On the Geometrical Interpretation of i ” Proc. Edin. Math. Soc., 1893-94.
“ On the Eight Queens’ Problem,” Proc. Edin. Math. Soc., 1898-99.

“ On the Singular Points of Plane Curves,” Proc. Edin. Math. Soc., 1902-03.

The following were communicated to the Edinburgh Field Naturalists
and Microscopical Society : —

“ Bones and Shells taken from a Kitchen Midden on Inchkeith during 1881.”
“ The ‘ Green Balls ’ of Loch Kildonan.”

“ On the Growth of Leaves.”

“ Fibre Balls.”

“ Ripple Marks on Sand,”

“ On the Occurrence of the Fresh- Water Mussel.”

“Notes on the Bournemouth Cliffs.”

“ Notes on the Entomostraca (Water Fleas) of Midlothian.”

Dr Sprague was twice married : first, in 1859, to Miss Margaret Vaughan
Steains, younger daughter of Mr James Steains of Liverpool, by whom he
had eleven children, eight of whom survive ; and second, in 1908, to Miss
Jean Elizabeth Stuart of Edinburgh, who also survives him.

He was elected to the Fellowship of the Royal Society of Edinburgh
in 1874, and served on the Council from 1885-1887. He died at West
Holme, Woldingham, Surrey, on 29th November 1920.

Obituaries.

207

1920-21.]

Walker, Robert, M.A. (Aberd. et Cantab.), LL.D., was born in Aber-
deen in 1842. He was well known to several generations of students in
connection with the part he took in arranging and supervising a number
of the more noteworthy functions of the University of Aberdeen, and his
services were especially outstanding in connection with the quatercentenary
celebrations and the visit of King Edward VII. to open the extension of
Marischal College in 1906. The following is a brief resume of his career : —
B.A. (fifteenth Wrangler) at Cambridge in 1865, and in 1868 M.A. Fellow
of Clare College, Cambridge, from 1866-1878. He taught mathematics for
some time in the Edinburgh Academy, and was examiner in that subject
in the Universities of Edinburgh and Aberdeen. In 1877 he was appointed
University Librarian at Aberdeen, and in 1893 Secretary to the Aberdeen
University Court, Registrar of the University and Clerk of the General
Council, which position he resigned in 1906. The following year he
received the honorary degree of LL.D. from Aberdeen University in
recognition of his valuable services.

Dr Walker was elected a Fellow of the Royal Society of Edinburgh
in 1873, and died at Aberdeen on 26th October 1920.

Woods, Geo. Arthur, L.R.C.P. Edin., and L.M. 1868, M.R.C.S. Eng.
1868, L.S.A. 1868 (St Bart.), Hunterian Gold Medal, was the author of the
following work : — Anat. Physiol, and Pathol, of the Third, Fourth, and
Sixth Nerves, as illustrated by Observation and Experiments in Health and
by References to Effects of Injury and Disease (Coll. Trien. Prize, R.C.S.
Eng.), and published papers in the Liverpool Medical Surgical Reports,
Lancet, International Medical Congress , and the Liverpool M.-C.
Journal.

He was elected to the Fellowship of the Society in 1884, and died,
after an illness of many years, on 30th June 1921.

APPENDIX.

CONTENTS

PAGE

PROCEEDINGS OF THE STATUTORY GENERAL MEETING, OCTOBER 1920 . 211

PROCEEDINGS OF THE ORDINARY MEETINGS, SESSION 1920-1921 . . 213

PROCEEDINGS OF THE STATUTORY GENERAL MEETING, OCTOBER 1921 . 219

THE KEITH, MAKDOUGALL-BRISBANE, NEILL, GUNNING VICTORIA JUBILEE, AND

JAMES SCOTT PRIZES . . . . . . .221

AWARDS OF THE KEITH, MAKDOUGALL-BRISBANE, NEILL, AND GUNNING PRIZES 224

ACCOUNTS OF THE SOCIETY, SESSION 1920-1921 .... 230

VOLUNTARY CONTRIBUTORS UNDER LAW VI (END OF PARA. 3) . . 236

THE COUNCIL OF THE SOCIETY AT OCTOBER 1921 . . . . 237

ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY . . 238

LIST OF HONORARY FELLOWS OF THE SOCIETY AT JANUARY 31, 1922 . 258

LIST OF ORDINARY FELLOWS OF THE SOCIETY ELECTED DURING SESSION

1920-1921 ........ 260

CHANGES IN FELLOWSHIP DURING SESSION 1920-1921 . . . 260

ADDITIONS TO LIBRARY BY GIFT OR PURCHASE . . . . 261

LAWS OF THE SOCIETY ....... 265

INDEX . . . . . . . . .272

INDEX, UNDER AUTHORS’ NAMES, OF PAPERS PUBLISHED IN “ TRANSACTIONS ” 275

Meetings of the Society.

211

PROCEEDINGS OF THE STATUTORY GENERAL
Beginning the 138th Session, 1920-1921.

MEETING

At the Statutory Meeting of the Royal Society of Edinburgh, held in the Society’s Lecture
Room, 24 George Street, on Monday, October 25, 1920, at 4.30 p.m.,

Professor Frederick 0. Bower, President, in the Chair,
the Minutes of Meeting of October 27, 1919, were read, approved, and signed.

The Chairman nominated as Scrutineers, Dr Inglis Clark and Mr Gall Inglis.

The ballot for the election of Office-Bearers and Members of Council was then taken.

The Secretary submitted the following Report : —

The number of papers read at our Meetings during the last Session was 27, as compared with
23 the previous Session. Of these, three were Addresses, of which two were delivered by Professor
R. A. Sampson, “ On Gravitation and Relativity,” and one by Principal Sir James Alfred Ewing,
‘ ; On the Molecular Energy of Gases. ” Of the others, 4 were in Mathematics, 7 in Physics, 4 in
Meteorology, 1 in Chemistry, 1 in Zoology, 1 in Botany, 5 in Geology, and 1 in Medicine.
23 have been, or are being, published in the Proceedings or Transactions.

Last Session the Society elected 20 new Fellows. Two Fellows have resigned, and we have lost
by death 3 Honorary Fellows and 16 Ordinary Fellows.

The Keith Prize was awarded to Professor John Stephenson, Lt.-Col. I.M.S., and the Neill
Prize to Professor John Tait.

Owing to the continued increase in the cost of publication the Council has to exercise great care
in order to meet the necessary expenses. The income of the Society remains practically the same ;
but the Special Fund to which many Fellows contributed has enabled us to meet the comparatively
small deficit this year. An Appeal by the Council to the Carnegie United Kingdom Trust for aid
in binding the loose journals in the Library was very generously met by the Trust, and already
£1500 (half the promised grant) has been received from the Trust and paid over to the binders.
The Society takes this opportunity of expressing its thanks to the Trust for their generous help.

An interesting event of the year was the election of the Prince of Wales as an Honorary Fellow.
Also the names of seven distinguished scientific men were added to the roll of Foreign Honorary
Fellows.

All who have had occasion to use the Library will hear with regret that Miss Le Harivel has
been obliged, for reasons of health, to resign her position as Assistant Librarian. Steps are being
taken to fill up the vacancy thus occasioned.

The Society is being called upon to take an increasing share in national developments. Thus
Dr E. M. Wedderburn has been appointed the Society’s representative on the newly constituted
Meteorological Committee under the Air Ministry. In connection with the International Associa-
tion of Scientific Bodies, Professor Whittakkr and Dr Knott have been appointed representatives
on the National Union of Mathematics, Dr H. R. Mill on the National Union of Geography, and
Dr Crichton Mitchell and Dr Erskine Murray on the National Union of Radio-Telegraphy.

It will interest the Fellows to know that the Society is associated with the Municipality and
the University in preparing for the Meeting of the British Association to be held in Edinburgh in
September 1921.

In order to give a distinct scientific flavour to the Statutory Meeting, the Council has adopted
a suggestion made last year by the previous President, Dr Horne, and asked the President to
deliver his Address at this Meeting instead of a week later at the first Ordinary Meeting of the
Session.

The Treasurer, in submitting his Report for the year, compared the income and expenditure
with those of the previous year, and called attention to the fact that the deficit of £34, 9s. 5d. on
the year’s working had been met from the Special Subscription Fund, which now stands at
£792, 11s. 5d. The full list of subscribers up to the present is given on pp. 208-209 (vol. xl).

Dr John Horne moved the adoption of the Reports, and the reappointment of Messrs Lindsay,
Jamieson & Haldane, C.A. , as auditors of the accounts for the ensuing Session.

This was unanimously agreed to.

212

Proceedings of the Royal Society of Edinburgh. [Sess.

- Vice-Presidents.

The Scrutineers reported that the Ballot Papers were in order, and that the following Office-
bearers and Members of Council had been elected : —

Professor Frederick 0. Bower, M.A. , D.Sc., LL.D., F.R.S., F.L.S., President.
Professor D. Noel Paton, M.D. , B.Sc., LL.D.

F.R.C.P.E., F.R.S.,

Professor Arthur Robinson, M.D., M. R.C.S.,

Sir George A. Berry, M.B., C.M., LL.D., F.R.C.S.E.,

Professor William Peddie, D.Sc.,

Principal Sir James Alfred Ewing, K.C. B., M.A.,

D.Sc., LL.D., M. Inst.C.E., F.R.S.,

Professor John Walter Gregory, D.Sc., F. R.S.,

Cargill G. Knott, D.Sc., LL.D., F. R.S., General Secretary.

Professor E. T. Whittaker, Sc.D., F.R.S., \ Secretaries to Ordinary
Professor J. H. Ashworth, D.Sc., F.R.S., J Meetings.

James Currie, M.A., LL.D., Treasurer.

A. Crichton Mitchell, D.Sc., Hon. D.Sc. (Geneva), Curator of Library and Museum.

ORDINARY MEMBERS OF COUNCIL.

Professor R. A. Sampson, M.A., D.Sc., F.R.S.
Professor J. Lorrain Smith, M.A., M.D.,
F.R.S.

W. A. Tait, D.Sc., M.Inst.C.E.

Maj. -General W. B. Bannkrman, C.S.I.,
I.M.S., M.D. , D.Sc.

Henry Moubray Cadell, of Grange, B.Sc.
Professor Arthur Robertson Cushny, M.A.,
M.D., LL.D., F.R.S.

Professor Francis Gibson Baily, M.A.,
M.Inst.E.E.

George James Lidstone, F.F.A., F.I.A.
Robert Campbell, D.Sc.

Professor James Colquhoun Irvine, C.B.E.,
Ph. D. , D.Sc., F.R.S.

The Hon. Lord Salvesen.

Professor J. Arthur Thomson, M.A., LL.D.

SOCIETY’S REPRESENTATIVE ON GEORGE HERIOT’S TRUST.

W. A. Tait, D.Sc., M.Inst.C.E.

The President, in the name of the Society, thanked the Scrutineers for their services.

1920-21.]

Meetings of the Society.

213

PROCEEDINGS OF THE ORDINARY MEETINGS,
Session 1920-1921.

FIRST ORDINARY MEETING.

Monday, November 1, 1920.

Professor Frederick 0. Bower, M.A., D.Sc. , LL. D., F.R.S., F.L.S., President, in the Chair.

The following Communications were submitted : —

1. “ Isle of Wight ” Disease in Hive Bees.

a. The Etiology of the Disease. By Elsie J. Harvey, John Rennie, I).Sc., and

P. Bruce White, B.Sc.

b. The Organism associated with the Disease. By John Rennie, D.Sc.

c. The Pathology of the Disease. By P. Bruce White, B.Sc.

d. Experiments in Infection. By Elsie J. Harvey.

Trans., vol. lii, pp. 737-779.

2. On the Equations of Motion of a Single Particle. By Professor J. H. Maclagan Wedder-
burn, M.A, , D.Sc. Proc., vol. xli, pp. 26- 33.

SECOND ORDINARY MEETING.

Monday, November 22, 1920.

Principal Sir J. A. Ewing, K.C.B., LL.D., M.Inst.C.E., F.R.S., Vice-President, in the Chair.

The Chairman announced that the Council had resolved to recommend to the Fellows certain
changes in the Bye-laws as follows

“ Each Fellow shall, before he is admitted to the privileges of Fellowship, pay an admission
fee of three guineas, and a subscription of three guineas for the year of election. He shall
continue to pay a subscription of three guineas at the beginning of each session so long as he
remains a Fellow. A Fellow may compound for the annual subscriptions by a single payment of
fifty guineas, or on such other terms as the Council may from time to time fix.

‘ ‘ Each Fellow who was elected previous to December 1916 shall pay four guineas at the beginning
of each session until he has made ten annual payments, and thereafter three guineas at the beginning
of each session until he has completed his twenty-fifth annual payment. Each Fellow who has
completed or shall complete his payments shall be invited to contribute one guinea per annum so
long as he remains a Fellow, or to pay a single sum of ten guineas. ”

The following Communications were submitted : —

1. Obituary Notice of Surgeon-General W. C. Gorgas, Honorary Fellow. By Major-General
W. B. Bannerman. Proc., vol. xl, pp. 187-190.

2. On Fechner’s Law and the Self-luminosity of the Eye. By Professor W. Peddie, D.Sc.
Proc., vol. xli, p. 60. (Abstract.)

3. Aether and the Quantum Theory. By Dr H. Stanley Allen. Proc., vol. xli, pp. 34-43.

THIRD ORDINARY MEETING.

Monday, December 6, 1920.

Professor Frederick O. Bower, M.A., D.Sc., LL.D., F.R.S., F.L.S., President, in the Chair.
The following Communications were submitted : —

1. Observations on the Behaviour of the Endodermis in the Secondarily Thickened Root of
Dracaena fruticosa (Koch). By Miss Annette G. Mann. Communicated by Professor F. O.
Bower, F.R. S. Proc., vol. xli., pp. 50-59.

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

2. On Cretaceous Ammonoidea from Angola, collected by Professor J. W. Gregory, F.R.S.
(With notes by the late G. C. Crick, F.G.S.) By L. F. Spath, M.Sc., F.G.S. Communicated by
Professor J. W. Gregory, F.R.S. ( With Lantern Illustrations.) Trans., vol. liii, pp. 91-160.
Note by Professor Gregory. Vol. liii, pp. 161-163.

The President drew the attention of the Fellows to the subjoined intimation on the Billet : —

It will be proposed and seconded at the Ordinary Meeting on 10th January 1921 that Rule VI
read as follows : —

“ Each Fellow shall, before he is admitted to the privileges of Fellowship, pay an admission
fee of three guineas, and a subscription of three guineas for the year of election. He shall continue
to pay a subscription of three guineas at the beginning of each session so long as he remains a
Fellow. A Fellow may compound for the annual subscriptions by a single payment of fifty
guineas, or on such other terms as the Council may from time to time fix.

“ Each Fellow who was elected previous to December 1916 shall pay four guineas at the
beginning of each session until he has made ten annual payments as reckoned from the year of
election, and thereafter three guineas at the beginning of each session until he has completed his
twenty-fifth annual payment. Each Fellow who has completed or shall complete his payments
shall be invited to contribute one guinea per annum so long as he remains a Fellow, or to pay
a single sum of ten guineas.”

FOURTH ORDINARY MEETING.

Monday, January 10, 1921.

Professor Frederick 0. Bower, M.A. , D.Sc.., LL. D., F.R.S., F.L.S., President, in the Chair.

The following Communications were submitted : —

1. Obituary Notice of Dr John Aitken, F.R.S. By Dr C. G. Knott, F.R.S. Proc., vol. xli,
pp. 177-181.

2. Thermometer Screens. By the late Dr John Aitken, F.R.S. Communicated by Dr C. G.
Knott, F.R.S. Proc., vol. xl, pp. 172-181.

3. The Avoidance of Relativity which is not of the Galileo-Newtonian Type. By Professor
Wm. Peddle, D.Sc.

4. On the Transverse Galvanomagnetic and Thermomagnetic Effects in several Metals. By
F. Unwin, M.Sc. Communicated by Professor F. G. Baily. Proc., vol. xli, pp. 44-49.

5. The Confluent Hypergeometric Functions, of two Variables. By Pierre Humbert. Com-
municated by Professor E. T. Whittaker, F.R.S. Proc., vol. xli, pp. 73-96.

The proposed Amendment to Law VI was discussed and some slight alteration proposed in the
wording and arrangement of certain sentences. The President ruled that, under the circumstances,
the final vote on the proposed Amendment should be postponed until the next Ordinary Meeting
(February 7).

FIFTH ORDINARY MEETING.

Monday , February 7, 1921.

’ ci .

Professor Frederick 0. Bower, M.A., D.Sc., LL,D., F.R.S., F.L.S., President, in the Chair.

The President proposed that Rule VI in its amended form should read as follows, and this
was agreed to with the suggestion that an explanatory footnote should be added to obviate
any ambiguity.

“Each Fellow shall, before he is admitted to the privileges of Fellowship, pay an admission
fee of three guineas, and a subscription of three guineas for the year of election. He shall
continue to pay a subscription of three guineas at the beginning of each session so long as he
remains a Fellow.

“ Each Fellow who was elected subsequent to December 1916 and previous to December 1920
shall also pay a subscription of three guineas at the beginning of each session so long as he
remains a Fellow.

“ Each Fellow who was elected previous to December 1916 and who has not completed his
twenty-five annual payments shall, at the beginning of each session, pay three guineas or four
guineas, according as he has or has not made ten annual payments as reckoned from the year of
election. Each Fellow who has completed or shall complete his payments shall be invited to
contribute one guinea per annum or to pay a single sum of ten guineas.

“ A Fellow may compound for the annual subscriptions by a single payment of fifty guineas,
or on such other terms as the Council may from time to time fix,”

1920-21.]

215

Meetings of the Society.

The following Communications were submitted : —

1. The Relation of the Soil Colloids to the Conductivity of the Soil. By T. Bedford
Franklin, B.A. Proc., vol. xli, pp. 61-67.

2. The Natural History of Pack Ice as observed in the Weddell Sea, December 1914 to April
1916. By J. M. Wordie, M.A., F.G.S. Communicated by Professor J. W. Gregory, F.R.S.
Trans., vol. lii, pp. 795-829.

3. Shackleton Antarctic Expedition, 1914-1917 : Bathymetrical Observations in the Weddell
Sea. By J. M. Wordie, M.A., F.G.S. Communicated by Professor J. W. Gregory, F.R.S.
Trans., vol. lii, pp. 781-793.

SIXTH ORDINARY MEETING.

Monday , March 7, 1921.

Professor Frederick 0. Bower, M. A., D.Sc., LL.D., F.R.S., F.L.S., President, in the Chair.

The Ballot for the election of Ordinary Fellows was taken. The Scrutineers were Mr Gall
Inglis and Dr J. M‘Lean Thompson. The undernoted Gentlemen were declared duly elected to
the Ordinary Fellowship of the Society : — Nelson Annandale, William Arthur, Bevan
Braith waite Baker, Archibald Barr, John Bartholomew, Alexander Bruce, Andrew
Campbell, Rasik lal Datta, John Dougall, Charles Vickery Drysdale, George Topham
Forrest. Walcot Gibson, John Wm. Heslop Harrison. James Alex. George Lamb, Rev.
Albert Ernest Laurie, Neil M'Akthitr, Dougald Black M‘Quistan, Thomas Murray
MacRobert, John M'Whan, John Mathieson, Sir Geo. Herbert Pollard, Edward Burns
Ross, Rt. Hon. James Parker Smith, Norman Kemp Smith, Ian Struthers Stewart.

The following Communications were submitted : —

1. On a Graphical Method of Determining Shear Influence Lines, and Diagrams of Maximum
Shearing Force, for a Beam subjected to a Series of Concentrated Rolling Loads. By Professor
A. R. Horne, B.Sc. Proc., vol. xli, pp. 68-72.

2. Studies in Floral Morphology. No. 2 : The Staminal Zygomorphy of Couroupita guianensis,
Aubl. By Dr J. M ‘Lean Thompson. Trans., vol. liii, pp. 1-15.

SEVENTH ORDINARY MEETING.

Monday , March 21, 1921.

Professor Frederick 0. Bower, F.R.S., President, and afterwards Professor R. A. Sampson,
F.R.S., Vice-President, in the Chair.

The following recently elected Ordinary Fellows were admitted and signed the Roll: — Mr
J. A. G. Lamb, the Rev. A. E. Laurie, Mr D. B. M'Quistan, Professor E. B. Ross, and the Rt.
Hon. J. Parker Smith.

The following Communications were submitted : —

1. An Experimental Analysis of the Losses by Evaporation of Liquid Air contained in Vacuum
Flasks. By Professor Henry Briggs, D.Sc. Proc., vol. xli, pp. 97-110.

2. A Generalisation of Lagrange’s Equations of Motion and their Hamiltonian Forms. By Dr
John Marshall, M.A.

3. Note on a Continuant of Cayley’s of the year 1874. By Sir Thomas Muir, C.M.G., LL.D.,
F.R.S. Proc., vol. xli, pp. 111-116.

EIGHTH ORDINARY MEETING.

Monday, May 2, 1921.

Professor Frederick 0. Bower, M.A., D.Sc., LL.D., F.R.S., F.L.S., President, in the Chair.

The following recently elected Ordinary Fellows were admitted and signed the Roll : — Mr B. B.
Baker and Dr Walcot Gibson.

The following Communications were submitted : —

1. Behaviour of an Electrified Pith Ball in an Ionised Atmosphere, illustrated with Experi-
ments. By Dr Dawson Turner and Mr D. M. R. Crombie. Proc., vol. xli, pp. 154-157.

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

2. On Old Red Sandstone Plants showing Structure, from the Rhynie Chert Bed, Aberdeen-
shire. Part IV : Restorations of the Vascular Cryptogams, and discussion of their bearing on the
General Morphology of the Pteridophyta and the Origin of the Organisation of Land-Plants.
Part V : The Thallophyta occurring in the Peat- Bed ; the succession of the Plants throughout a
Vertical Section of the Bed, and the conditions of Accumulation and Preservation of the Deposit.
By Dr R. Kidston, F.R.S., and Professor W. H. Lang, D.Sc., F.R.S. Trans., vol. lii, pp.
831-854, 855-902.

NINTH ORDINARY MEETING.

Monday , June 6, 1921.

Professor Frederick 0. Bower, M.A., D.Sc., LL.D., F. R.S. , F.L.S., President, in the Chair.

By request of the Council, Lt.-Col. Wm. Glen Liston, M.D., Indian Medical Service, gave
an address on “ Plague and Rats.”

A vote of thanks to Col. Liston was proposed by the President, seconded by Major-Gen.
Bannerman, and carried unanimously.

The President announced the award of the Gunning Victoria Jubilee Prize to Mr C. T. R.
Wilson, F. R.S., in recognition of his important discoveries in relation to Condensation Nuclei,
Ionisation of Gases, and Atmospheric Electricity ; and the Makdougall-Brisbane Prize for the
Period 1918-1920 to Professor J. H. Maclagan Wedderburn, M.A., D.Sc., for his many
valuable memoirs in universal algebra which he has published in the Society’s Transactions
and Proceedings and elsewhere. One of these papers, ‘'On the Equations of Motion of a Single
Particle,” falls within the period of award.

The Prizes will he presented at the Meeting on July 4.

TENTH ORDINARY MEETING.

Monday , June 20, 1921.

Professor Frederick 0. Bower, F.R. S. , and afterwards Professor R. A. Sampson, F.R. S.,
Vice-President, in the Chair.

The following Ordinary Fellows were admitted and signed the Roll : — Professor Norman
Kemp Smith, Dr Nelson Annandale, and Mr Ian Bartholomew.

The President announced that the Council had approved of the following nominations for
Honorary Fellowship of the Royal Society of Edinburgh : —

British.

William Henry Perkin, F.R.S., Waynflete Professor of Chemistry in the University of
Oxford; Sir Ronald Ross, K.C.B. , K.C.M.G., F.R.S., Consultant in Malaria, Ministry of
Pensions, London; Sir Ernest Rutherford, Kt., F.R. S., Cavendish Professor of Experimental
Physics in the University of Cambridge; Sir Jethro J. H. Teall, Kt., F.R.S., lately Director
of the Geological Survey of Great Britain and of the Museum of Practical Geology.

Foreign.

Reginald Aldworth Daly, Professor of Geology, Harvard University, Cambridge, Mass. ;
Johan Hjort, Director of Norwegian Fisheries, Bergen; Charles Louis Alphonse Laveran,
Nobel Laureate, Medicine, 1907, Paris ; Heike Kamerlingh Onnes, Nobel Laureate, Physics,
1913, Leiden, Holland; Salvatore Pincherle, Professor of Mathematics in the University of
Bologna.

The following Communications were submitted : —

1. The Annual Incidence of Intelligence and its Measurement by the American Army Tests.
By Mungo M'Callum Fairorieve, M.A. Proc., vol. xli, pp. 150-153.

2. Shackleton Antarctic Expedition, 1914-1917: Geological Observations in the Weddell Sea
Area. By J. M. Wordie, M.A. , F.G.S. Communicated by Professor J. W. Gregory, F.R.S.
Trans., vol. liii, pp. 17-27.

3. On the Criterion for Stable Flow of a Fluid in a Uniform Channel. By Hyman Levy,
M.A., D.Sc. Proc., vol. xli, pp. 136-147.

4. The Genus Clisiophyllum. By Professor P. Macnair, F.G.S., and Colin M. Leitch,
O.B.E., B.Sc.

5. Exhibition of Lantern Slides by Dr Nelson Annandale, Director Zoological Survey of
India.

1920-21.]

Meetings of the Society.

217

ELEVENTH ORDINARY MEETING.

Monday , July 4, 1921.

Professor Frederick 0. Bower, M.A., D.Sc., LL.D., F.R.S., F.L.S., President, in the Chair.

A Ballot was taken for election to the Honorary Fellowship of the Society. Dr H. S. Allen
and Dr G. A. Carse were nominated as Scrutineers and the undernoted gentlemen were declared
duly elected to the Honorary Fellowship : —

British Honorary Fellows.

Foreign Honorary Fellows.

William Henry Perkin.
Sir Ronald Ross.

Sir Ernest Rutherford.
Sir Jethro J. H. Teall.

Reginald Aldworth Daly.

Johan Hjort.

Charles Louis Alphonse Laveran.
Heike Kamerlingh Onnes.
Salvatore Pincherle.

Dr T. M. MacRobert and Mr Wm. Arthur signed the Roll and were admitted as Ordinary
Fellows of the Society.

The President announced the awards of the Gunning Victoria Jubilee and Makdougall-Brisbane
Prizes, in the following terms, and presented the Prizes.

The Gunning Victoria Jubilee Prize is awarded to Mr C. T. R. Wilson, F. R.S., in recognition
of his important discoveries in relation to Condensation Nuclei, Ionisation of Gases, and Atmo-
spheric Electricity.

Mr Wilson’s first group of important contributions to science {Phil. Trams., vol. clxxxix,
1897 : vol. cxciii, 1899) related to Condensation Nuclei, a subject which had been initiated by
our distinguished Fellow — Dr John Aitken. He discovered the existence of two definite limits
to the supersaturation in moist dust-free gases, a lower limit beyond which rain-like condensation
occurs, and an upper limit beyond which cloud-like condensation occurs. He showed that nuclei
identical with those which give rise to the rain-like condensation are produced in great numbers
by X-rays and other agents which give conducting power to a gas ; and proved that such nuclei
are removed by an electric field and are therefore identical with the charged “ions” to which the
conducting power of the gas is due. This discovery furnished much more direct evidence than
any previously available for the existence of discrete “ions,” each individual ion being made
visible by the condensation of water upon it. The earliest determinations of the charge carried
by an ion were made by J. J. Thomson and H. A. Wilson by applying this method.

Mr Wilson’s next group of researches (Camb. Phil. Soc. Proc., 1900-1902; Proc. Roy.
Soc., vol. lxviii, 1901 ; vol. lxix, 1902) related to the natural ionisation of gases. He showed
that air and other gases conduct electricity to a minute extent under normal conditions, even
when dust-free and contained in closed vessels. This conduction he proved to be due to the
continual production of ions, the number produced per sec. being determined. The method
introduced for the purpose of this investigation has since been extensively used in radio-active and
similar work.

After this Mr Wilson’s attention was turned to Atmospheric Electricity (Camb. Phil. Soc.
Proc., vol. xiii, 1905-06; Proc. Roy. Soc., vol. lxxx, 1908). He devised a new method for
measuring the surface charge on the ground (and hence the vertical electric force) and at the
same time determined directly the current from the atmosphere into the ground. These experi-
ments, which were made at Peebles, gave the first direct measures of this current.

In 1911-1912 (Proc. Roy. Soc., vol. lxxxv, 1911 ; vol. lxxxvii, 1912) he published important
work on the Tracks of Ionising Particles. The expansion apparatus of the earlier condensation
experiments was modified so that the ions were made visible as minute drops and photographed
in the position which they occupied immediately after their liberation. The tracks of the indivi-
dual alpha and beta rays from radium and its products, and of the electrons emitted in air when
exposed to X-rays, were thus made visible. In the case of the fast /3-rays the individual ions
liberated along the track of the corpuscle are made visible in the photographs. This work made
clear the nature of the ionisation of a gas by X-rays, viz., that it consists in the ejection, from
the atoms of the gas, of electrons, each of which ionises the gas along the course of its flight.

In more recent years Mr Wilson has published further researches in Atmospheric Electricity
and Thunderstorms {Proc. Roy. Soc., vol. xcii, 1916; Phil. Trans., vol. ccxxi, 1920). The
method of measuring the surface charge on the ground was modified so as to allow of automatic
records being obtained, a special type of capillary electrometer being devised for the purpose of
measuring charges. This was applied to study the variations in the electric field during thunder-
storms, including the sudden changes produced by the passage of lightning flashes at various
distances. The “electric moments” of a large number of flashes were thus measured, and
estimates obtained of the quantity of electricity which passes in a flash. The results of these
observations have been applied to the Theory of Thunderstorms.

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

The Makdougall-Brisbane Prize for the period 1918-1920 is awarded to Professor J. H.
Maclagan Wedderbukn of Princeton University for the many valuable memoirs which he has
published in our Transactions and Proceedings and elsewhere. One of these memoirs falls within
the period of award of the prize — “On the Equations of Motion of a Single Particle.” Among
the other memoirs may be mentioned —

Isoclinal Lines of a Differential Equation of the 1st Order. Proc.R.S.E., vol. xxiv, p. 400,
1903.

General Scalar Functions of a Vector. Proc.R.S.E vol. xxiv, p. 409, 1903.

Applications of Quaternions in the Theory of Differential Equations. Trans.R.S.E. , vol.
xl, p. 709, 1903.

And a number of important papers on Hypercomplex Numbers published in the Transactions of the
American Mathematical Society.

By request of the Council, Mr 0. T. R. Wilson, M.A., B.Sc., F.R.S. , gave an address on
“ Some Recent Work on Lightning and Thunderstorms.”

The following Communications were submitted : —

1. The Adsorption of Gas under Pressure. By Professor Henry Briggs, D.Sc., and Wm.
Cooper, M.A., B.Sc. Proc., vol. xli, pp. 119-127.

2. The Utilisation of Solid Caustic Soda in the Absorption of Carbon Dioxide. By Miss
Elizabeth Gilchrist, M.A., B.Sc, Communicated by Professor Henry Briggs, D.Sc. Proc.,
vol. xli, pp. 128-135.

3. On the Development of the Feathers of the Duck during the Incubation Period. By Miss
Augusta Lamont, B.Sc. Communicated by Professor J. Cossar Ewart, F.R.S.

4. Note on Conditions for Mirage. By Alex. G. Ramage. Proc., vol. xli, pp. 148-149.

1920-21.

Meetings of the Society.

219

PROCEEDINGS OF THE STATUTORY GENERAL MEETING
Ending the 138th Session, 1920-1921.

* At the Statutory Meeting of the Royal Society of Edinburgh, held in the Society’s Lecture
Room, 24 George Street, on Monday, October 24, 1921, at 4.30 p.m.,

Professor F. 0. Bower, F. R.S., President, in the Chair,
the Minutes of the last Statutory Meeting of October 25, 1920, were read, approved, and signed.

The Chairman nominated as Scrutineers Mr C. H. Milne and Dr J. B. Ritchie.

The Ballot for the Election of Office-Bearers and Members of Council was then taken.

The Secretary submitted the following Report : —

The number of papers read at our meetings during the last Session was 35, as compared with
27 the previous Session. Of these, 3 were addresses: the first by the President on “Size a
Neglected Factor in the Internal Morphology of Plants”; the second by Lt.-Col. Liston on
“Plague and Rats” ; and the third by Mr C. T. R. Wilson on “Some Recent Work on Lightning
and Thunderstorms.’’ Of the others, 5 were in mathematics, 1 in statistics, 9 in physics, 2 in
chemistry, 5 in zoology, 2 in botany, 5 in geology, 2 in oceanography, and 1 in engineering.
Twenty-eight of these have been, or are being, published — 11 in the Transactions and 17 in the
Proceedings.

Last Session the Society elected 25 new Ordinary Fellows, and 9 Honorary Fellows — 4 British
and 5 Foreign. Three Fellows have resigned, and we have lost by death 4 Honorary Fellows and
22 Ordinary Fellows.

The Makdougall-Brisbane Prize was awarded to Professor J. H. Maclagan Wedderburn of
Princeton, U. S. A. ; and the Gunning Victoria Jubilee Prize to Mr C. T. R. Wilson of Cambridge.

The vacancy in the post of Assistant Librarian, occasioned by the resignation of Miss Le
Harivel, has been filled up by the appointment of Mr Ernst M. Stewart.

The high cost of printing and publication still continues to hamper the work of the Society .
To meet to some extent the increased expense, the Council asked the Society to amend Law VI
and raise the annual subscription by one guinea. This was agreed to, and the amendment of
Law VI was duly carried out at the Meeting of February 7, 1921.

The Grant of £3000 from the Carnegie United Kingdom Trust for binding the journals in the
Library is now nearly all expended ; and again the Society takes the opportunity of expressing its
thanks to the Trust for their generous help.

The Conjoint Board of Scientific Societies has prepared an important report on the question of
aid to Scientific Societies for publication of papers, and our representatives have been instructed
to look specially to our interests in any further developments which may occur.

One of the great events of the year was the Meeting of the British Association for the Advance-
ment of Science. This our Society helped by a donation of £100 towards the local expenses and
by inviting the Members to a free use of the Library and Reading-room. The Secretaries also
organised, by request of the Council, a Royal Societies dinner, at which our Society entertained
Fellows of the Royal Society of London, Members of the Royal Irish Academy, and distinguished
Foreign visitors who were members of their National Academies. The dinner was held in the
Freemasons’ Hall on Monday, September 12, when our President, with the Maharaj Rana of
Jhalawar on his right hand, presided over a gathering of one hundred and eighty-one scientific
men from many lands.

During the summer, and especially in view of the British Association Meeting, the Council
arranged for cleaning and painting the west staircase and lecture room, and laying new matting
on the stairs.

As will be seen from the Treasurer’s Report, the financial condition of the Society is fairly satis-
factory. notwithstanding these exceptional but necessary outlays during the Session.

The Treasurer in submitting his Report for the year compared the Income and Expenditure
with those of the previous year.

Dr R. Kidston, F. R S. , moved the adoption of the Reports and the reappointment of Messrs
Lindsay, Jamieson & Haldane, C.A., as auditors of the accounts for the ensuing Session.

This was unanimously agreed to.

220

Proceedings of the Boyal Society of Edinburgh.

The Scrutineers reported that the Ballot Papers were in order, and that the following Office-
Bearers and Members of Council had been elected : —

Professor Frederick 0. Bower, M.A., D.Sc., LL.D., F.R.S
Sir George A. Berry, M.B., C.M., LL.D., F.R.C.S.E., „

Professor William Peddie, D.Sc.,

Principal Sir James Alfred Ewing, K.C.B., M.A., D.Sc.,
LL.D., M.Inst.C.E., F.R.S.

Professor John Walter Gregory, D.Sc., F.R.S.
Major-General W. B. Bannerman, C.S.I., I.M.S., M.D.,
D.Sc.

W. A. Tait, D.Sc., M.Inst.C.E.

F.L.S. , President.

Vice-Presidents.

Cargill G. Knott, D.Sc., LL.D., F.R.S., General Secretary.

Professor E. T. Whittaker, Sc.D., F.R.S., \ Secretaries to Ordinary

Professor J. H. Ashworth, D.Sc., F.R.S., j Meetings.

James Currie, M.A., LL.D., Treasurer.

A. Crichton Mitchell, D.Sc., Hon. D.Sc. (Geneva), Curator of Library and Museum.

ORDINARY MEMBERS OF COUNCIL.

Henry Moubray Cadell, of Grange, B.Sc.
Professor Arthur Robertson Cushny, M.A.,
M.D., LL.D., F.R.S.

Professor Francis Gibson Baily, M.A.,
M.Inst.E.E.

George James Lidstone, F.F.A., F.I.A.
Robert Campbell, M.A. , D.Sc., F.G.S.
Principal James Colquhoun Irvine, C.B.E.,
Ph.D., D.Sc., LL.D., F.R.S.

The Hon. Lord Salvesen.

Professor J. Arthur Thomson, M.A., LL.D.
Herbert Stanley Allen, M.A., D.Sc.

Sir Robert Blyth Greig, M.A., LL.D.,
F.Z.S.

James Ritchie, D.Sc.

Ernest Maclagan Wedderburn, M.A., LL.B.,
W.S., D.Sc.

SOCIETY’S REPRESENTATIVE ON GEORGE HERIOT’S TRUST.

W. A. Tait, D.Sc., M.Inst.C.E.

The Chairman, in the name of the Society, thanked the Scrutineers for their services

PUBLIC BUSINESS.

An Obituary Notice of Robert Munro, M.A., M.D., LL.D., by Dr George Macdonald, C.B.,
was read by Dr C. G. Knott, General Secretary. Proc., vol. xli, pp 158-169.

The President summarised the position of the Society on the working of the year just closed,
as regards the volume of work presented for publication and the showings of the Balance Sheet.
He pointed out that the volume of work was at present considerably below the average of pre-war
years, and forecasted the strong probability that in the near future, when the immediate effects of
the war had been worked off, an even larger volume of work would be offered than the average of
the years before the war.

He drew attention to the importance of keeping in close touch with the younger men, who are
at the outset of their productive period : and he suggested as being worthy of consideration by the
Society, the possible constitution of a junior grade of membership to which the younger men might
belong. It might stand to the full Fellowship in somewhat the same relation as in the Royal
Academy the A.R. A. stands to the rank of full Academician.

Keith, Brisbane, Neill, Gunning, and Scott Prizes. 221

THE KEITH, MAKDOUGALL-BRISBANE, NEILL, GUNNING
VICTORIA JUBILEE, AND JAMES SCOTT PRIZES.

The above Prizes will be awarded by the Council in the following manner : —

I. KEITH PRIZE.

The Keith Prize, consisting of a Gold Medal and from £40 to £50 in Money,
will be awarded in the Session 1923-1924 for the “ best communication on a scientific
subject, communicated,* in the first instance, to the Royal Society of Edinburgh
during the Sessions 1921-1922 and 1922-1923.” Preference will be given to a
paper containing a discovery.

II. MAKDOUGALL-BRISBANE PRIZE.

This Prize is to be awarded biennially by the Council of the Royal Society of
Edinburgh to such person, for such purposes, for such objects, and in such manner
as shall appear to them the most conducive to the promotion of the interests of
science ; with the proviso that the Council shall not be compelled to award the
Prize unless there shall be some individual engaged in scientific pursuit, or some
paper written on a scientific subject, or some discovery in science made during the
biennial period, of sufficient merit or importance in the opinion of the Council to
be entitled to the Prize.

1. The Prize, consisting of a Gold Medal and a sum of Money, will be awarded
before the close of the Session 1922-1923, for an Essay or Paper having reference
to any branch of scientific inquiry, whether Material or Mental.

2. Competing Essays to be addressed to the Secretary of the Society, and trans-
mitted not later than 8th July 1922.

3. The Competition is open to all men of science.

4. The Essays may be either anonymous or otherwise. In the former case,
they must be distinguished by mottoes, with corresponding sealed billets, super-
scribed with the same motto, and containing the name of the Author.

5. The Council impose no restriction as to the length of the Essays, which may
be, at the discretion of the Council, read at the Ordinary Meetings of the Society.
They wish also to leave the property and free disposal of the manuscripts to the
Authors ; a copy, however, being deposited in the Archives of the Society, unless
the paper shall be published in the Transactions.

* For the purposes of this award the word “communicated” shall be understood to mean the
date on which the manuscript of a paper is received in its final form for printing, as recorded by
the Genera] Secretary or other responsible official.

222 Proceedings of the Royal Society of Edinburgh.

6. In awarding the Prize, the Council will also take into consideration any
scientific papers presented* to the Society during the Sessions 1918-19, 1919-20,
whether they may have been given in with a view to the prize or not.

III. NEILL PRIZE.

The Council of the Royal Society of Edinburgh having received the bequest of
the late Dr Patrick Neill of the sum of £500, for the purpose of “the interest
thereof being applied in furnishing a Medal or other reward every second or third
year to any distinguished Scottish Naturalist, according as such Medal or reward
shall be voted by the Council of the said Society,” hereby intimate :

1. The Neill Prize, consisting of a Gold Medal and a sum of Money, will be
awarded during the Session 1923-1924.

2. The Prize will be given for a Paper of distinguished merit, on a subject of
Natural History, by a Scottish Naturalist, which shall have been presented * to the
Society during the two years preceding the fourth Monday in October 1923, — or
failing presentation of a paper sufficiently meritorious, it will be awarded for a work
or publication by some distinguished Scottish Naturalist, on some branch of Natural
History, bearing date within five years of the time of award.

IV. GUNNING VICTORIA JUBILEE PRIZE.

This Prize, founded in the year 1887 by Dr R, H. Gunning, is to be awarded
quadrennially by the Council of the Royal Society of Edinburgh, in recognition of
original work in Physics, Chemistry, or Pure or Applied Mathematics.

Evidence of such work may be afforded either by a Paper presented to the
Society, or by a Paper on one of the above subjects, or some discovery in them
elsewhere communicated or made, which the Council may consider to be deserving
of the Prize.

The Prize consists of a sum of money, and is open to men of science resident in
or connected with Scotland. The first award was made in the year 1887. The
next award will be made in 1924-1925.

In accordance with the wish of the Donor, the Council of the Society may on
fit occasions award the Prize for work of a definite kind to be undertaken during
the three succeeding years by a scientific man of recognised ability.

V. JAMES SCOTT PRIZE.

This Prize, founded in the year 1918 by the Trustees of the James Scott
Bequest, is to be awarded triennially, or at such intervals as the Council of the
Royal Society of Edinburgh may decide, “ for a lecture or essay on the funda-
mental concepts of Natural Philosophy.”

The first award will be in the year 1922.

* For the purposes of this award the word “presented ” shall be understood to mean the date
on which the manuscript of a paper is received in its final form for printing, as recorded by the
General Secretary or other responsible official.

Keith, Brisbane, Neill, Gunning, and Scott Prizes. 223

RESOLUTIONS OF COUNCIL IN REGARD TO THE MODE
OF AWARDING PRIZES.

(See Minutes of Meeting of January 18, 1915.)

I. With regard to the Keith and Makdougall-Brisbane Prizes, which are open
to all Sciences, the mode of award will be as follows : —

1. Papers or essays to be considered shall be arranged in two groups, A and B,

— Group A to include Astronomy, Chemistry, Mathematics, Metallurgy,
Meteorology and Physics ; Group B to include Anatomy, Anthropology,
Botany, Geology, Pathology, Physiology, and Zoology.

2. These two Prizes shall be awarded to each group in alternate biennial periods,

provided papers worthy of recommendation have been communicated to
the Society.

3. Prior to the adjudication the Council shall appoint, in the first instance, a

Committee composed of representatives of the group of Sciences which did
not receive the award in the immediately preceding period. The Com-
mittee shall consider the Papers which come within their group of Sciences,
and report in due course to the Council.

4. In the event of the aforesaid Committee reporting that within their group of

subjects there is, in their opinion, no paper worthy of being recommended
for the award, the Council, on accepting this report, shall appoint a
Committee representative of the alternate group to consider papers coming
within their group and to report accordingly.

5. Papers to be considered by the Committees shall fall within the period dating

from the last award in groups A and B respectively.

II. With regard to the Neill Prize, the term “Naturalist” shall be understood
to include any student in the Sciences composing group B, namely, Anatomy,
Anthropology, Botany, Geology, Pathology, Physiology, Zoology.

224 Proceedings of the Royal Society of Edinburgh.

AWARDS OF THE KEITH, MAKDOUGALL - BRISBANE,
NEILL, AND GUNNING PRIZES.

I. KEITH PRIZE.

1st Biennial Period, 1827-29. — Dr Brewster, for his papers “on his Discovery of Two New
Immiscible Fluids in the Cavities of certain Minerals,’’ published in the Transactions of
the Society.

2nd Biennial Period, 1829-31. — Dr Brewster, for his paper “on a New Analysis of Solar
Light,” published in the Transactions of the Society.

3rd Biennial Period, 1831-33. — Thomas Graham, Esq., for his paper “on the Law of the
Diffusion of Gases,” published in the Transactions of the Society.

4th Biennial Period, 1833-35.— Professor J. D. Forbes, for his paper “ on the Refraction and
Polarization of Heat,” published in the Transactions of the Society.

5th Biennial Period, 1835-37. — John Scott Russell, Esq., for his researches “on Hydro-
dynamics,” published in the Transactions of the Society.

6th Biennial Period, 1837-39. — Mr John Shaw, for his experiments “ on the Development
and Growth of the Salmon,” published in the Transactions of the Society.

7th Biennial Period, 1839-41. — Not awarded.

8th Biennial Period, 1841-43. — Professor James David Forbes, for his papers “on
Glaciers,” published in the Proceedings of the Society.

9th Biennial Period, 1843-45. — Not awarded.

10th Biennial Period, 1845-47.— General Sir Thomas Brisbane, Bart., for the Makerstoun
Observations on Magnetic Phenomena, made at his expense, and published in the Trans-
actions of the Society.

11th Biennial Period, 1847-49. — Not awarded.

12th Biennial Period, 1849-51. — Professor Kelland, for his papers “on General Differentia-
tion, including his more recent Communication on a process of the Differential Calculus, and
its application to the solution of certain Differential Equations,” published in the Transac-
tions of the Society.

13th Biennial Period, 1851-53. — W. J. Macquorn Rankine, Esq., for his series of papers
“on the Mechanical Action of Heat,” published in the Transactions of the Society.

14th Biennial Perioo, 1853-55.— Dr Thomas Anderson, for his papers “on the Crystalline
Constituents of Opium, and on the Products of the Destructive Distillation of Animal
Substances,” published in the Transactions of the Society.

15th Biennial Period, 1855-57. — Professor Boole, for his Memoir “on the Application of
the Theory of Probabilities to Questions of the Combination of Testimonies and Judgments,”
published in the Transactions of the Society.

16th Biennial Period, 1857-59. — Not awarded.

17th Biennial Period, 1859-61. — John Allan Broun, Esq., F.R.S., Director of the Trevandrum
Observatory, for his papers “on the Horizontal Force of the Earth’s Magnetism, on the
Correction of the Bifilar Magnetometer, and on Terrestrial Magnetism generally,” published
in the Transactions of the Society.

18th Biennial Period, 1861-63. — Professor William Thomson, of the University of Glasgow,
for his Communication “on some Kinematical and Dynamical Theorems.”

19th Biennial Period, 1863-65. — Principal Forbes, St Andrews, for his “Experimental
Inquiry into the Laws of Conduction of Heat in Iron Bars,” published in the Transactions
of the Society.

20th Biennial Period, 1865-67. — Professor C. Piazzi Smyth, for his paper “on Recent
Measures at the Great Pyramid,” published in the Transactions of the Society.

21st Biennial Period, 1867-69. — Professor P. G. Tatt, for his paper “on the Rotation of a
Rigid Body about a Fixed Point,” published in the Transactions of the Society.

22nd Biennial Period, 1869-71. — Professor Clerk Maxwell, for his paper “on Figures,
Frames, and Diagrams of Forces,” published in the Transactions of the Society.

225

Keith, Brisbane, Neill and Gunning Prizes.

23rd Biennial Period, 1871-73. — Professor P. G. Tait, for his paper entitled ‘ ‘ First Approxi-
mation to a Thermo-electric Diagram,” published in the Transactions of the Society.

24th Biennial Period, 1873-1875. — Professor Crum Brown, for his Researches “ on the Sense of
Rotation, and on the Anatomical Relations of the Semicircular Canals of the Internal Ear.”

25th Biennial Period, 1875-77.— Professor M. Forster Heddle, for- his papers ££on the
Rhombohedral Carbonates,” and “on the Felspars of Scotland,” published in the Transac-
tions of the Society.

26th Biennial Period, 1877-79. — Professor H. C. Fleeming Jenkin, for his paper “on the
Application of Graphic Methods to the Determination of the Efficiency of Machinery,”
published in the Transactions of the Society ; Part II having appeared in the volume for
1877-78.

27th Biennial Period, 1879-81. — Professor George Chrystal, for his paper “ on the Differ-
ential Telephone, ” published in the Transactions of the Society.

28th Biennial Period, 1881-83. — Thomas Muir, Esq., LL.D., for his “ Researches into the
Theory of Determinants and Continued Fractions,” published in the Proceedings of the
Society.

29th Biennial Period, 1883-85. — John Aitken, Esq., for his paper “on the Formation of
Small Clear Spaces in Dusty Air,” and for previous papers on Atmospheric Phenomena,
published in the Transactions of the Society.

30th Biennial Period, 1885-87. — John Young Buchanan, Esq., for a series of communica-
tions, extending over several years, on subjects connected with Ocean Circulation,
Compressibility of Glass, etc.; two of which, viz., “On Ice and Brines,” and “On the
Distribution of Temperature in the Antarctic Ocean, ’’have been published in the Proceedings
of the Society.

31st Biennial Period, 1887-89. — Professor E. A. Letts, for his papers on the Organic
Compounds of Phosphorus, published in the Transactions of the Society.

32nd Biennial Period, 1889-91. — R. T. Omond, Esq., for his contributions to Meteorological
Science, many of which are contained in vol. xxxiv of the Society’s Transactions.

33rd Biennial Period, 1891-93. — Professor Thomas R. Fraser, F.R.S., for his papers on
Strophanthus hispidus, Strophanthin , and Strophanthidin, read to the Society in February
and June 1889 and in December 1891, and printed in vols. xxxv, xxxvi, and xxxvii of
the Society’s Transactions.

34th Biennial Period, 1893-95. — Dr Cargill G. Knott, for his papers on the Strains produced
by Magnetism in Iron and in Nickel, which have appeared in the Transactions and
Proceedings of the Society.

35th Biennial Period, 1895-97. — Dr Thomas Muir, for his continued communications on
Determinants and Allied Questions.

36th Biennial Period, 1897—99. — Dr James Burgess, for his paper “on the Definite Integral
2

6 ~t2dt, with extended Tables of Values,” printed in vol. xxxix of the Transactions

y}

V7

of the Society.

37th Biennial Period, 1899-1901. — Dr Hugh Marshall, for his discovery of the Persulphates,
and for his Communications on the Properties and Reactions of these Salts, published in the
Proceedings of the Society.

38th Biennial Period, 1901-03.— Sir William Turner, K.C.B., LL.D., F.R.S., etc., for his
memoirs entitled “A Contribution to the Craniology of the People of Scotland,” published in
the Transactions of the Society, and for his £ £ Contributions to the Craniology of the People
of the Empire of India,” Parts I, II, likewise published in the Transactions of the
Society.

39th Biennial Period, 1903-05.— Thomas H. Bryce, M.A., M.D., for his two papers on “The
Histology of the Blood of the Larva of Lepidosiren paradoxa” published in the Transactions
of the Society within the period.

40th Biennial Period, 1905-07. — Alexander Bruce, M.A., M.D., F.R.C.P.E., for his paper
entitled “Distribution of the Cells in the Intermedio-Lateral Tract of the Spinal Cord,”
published in the Transactions of the Society within the period.

41st Biennial Period, 1907-09. — Wheelton Hind, M.D., B.S., F.R.C.S., F.G.S., for a paper
published in the Transactions of the Society, “On the Lamellibranch and Gasteropod Fauna
found in the Millstone Grit of Scotland.”

42nd Biennial Period, 1909-11. — Professor Alexander Smith, B.Sc., Ph.D., of New York,
for his researches upon “Sulphur” and upon “Vapour Pressure,” appearing in the
Proceedings of the Society.

VOL. XLI.

15

226 Proceedings of the Royal Society of Edinburgh.

43rd Biennial Period, 1911-1913. — James Russell, Esq., for his series of investigations
relating to magnetic phenomena in metals and the molecular theory of magnetism, the
results of which have been published in the Proceedings and Transactions of the Society,
the last paper having been issued within the period.

44th Biennial Period, 1913-15. — James Hartley Ashworth, D.Sc., for his papers on
“Larvae of Lingula and Pelagodiscus,” and on “ Sclerocheilus,” published in the Transac-
tions of the Society, and for other papers on the Morphology and Histology of Polychseta.

45th Biennial Period, 1915-17. — Robert C. Mossman, for his work on the Meteorology of the
Antarctic Regions, which originated with the important series of observations made by him
during the voyage of the “Scotia” (1902-1904), and includes his paper “On a Sea-Saw
of Barometric Pressure, Temperature, and Wind Velocity between the Weddell Sea and the
Ross Sea,” published in the Proceedings of the Society.

46th Biennial Period, 1917-19. — John Stephenson, Lt.-Col. I.M.S., for his series of papers
on the Oligochaeta and other Annelida, several of which have been published in the
Transactions of the Society.

II. MAKDOUGALL-BRISBANE PRIZE.

1st Biennial Period, 1859. — Sir Roderick Impey Murchison, on account of his Contributions
to the Geology of Scotland.

2nd Biennial Period, 1860-62. — William Seller, M.D., F.R.C.P.E., for his “Memoir of the
Life and Writings of Dr Robert Whytt,” published in the Transactions of the Society.

3rd Biennial Period, 1862-64. — John Denis Macdonald, Esq., R.N., F.R.S., Surgeon of
H.M.S. “Icarus,” for his paper “ on the Representative Relationships of the Fixed and Free
Tunicata, regarded as Two Sub-classes of equivalent value; with some General Remarks on
their Morphology,” published in the Transactions of the Society.

4th Biennial Period, 1864-66. — Hot awarded.

5th Biennial Period, 1866-68. — Dr Alexander Crum Brown and Dr Thomas Richard
Fraser, for their conjoint paper “on the Connection between Chemical Constitution and
Physiological Action,” published in the Transactions of the Society.

6th Biennial Period, 1868-70. — Not awarded.

7th Biennial Period, 1870-72. — George James Allman, M.D., F.R.S., Emeritus Professor of
Natural History, for his paper “on the Homological Relations of the Ccelenterata,” published
in the Transactions, which forms a leading chapter of his Monograph of Gymnoblastic or
Tubularian Hydroids — since published.

8th Biennial Period, 1872-74. — Professor Lister, for his paper “on the Germ Theory of
Putrefaction and the Fermentive Changes,” communicated to the Society, 7th April 1873.

9th Biennial Period, 1874-76. — Alexander Buchan, A.M., for his paper “on the Diurnal
Oscillation of the Barometer,” published in the Transactions of the Society.

10th Biennial Period, 1876-78. — Professor Archibald Geikie, for his paper “on the Old
Red Sandstone of Western Europe,” published in the Transactions of the Society.

11th Biennial Period, 1878-80. — Professor Piazzi Smyth, Astronomer- Royal for Scotland, for
his paper “on the Solar Spectrum in 1877-78, with some Practical Idea of its probable
Temperature of Origination,” published in the Transactions of the Society.

12th Biennial Period, 1880-82. — Professor James Geikie, for his “Contributions to the
Geology of the North-West of Europe,” including his paper “on the Geology of the
Faroes,” published in the Transactions of the Society.

13th Biennial Period, 1882-84. — Edward Sang, Esq., LL.D., for his paper “on the Need of
Decimal Subdivisions in Astronomy and Navigation, and on Tables requisite therefor,” and
generally for his Recalculations of Logarithms both of Numbers and Trigonometrical Ratios,
— the former communication being published in the Proceedings of the Society.

14th Biennial Period, 1884-86. — John Murray, Esq., LL.D., for his papers “ On the Drainage
Areas of Continents, and Ocean Deposits,” “The Rainfall of the Globe, and Discharge of
Rivers,” “The Height of the Land and Depth of the Ocean,” and “The Distribution of
Temperature in the Scottish Lochs as affected by the Wind.”

15th Biennial Period, 1886-88. — Archibald Geikie, Esq., LL.D., for numerous Communica-
tions, especially that entitled “ History of Volcanic Action during the Tertiary Period in the
British Isles,” published in the Transactions of the Society.

16th Biennial Period, 1889-90. — Dr Ludwig Becker, for his paper on “The Solar Spectrum at
Medium and Low Altitudes,” printed in vol. xxxvi, Part I, of the Society’s Transactions.

227

Keith, Brisbane, Neill, and Gunning Prizes.

17th Biennial Period, 1890-92. — Hugh Robert Mill, Esq., D.Sc., for his papers on ‘'The
Physical Conditions of the Clyde Sea Area,” Part I being already published in vol. xxxvi
of the Society’s Transactions.

18th Biennial Period, 1892-94. — Professor James Walker, D.Sc., Ph.D., for his work on
Physical Chemistry, part of which has been published in the Proceedings of the Society, vol.
xx, pp. 255-263. In making this award, the Council took into consideration the work
done by Professor Walker along with Professor Crum Brown on the Electrolytic Synthesis
of Dibasic Acids, published in the Transactions of the Society.

19th Biennial Period, 1894-96. — Professor John G. M'Kendrick, for numerous Physiological
papers, especially in connection with Sound, many of which have appeared in the Society’s
publications.

20th Biennial Period, 1896-98. — Dr William Peddie, for his papers on the Torsional Rigidity
of Wires.

21st Biennial Period, 1898-1900. — Dr Ramsay H. Traquair, for his paper entitled “ Report on
Fossil Fishes collected by the Geological Survey in the Upper Silurian Rocks of Scotland,”
printed in vol. xxxix of the Transactions of the Society.

22nd Biennial Period, 1900-02. — Dr Arthur T. Masterman, for his paper entitled “The
Early Development of Cribrella oculata (Forbes), with remarks on Echinoderm Development,”
printed in vol. xl of the Transactions of the Society.

23rd Biennial Period, 1902-04. — Mr John Dougall, M.A., for his paper on “An Analytical
Theory of the Equilibrium of an Isotropic Elastic Plate,” published in vol. xli of the
Transactions of the Society.

24th Biennial Period, 1904-06.— Jacob E. Halm, Ph.D., for his two papers entitled “Spectro-
scopic Observations of the Rotation of the Sun,” and “ Some Further Results obtained with
the Spectroheliometer,” and for other astronomical and mathematical papers published in
the Transactions and Proceedings of the Society within the period.

25th Biennial Period, 1906-08. — D. T. Gwynne-Vaughan, M.A., F.L.S., for his papers,
1st, “ On the Fossil Osmundacese, ” and 2nd, “ On the Origin of the Adaxially-curved Leaf-
trace in the Filicales,” communicated by him conjointly with Dr R. Kidston.

26th Biennial Period, 1908-10. — Ernest MacLagan Wedderburn, M.A., LL.B., for his
series of papers bearing upon “ The Temperature Distribution in Fresh-water Lochs,” and
especially upon “The Temperature Seiche.”

27th Biennial Period, 1910-12. — John Brownlee, M.A., M.D., D.Sc., for his contributions
to the Theory of Mendelian Distributions and cognate subjects, published in the Proceedings
of the Society within and prior to the prescribed period.

28th Biennial Period, 1912-14. — Professor C. R. Marshall, M.D., M.A., for his studies “On
the Pharmacological Action of Tetra-alkyl-ammonium Compounds.”

29 th Biennial Period, 1914-16. —Robert Alexander Houstoun, Ph.D., D.Sc., for his series
of papers on “The Absorption of Light by Inorganic Salts,” published in the Proceedings
of the Society.

30th Biennial Period, 1916-18. — Professor A. Anstruther Lawson for his Memoirs on “The
Prothalli of Tmesipteris Tannensis and of Psilotum ,” published in the Transactions of the
Society, together with previous papers on Cytology and on The Gametophytes of various
Gym nos perms.

31st Biennial Period, 1918-20. — Professor J. H. Maclagan Wedderburn of Princeton
University for his Memoirs in Universal Algebra, etc., published in the Transactions and
Proceedings of the Society, and elsewhere.

III. THE NEILL PRIZE.

1st Triennial Period, 1856-59. — Dr W. Lauder Lindsay, for his paper “on the Spermogones
and Pycnides of Filamentous, Fruticulose, and Foliaceous Lichens,” published in the Trans-
actions of the Society.

2nd Triennial Period, 1859-61. — Robert Kaye Greville, LL.D., for his contributions to
Scottish Natural History, more especially in the department of Cryptogamic Botany,
including his recent papers on Diatomaceie.

3rd Triennial Period, 1862-65. — Andrew Crombie Ramsay, F.R.S., Professor of Geology in
the Government School of Mines, and Local Director of the Geological Survey of Great
Britain, for his various works and memoirs published during the last five years, in which he
has applied the large experience acquired by him in the Direction of the arduous work of
the Geological Survey of Great Britain to the elucidation of important questions bearing on
Geological Science.

228

Proceedings of the Royal Society of Edinburgh.

4th Triennial Period, 1865-68. — Dr William Carmichael M‘Intosh, for his paper “on the
Structure of the British Nemerteans, and on some New British Annelids,’’ published in the
Transactions of the Society.

5th Triennial Period, 1868-71. — Professor William Turner, for his papers “ on the Great
Finner Whale ; and on the Gravid Uterus, and the Arrangement of the Foetal Membranes
in the Cetacea,” published in the Transactions of the Society.

6th Triennial Period, 1871-74. — Charles William Peach, Esq., for his Contributions to
Scottish Zoology and Geology, and for his recent contributions to Fossil Botany.

7th Triennial Period, 1874-77. — Dr Ramsay H. Traquair, for his paper “ on the Structure
and Affinities of Tristichopterus alatus (Egerton),” published in the Transactions of the
Society, and also for his contributions to the Knowledge of the Structure of Recent and
Fossil Fishes.

8tii Triennial Period, 1877-80. — John Murray, Esq., for his paper “on the Structure
and Origin of Coral Reefs and Islands,” published (in abstract) in the Proceedings of
the Society.

9th Triennial Period, 1880-83. — Professor Herdman, for his papers “on the Tunicata,”
published in the Proceedings and Transactions of the Society.

10th Triennial Period, 1883-86. — B. N. Peach, Esq., for his Contributions to the Geology and
Palaeontology of Scotland, published in the Transactions of the Society.

1 1th Triennial Period, 1886-89.— Robert Kidston, Esq., for his Researches in Fossil Botany,
published in the Transactions of the Society.

12tb Triennial Period, 1889-92. — John Horne, Esq., F.G.S., for his Investigations into the
Geological Structure and Petrology of the North-West Highlands.

13th Triennial Period, 1892-95. — Robert Irvine, Esq., for his papers on the Action of
Organisms in the Secretion of Carbonate of Lime and Silica, and on the solution of these
substances in Organic Juices. These are printed in the Society’s Transactions and
Proceedings.

14th Triennial Period, 1895-98. — Professor Cossar Ewart, for his recent Investigations con-
nected with Telegony.

15th Triennial Period, 1898-1901. — Dr John S. Flett, for his papers entitled “The Old Red
Sandstone of the Orkneys” and “The Trap Dykes of the Orkneys,’’ printed in vol.
xxxix of the Transactions of the Society.

16th Triennial Period, 1901-04. — Professor J. Graham Kerr, M.A., for his Researches on
Lepidosiren paradoxa , published in the Philosophical Transactions of the Royal Society,
London.

17th Triennial Period, 1904-07. — Frank J. Cole, B.Sc., for his paper entitled “A Monograph
on the General Morphology of the Myxinoid Fishes, based on a Study of Myxine,” published
in the Transactions of the Society, regard being also paid to Mr Cole’s other valuable contri-
butions to the Anatomy and Morphology of Fishes,

1st Biennial Period, 1907-09. — Francis J. Lewis, M.Sc., F.L.S., for his papers in the Society’s
Transactions “ On the Plant Remains of the Scottish Peat Mosses.”

2nd Biennial Period, 1909-11. — James Murray, Esq., for his paper on “Scottish Rotifers
collected by the Lake Survey (Supplement),” and other papers on the “Rotifera” and
“ Tardigrada, ” which appeared in the Transactions of the Society — (this Prize was awarded
after consideration of the papers received within the five years prior to the time of award :
see Neill Prize Regulations).

3rd Biennial Period, 1911-13. — Dr W. S. Bruce, in recognition of the scientific results of his
Arctic and Antarctic explorations.

4th Biennial Period, 1913-15) — Robert Campbell, D.Sc., for his paper on “The Upper
Cambrian Rocks at Craigeven Bay, Stonehaven,” and “ Downtonian and Old Red Sandstone
Rocks of Kincardineshire,” published in the Transactions of the Society.

5th Biennial Period, 1915-17. — W. H. Lang, F.R.S., M.B., D.Sc., for his paper in conjunction
with Dr R. Kidston, F.R.S., on Rhynia Gwynne-Vaughani, Kidston and Lang, published
in the Transactions of the Society, and for his previous investigations on Pteridophytes
and Cycads.

6th Biennial Period, 1917-19. — John Tait, D.Sc., M.D., for his work on Crustacea, published
in the Proceedings of the Society, and for his papers on the blood of Crustacea,

Keith, Brisbane, Neill, and Gunning Prizes.

229

IY. GUNNING VICTORIA JUBILEE PRIZE.

1st Triennial Period, 1884-87. — Sir William Thomson, Pres. R.S.E. , F.R.S., for a remark-
able series of papers “on Hydrokinetics,” especially on Waves and Vortices, which have
been communicated to the Society.

2nd Triennial Period, 1887-90. — Professor P. G. Tait, Sec. R.S.E. , for his work in connection
with the “Challenger” Expedition, and his other Researches in Physical Science.

3rd Triennial Period, 1890-93. — Alexander Buchan, Esq., LL.D., for his varied, extensive,
and extremely important Contributions to Meteorology, many of which have appeared in the
Society’s publications.

4th Triennial Period, 1893-96. — John Aitken, Esq., for his brilliant Investigations in
Physics, especially in connection with the Formation and Condensation of Aqueous Vapour.

1st Quadrennial Period, 1896-1900. — Dr T. D. Anderson, for his discoveries of New and
Variable Stars.

2nd Quadrennial Period, 1900-04.— Sir James Dewar, LL.D., D.C.L., F.R.S., etc., for his
researches on the Liquefaction of Gases, extending over the last quarter of a century, and
on the Chemical and Physical Properties of Substances at Low Temperatures : his earliest
papers being published in the Transactions and Proceedings of the Society.

3rd Quadrennial Period, 1904-08. — Professor George Chrystal, M.A., LL.D., for a series of
papers on “ Seiches,” including “ The Hydrodynamical Theory and Experimental Investiga-
tions of the Seiche Phenomena of Certain Scottish Lakes.”

4th Quadrennial Period, 1908-12. — Professor J. Norman Collie, Ph.D., F.R.S. , for his
distinguished contributions to Chemistry, Organic and Inorganic, during twenty-seven
years, including his work upon Neon and other rare gases. Professor Collie’s early papers
were contributed to the Transactions of the Society.

5th Quadrennial Period, 1912-16. — Sir Thos. Muir, C.M.G., LL.D., F.R.S., for his series
of Memoirs upon “ The Theory and History of Determinants and Allied Forms,” published
in the Transactions and Proceedings of the Society between the years 1872 and 1915.

<6th Quadrennial Period, 191 6-20. ^-C. T. R. Wilson, Esq., F.R.S., in recognition of his
important discoveries in relation to Condensation Nuclei, Ionisation of Gases, and Atmo-
spheric Electricity.

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

ABSTRACT

OF

THE ACCOUNTS OF JAMES CURRIE, ESQ., LL.D.

As Treasurer of the Royal Society of Edinburgh.

SESSION 1920-1921.

I. GENERAL FUND.

CHARGE.

1. Arrears of Contributions at 30th September 1920 £92 8 0

2. Contributions for present Session : —

1. 234 Fellows at £2, 2s. each £491 8 0

51 Fellows at £3, 3s. each 160 13 0

£652 1 0

Deduct —

Commutation of Contributions of one Fellow — proportion

thereof included in above ....... 220

£649 19 0

2. Fees of Admission and Contributions of twenty-five new

Fellows at £6, 6s. each 157 10 0

3. Commutation Fee in lieu of future Contributions of one

Fellow 7 17 6

815 6 6

3. Extra Contributions for 1920-1921 under Amended Law, No. 6 —

V oluntary Contributions — 34 Fellows at £1, Is. each . £35 14 0

Additional Contributions — 173 Fellows at £1, Is. each . 181 13 0

Commutations — 12 Fellows at £10, 10s. each . . . 126 0 0

343 7 0

4. Interest received —

Interest on £7830 five per cent. War Loan, 1929-47,

Untaxed £391 10 0

Annuity from Edinburgh and District Water Trust, less Tax,

£15, 15s 36 15 0

Interest on Deposit Receipts . . . . . . 551910

484 4 10

5. Transactions and Proceedings . . . . . . . . . . 10175

6. Annual Grant from Government 600 0 0

7. Income Tax repaid for year to 5th April 1921 . . . . . . . 15 15 0

8. Receipts from Sale of Napier Tercentenary Memorial Volume . . . 4 6 7

9. Anonymous Donation towards Napier Tercentenary Expenses .... 500

Amount of the Charge . . £2461 15 4

DISCHARGE.

1. Taxes, Insurance, Coal and Lighting: —

Inhabited House Duty £0 6 3

Insurance .......... 25 2 4

Coal, etc. , to 18th March 1921 ...... 38 8 8

Gas to 10th May 1921 ........ 4 19 0

Electric Light to 15th September 1921 9 19 4

Water, 1920-21 440

£82 19 7

Carry forward

£82 19 7

1920-21.] Abstract of Accounts.

2. Salaries : — Brought forward

#

#

General Secretary, 1920-21

£100

0

0

Librarian and Assistant Secretary .....

252

0

0

Assistant Librarian

49

16

8

Office Keeper .........

122

9

0

Treasurer’s Clerk ........

35

0

0

3. Expenses of Transactions : —

Neill & Co. , Ltd., Printers ......

£269

12

0

Hislop & Day, Ltd., Engravers .....

31

12

1

M‘Farlane & Erskine .......

16

3

6

The Zinco-Collotype Co. ......

56

7

6

Less Receipts —

£373

15

1

Grants by Carnegie Trustees towards Messrs

* Thompson’s, Kidston’s, and Gordon’s Papers £170 0

0

Grant by Scott Polar Research Fund towards

J. M. Wordie’s Papers .... 161 13

3

—

331

13

3

4. Expenses of Proceedings

Neill & Co., Ltd., Printers ......

£560

10

0

Hislop & Day, Ltd., Engravers .....

19

5

1

Macmillan & Co., Ltd. .

0

8

0

Less —

£580

3

1

Carnegie Trustees — Grant towards Dr J. R. Milne’s Paper

3

17

6

5. Books, Periodicals, Newspapers, etc. : —

James Thin, Bookseller .......

£148

7

1

R. Grant & Son, Booksellers . . ...

6

8

9

W. Green & Son, Ltd., Booksellers ....

1

10

0

Robertson & Scott, News Agents

8

12

7

Ray Society, Subscription ....

1

1

0

Palseontographical Society, Do. ....

1

1

0

Board of Scientific Societies, London, Donation

5

0

0

Williams & Norgate .......

2

0

0

Dowell’s, Ltd. . ......

0

2

6

Edinburgh and Leith Post Office Directory, Ltd.

0

16

6

6. Orrock & Son, Bookbinders

£2000

0

0

Less — Received from Carnegie Trust ....

2000

0

0

7. Loan to Makerstoun Magnetic Meteorological Observation Fund

£100, less repaid £48, 12s. lid. .....

£51

7

1

8. Other Payments : —

Neill & Co., Ltd., Printers ......

£133

7

11

J. & T. Scott

37

3

6

S. Duncan & Sons, Tailors (uniforms) ....

11

19

0

S. Heddle — Bonus ........

25

0

0

Andrew H. Baird ........

10

11

0

Lindsay, Jamieson & Haldane, C.A., Auditors

10

10

0

A. Muirhead & Son .......

99

12

6

A. Cowan & Sons, Ltd. .......

8

18

4

Orrock & Son, Bookbinders ......

8

15

0

Gillies & Wright, Joiners ......

8

2

0

R. Graham, Slater .......

17

0

0

Burn Brothers, Plumbers ......

2

6

8

A. Black & Co., Brushmakers .....

5

12

0

R. G. Hislop

5

5

6

G. Waterston & Sons, Ltd. ......

6

0

6

Jas. Gray & Son . . . . .

3

10

6

Travelling Expenses of Delegate to London

11

11

8

W. Blackwood & Sons

6

5

6

John Wright

22

12

8

Petty Expenses, Postages, Carriage, etc.

243

0

3

£82

559

42

576

174

677

231

19 7

5 8

1 10

5 7

19 5

4 6

Carry forward

£2112 16 7

232

Proceedings of the Royal Society of Edinburgh. [Sess.

Brought forward . . . £211216 7

9. Arrears of Contributions written off 17 17 0

10. Arrears of Contributions outstandingat 30th September 1921 : —

Present Session £50 8 0

Previous Sessions . . 35 14 0

86 2 0

Amount of the Discharge . £ 2216 15 7

Amount of the Charge ... £ 2461 15 4

Amount of the Discharge 2216 15 7

Excess of Receipts over Payments for 1920-1921 transferred

to Special Subscription Fund £24:4: 19 9

SPECIAL SUBSCRIPTION FUND.

To 30 th September 1921.

Charge.

1. Balance at 30th September 1920 : —

Due by Union Bunk of Scotland, Ltd., on Deposit Receipt .... £700 0 0

Due by Union Bank of Scotland, Ltd., on Account Current .... 88 11 11

Due by Treasurer . . . . 3196

£792 11 5

2. Amount transferred from General Fund being surplus for year to 30th

September 1921 ........... 244 19 9

£1037 11 2

Discharge.

1. Balance at 30th September 1921 : —

Due by Union Bank of Scotland, Ltd. , on Deposit Receipt .... £350 0 0

Due by Union Bank of Scotland, Ltd., on Account Current .... 629 18 8

Balance of Loan to Makerstoun Magnetic Meteorological Observation Fund . 51 7 1

Due by Treasurer 655

£1037 11 2

Note : —

Total Subscriptions received towards Special Subscription Fund . . .£1128 17 9

Sums transferred to General Fund to meet Deficiency on Accounts —

To 30th September 1919 ...... £301 16 11

To 30th September 1920 ...... 34 9 5

£336 6 4

Amount transferred from General Fund, being Surplus

for Year to 30th September 1921 ..... 244 19 9

Net Amount transferred to General Fund out of Special

Subscription Fund as at 30th September 1921 . . £91 6 7

91 6 7

Amount of Special Subscription Fund at 30th September 1921, as above . £1037 11 2

II. KEITH FUND

To SOth September 1921.

CHARGE.

1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 30th

September 1920 ............ £39 14 10

2. Interest Received : —

On £650 five per cent. War Loan, 1929-47, Untaxed . . . . . 32 10 0

£72 4 10

1920-21.]

233

Abstract of Accounts.

DISCHARGE.

1. Balance due by Union Bank of Scotland, Ltd., on Deposit Receipt at 30th

September 1921 . . . . . . . . £72 4 10

III. NEILL FUND

To 30 th September 1921.

CHARGE.

1. Balance due by Union Bank of Scotland, Ltd., on Account Current, at 30th

September 1920 ............ £15 10 6

2. Interest Received : —

On £300 five per cent. War Loan, 1929-47, Untaxed . . . . . 15 0 0

£30 10 6

DISCHARGE.

1. Balance due by Union Bank of Scotland, Ltd., on Deposit Receipt at 30th

September 1921 £30 10 6

IV. MAKDOUG ALL-BRISBANE FUND

To 30 th September 1921.

CHARGE.

1. Balance due by Union Bank of Scotland, Ltd., at 30th September 1920 : —

On Deposit Receipt ........... £35 15 6

On Account Current 20 0 0

£55 15 6

2. Interest Received

On £400 five per cent. War Loan, 1929-47, Untaxed . . £20 0 0

On Deposit Receipt — Union Bank of Scotland, Ltd. . . 2 18 5

22 18 5

£78 13 11

DISCHARGE.

1. Prof. J. H. M. Wedderburn — Money Portion of Prize, 1918-20 .... £15 0 0

2. Alex. Kirkwood & Son, Engravers, Gold Medal 22 10 0

3. Balance due by Union Bank of Scotland, Ltd., at 30th September 1921 : —

On Deposit Receipt . . £38 13 11

On Account Current ........ 2100

41 3 11

£78 13 11

V. MAKERSTOUN MAGNETIC METEOROLOGICAL OBSERVATION FUND

To 2>0th September 1921.

CHARGE.

1. Balance due by Union Bank of Scotland, Ltd., on Account Current at

30th September 1920 £36 2 11

2. Interest Received : —

On £250 five per cent. War Loan, 1929-47, Untaxed 12 10 0

3. Borrowed from General Fund £100, less repaid £48, 12s. lid . £51 7 1

4. Balance due to General Fund at 30th September 1921 51 7 1

£100 0 0

DISCHARGE.

1. Donation to British Association for the Advancement of Science . . . £100 0 0

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

VI. GUNNING VICTORIA JUBILEE PRIZE FUND

To 30 th September 1921.

(Instituted by Dr R. H. Gunning of Edinburgh and Rio de Janeiro.)
CHARGE.

1. Balance due by Union Bank of Scotland, Ltd., at 30th September 1920 : —

On Deposit Receipt £57 14 2

On Account Current . . 7150

£128 19 2

2. Interest Received : —

On £570 five per cent. War Loan, 1929-47, Untaxed . . £28 10 0

On Deposit Receipt — Union Bank of Scotland, Ltd. . . 4 14 11

33 4 11

DISCHARGE.

1. C. T. R. Wilson, Esq. — Money Portion of Prize 1916-20 .

2. Balance due by Union Bank of Scotland. Ltd., on Deposit Receipt, at 30th

September 1921

£162 4 1

£105 0 0

57 4 1
£162 4 1

VII. JAMES SCOTT PRIZE FUND

To 30 th September 1921.

CHARGE.

1. Balance due by Union Bank of Scotland, Ltd., on Deposit Receipt at 30th

September 1920 £264 4 0

2. Interest Received : —

On Deposit Receipt — Union Bank of Scotland, Ltd. . . . . . 22 10 6

£286 14 6

DISCHARGE.

1. Balance due by Union Bank of Scotland, Ltd., on Deposit Receipt at 30th

September 1921 £286 14 6

VIII. DR JOHN AITKEN FUND

(For Publication of his Scientific Work.)

To 30 th September 1921.

CHARGE.

1. Balance due by Union Bank of Scotland, Ltd., on Deposit Receipt at 30th

September 1920 £1040 1 11

2. Interest Received : —

On Deposit Receipts, Union Bank of Scotland, Ltd. 43 6 0

£1083 7 11

DISCHARGE.

1. Accounts Paid : —

Zinco Collotype Co., Portraits £20 0 0

Hislop & Day, Ltd., Line Blocks 21 19 1

£41 19 1

2. Balance due by Union Bank of Scotland, Ltd., on Deposit Receipt at

30th September 1921 . 1041 8 10

£1083 7 11

1920-21.]

Abstract of Accounts.

235

STATE OF THE FUNDS BELONGING TO THE ROYAL
SOCIETY OF EDINBURGH

1. GENERAL FUND—

As at 30th September 1921.

1. £7830 five per cent. War Loan, 1929-47, at 88| per cent. ....

2. £52, 10s. Annuity of the Edinburgh and District Water Trust, equivalent

to £875 at 100 per cent

3. Deposit Receipt Union Bank of Scotland, Ltd., being balance of Legacy

received during 1917-18, from the Trustees of the late Mr Robert
Mackay Smith, £500 less legacy duty £50 ......

4. Arrears of Contributions, as per preceding Abstract of Accounts .

5. Balance of Special Subscription Fund

6. Balance of Loan to Makerstoun Magnetic Meteorological Observation Fund

£6929 11
875 0

450 0

86 2
1037 11
51 7

0

0

0

0

2

1

Amount . . . £9429 11 3

Exclusive of Library, Museum, Pictures, etc., and Furniture in the Society’s Rooms
at George Street, Edinburgh.

2. KEITH FUND—

1. £650 five per cent. War Loan, 1929-47, at 88J per cent.

2. Balance due by Union Bank of Scotland, Ltd., on Deposit Receipt

Amount

3. NEILL FUND—

1. £300 five per cent. War Loan, 1929-47, at 88| per cent.

2. Balance due by Union Bank of Scotland, Ltd. on Deposit Receipt

. £575 5 0

72 4 10

. £647 9 10

£265 10 0
30 10 6

Amount

. £296

0 6

4. MAKDOUGALL-BRISBANE FUND—

1. £400 five per cent. War Loan, 1929-47, at 88| per cent.

2. Balance due by Union Bank of Scotland, Ltd. : —

On Deposit Receipt .......

On Account Current .......

. £354

0 0

£38 13 11
2 10 0

41

3 11

Amount . . . £395 3 11

5. MAKERSTOUN MAGNETIC METEOROLOGICAL OBSERVATION FUND—

1. £250 five per cent. War Loan, 1929-47, at 88| per cent.

Less — Balance of Loan from General Fund .....

£221 5 0

51 7 1

Amount . . . £169 17 11

6. GUNNING VICTORIA JUBILEE PRIZE FUND — Instituted by Dr Gunning of Edinburgh
and Rio de Janeiro —

1. £570 five per cent. War Loan, 1929-47, at 88J per cent £504 9 0

2. Balance due by Union Bank of Scotland, Ltd., on Deposit Receipt . . 57 4 1

Amount

7. JAMES SCOTT PRIZE FUND—

Balance due by Union Bank of Scotland, Ltd., on Deposit Receipt

£561 13 1

. £286 14 6

236 Proceedings of the Royal Society of Edinburgh.

8. TAIT MEMORIAL FUND—

This Fund consists of War Loan, and is to mature for a period of about ten years from
1918, when it is expected to yield about £75 per annum.

9. DR JOHN AITKEN FUND—

Balance due by Union Bank of Scotland, Ltd., on Deposit Receipt . . . £1041 8 10

Edinburgh, 13th October 1921. — We have examined the preceding Accounts of the Treasurer
of the Royal Society of Edinburgh for the Session 1920-1921, and have found them to be correct.
The securities of the various Investments at 30th September 1921, as noted in the foregoing
Statement of Funds (with the exception of No. 8), have been exhibited to us.

LINDSAY, JAMIESON & HALDANE, C.A.,

Auditors.

LIST OF VOLUNTARY CONTRIBUTORS OF TEN GUINEAS
(Single Payment) under Law VI (end of para. 3) up to 30th
September 1921.

Dr John Alison.

Sir James Dewar, F.R.S.
Mr W. F. King.

Prof. Graham Lusk.

Geo. A. Mitchell, M.A.
Sir F. G. Ogilvie, LL.D,

Sir Wm. Peck.

Alex. Philip, M.A,, LL.B.
Dr J. Stephenson.

Prof. E. Talmage.

Dr A. F. Tredgold.

James Watt, W.S.

LIST OF VOLUNTARY CONTRIBUTORS OF ONE GUINEA
under Law VI (end of para. 3) up to 30th September 1921.

The late R. G. Alford, M.Inst.C.E.
Maj.-Gen. W. B. Bannerman.

G. W. W. Barclay, M.A.

Prof. T. Hudson Beare.

J. P. F. Bell, F.Z.S.

Prof. A. C. Boon.

Mr T. C. Day.

Sir Arch. Denny.

Dr L. Dobbin.

John S. Ford, F.C.S.

Dr John Fraser.

Prof. Andrew Gray, F.R.S.

Sir R. B. Greig.

Dr D. Fraser Harris.

Prof. Sir W. A. Herdman, F.R.S.

Dr John Horne, F.R.S.

Dr W. F. Hume.

Sir J. H. Kemnal.

Dr R. Kidston, F.R.S.

Em. -Prof. Sir P. R. Scott Lang.
Dr D. F. Lowe.

Dr A. M. M‘Aldowie.

Dr P. M‘ Bride.

Dr Geo. M'Gowan.

Dr John Macintyre.

Dr H. R. Mill.

Prof. W. Peddie.

H. A. Reid, O.B.E., F.R.C.Y.S.
Prof. Sutherland Simpson.

Mr James Sorley.

Prof. Sir J. Walker, F.R.S.

A. C. Wilson, F.C.S.

Mr J. C. Wright.

Sir R. P. Wright.

Council of the Society.

237

THE COUNCIL OF THE SOCIETY.

October 1921.

President.

Professor FREDERICK 0. BOWER, M.A., D.Sc., LL.D., F.R.S., F.L.S.

Vice-Presidents.

Sir GEORGE A. BERRY, M.B., C.M., LL.D., F.R.O.S.E.

Professor WILLIAM PEDDIE, D.Sc., Professor of Natural Philosophy in University College,
Dundee.

Principal Sir JAMES ALFRED EWING, K.C.B., M.A., D.Sc., LL.D., M.Inst.C.E., F.R.S.,
Principal, University of Edinburgh.

Professor JOHN WALTER GREGORY, D.Sc., F.R.S., Professor of Geology, University of
Glasgow.

Major-General W. B. BANNERMAN, C.S.I., I.M.S., M.D., D.Sc.

W. A. TAIT, D.Sc., M.Inst.C.E.

General Secretary.

CARGILL G. KNOTT, D.Sc., LL.D., F.R.S.

Secretaries to Ordinary Meetings.

Professor E. T. WHITTAKER, Sc.D., F.R.S. , Professor of Mathematics, University, Edinburgh.
Professor J. H. ASHWORTH, D.Sc., F.R.S., Professor of Zoology, University, Edinburgh.

Treasurer.

JAMES CURRIE, M.A., LL.D.

Curator of Library and Museum.

A. CRICHTON MITCHELL, D.Sc., Hon. D.Sc. (Geneva).

Councillors.

HENRY MOUBRAY CADELL, of Grange,

B. Sc.

Professor ARTHUR ROBERTSON CUSHNY,
M.A., M.D., LL.D., F.R.S.

Professor FRANCIS GIBSON BAILY,
M.A., M.Inst.E.E.

GEORGE JAMES LIDSTONE, F.F.A., F.I.A.
ROBERT CAMPBELL, M.A., D.Sc., F.G.S.

Principal JAMES COLQUHOUN IRVINE,

C. B.E., Ph.D., D.Sc., F.R.S.

The Hon. LORD SALVESEN.

Professor J. ARTHUR THOMSON, M.A.,
LL.D.

HERBERT STANLEY ALLEN, M.A., D.Sc.

Sir ROBERT BLYTH GREIG, M.A., LL.D.,
F.Z.S.

JAMES RITCHIE, D.Sc.

ERNEST MACLAGAN WEDDERBURN,
M.A., LL.B., W.S., D.Sc.

238

Proceedings of the Royal Society of Edinburgh.

Date of
Election.

1898

1898

1896

1889

1894

1888

1920

1906

1920
1905
1903

1905
1881

1921
1915

1906

1910

1907
1921

1911

ALPHABETICAL LIST OF THE ORDINARY FELLOWS
OF THE SOCIETY,

Corrected to January 31, 1922.

N.B. — Those marked * are Annual Contributors.

,, ,, + have commuted Voluntary Contribution ( see 3rd Paragraph , Law VI).

B. prefixed to a name indicates that the Fellow has received a Makdougall-Brisbane Medal.

K.

„

„ Keith Medal.

N. „

„ Neill Medal.

V. J. „

,,

,, the Gunning Victoria Jubilee Prize.

c.

„

,, contributed one or more Communications 1

Society’s Transactions or Proceedings.

Service on
Council, etc.

c.

c.

c.

c.

c.

c.

c.

!. K.

* Abercromby, the Rt. Hon. Lord, LL. D. , 62 Palmerston Place, Edinburgh
Adami, J. G., C.B.E., M.A., M.D. (Camb., M‘Gill, and Belfast), LL.D., F.R.S.,

Vice-Chancellor of the University of Liverpool,
t Affleck, Sir Jas. Ormiston, M.D., LL.D., F.R.O.P.E., 38 Heriot Row, Edinburgh
t Alison, John, M. A., LL.D., Head Master, George Watson’s College, Edinburgh
Allan, Francis John, M.D., C.M. , Edin., M.O.H. City of Westminster, West-
minster City Hall, Charing Cross Road, London 5

Allardice. R. E., M.A., Professor of Mathematics in Stanford University, Palo
Alto, Santa Clara Co., California

* Allen, Herbert Stanley, M.A. (Cambridge), D.Sc. (London), Lecturer in Natural

Philosophy in the University of Edinburgh
Anderson, Daniel E., M.D., B.A., B.Sc., Green Bank, Merton Lane, Highgate,
London, N.

* Anderson, Ernest Masson, M.A., B.Sc., F.G.S., Geologist, H.M. Geological Survey

of Scotland, 5 Riselaw Road, Edinburgh

* Anderson, William, M.A., Head Science Master, George Watson’s College, Edin-

burgh, 6 Lockharton Crescent, Edinburgh 10

Anderson-Berry, David, M.D., LL.D., F.R.S.L., M. R. A.S., F.S.A. (Scot.),
Versailles, Highgate, London, N.

* Andrew, George, M.A., B.A. , H.M.I.S. , Balgillo Cottage, Seafield Road,

Brouglity Ferry

Anglin, A. H., M.A., LL.D., M.R.I. A., Professor of Mathematics, Queen’s
College, Cork

* Annandale, Nelson, B.A. (Oxon.), D.Sc. (Edin.), Director of the Zoological Survey

of India, and Vice-Chairman of the Trustees of the Indian Museum, Calcutta
Anthony, Charles, M. Inst.C.E. , M. Am. Soc. C.E., F.R.San.I., F. R.Met.S.,
F.R.A.S. , F.C.S., General Manager, Water Works Company, Vieytes y
Gorriti, Bahia Blanca, Argentina 15

Appleton, Colonel Arthur Frederick, F.R.C.V.S., 19 Cumberland Road, Bromley,
Kent

Archibald, E. H., B.Sc., Professor of Chemistry, University of British Columbia,
Vancouver, Canada

* Archibald, James, M.A., 31 Leamington Terrace, Edinburgh

* Arthur, William, M.A., Assistant to the Professor of Mathematics in the

University of Glasgow. 149 Stanmore Road, Mount Florida, Glasgow

* Ashworth, James Hartley, D.Sc., F.R.S., Professor of Zoology, University J

of Edinburgh (Secretary), 69 Braid Avenue, Edinburgh 20 |

* Badre, Muhammad, Ph.D. , Almuneerah, Cairo, Egypt

1921-

1912-14,
1915-18.
* Sec.
1918-

1907

Date of

Election.

1920

1920

1896

1921

1877

1905

1892

1918

1902

1889

1886

1883

1903

1914

1921

1904

1874

1921

1895

1904

1913

1888

1897

1893

1882

1887

1906

1916

1915

1893

1897

1880

1907

1884

phabetical List of the Ordinary Fellows of the Society. 239

* Bagnall, Richard Siddoway, 15 Grey Street, Newcastle-on-Tyne

* Bailey, Edward Battersby, M.G., B.A., F.G.S., District Geologist, H.M. Geological

Survey of Scotland, 23 Pentland Terrace, Edinburgh
Baily, Francis Gibson, M.A., M.Inst.E. E., Professor of Electrical Engineering,/
Heriot-Watt College, Edinburgh, Newbury, Colinton, Midlothian \

* Baker, Bevan Braithwaite, M.A., B.Sc. (Lond. ), Lecturer in Mathematics in the

University of Edinburgh. 30 Murrayfield Gardens, Edinburgh 25

Balfour, Sir I. Bayley, K.B.E., M.A., Sc.D., M.D., LL.D., F.R.S., F.L.S.,
King’s Botanist in Scotland, Professor of Botany in the University of Edin-
burgh and Keeper of the Royal Botanic Garden, Inverleith House, Edinburgh
Balfour-Browne, William Alexander Francis, M.A., F.Z.S. , F.E.S. , Barrister-at-
Law, Lecturer in Zoology (Entomology) in the University of Cambridge),
Oaklands, Fenstanton, near St Ives, Hunts
Ballantyne, J. W., M.D., F.R.C.P.E., 19 Rothesay Terrace, Edinburgh

* Balsillie, David, B.Sc., F.G.S. , Department of Mineralogy and Geology, Royal

Scottish Museum, Edinburgh

Bannerman, W. B., C.S.I., I.M.S., M.D., D.Sc., Maj. -General, Indian Medical f
Service, 11 Strathearn Place, Edinburgh (Vice-President) 30 |

Barbour, A. H. F., M.A., M.D., LL.D., F.R.C.P.E,, 4 Charlotte Square, Edinburgh
Barclay, A. J. Gunion, M.A., 3 Chandos Avenue, Oakleigh Park, London, N.
Barclay, G. W. W. , M.A., Raeden House, Aberdeen

Bardswell, Noel Dean, M.D., M.R.C.P. Ed. and Lond., King Edward VII Sana-
torium, Midhurst

* Barkla, Charles Glover, M.A., D.Sc., F.R.S., Professor of Natural Philosophy in

the University of Edinburgh, Nobel Laureate, Physics, 1917, 20 Hermitage
Drive, Edinburgh 35

* Barr, Archibald, D.Sc., LL.D. (Glasgow and Birmingham), Em.-Professor of

Engineering in the University of Glasgow. Westerton of Mugdock, Milngavie
Barr, Sir James, C.B.E., M. D., LL.D., F.R. C.P. Lond., 72 Rodney Street,
Liverpool

Barrett, Sir William F., Kt., F.R.S. , M.R.I.A. , formerly Professor of Physics,
Royal College of Science, Dublin, 31 Devonshire Place, London, W. 1

* Bartholomew, John, M.C., M.A., F.R.G.S., Geographical Institute, Edinburgh
Barton, Edwin H., D.Sc., F.R.S., F. P.S.L., F. Inst. P., Professor of Physics,

University College, Nottingham 40

* Baxter, William Muirhead, Glenalmond, Sciennes Gardens, Edinburgh

Beard, Joseph, F.R.C.S. (Edin.), M.R.C.S. (Eng.), L.R.C.P. (Lond.), D.P.H.
(Camb. ), Medical Officer of Health and School Medical Officer, City of
Carlisle, 8 Carlton Gardens, Carlisle

Beare, Thomas Hudson, B.A., B.Sc., M.Inst.C.E., J.P., D.L., Professor off
Engineering in the University of Edinburgh |

Beattie, Sir John Carruthers, K.B., D.Sc., Vice-Chancellor and Principal, The
University, Cape Town

Becker, Ludwig, Ph. D., Regius Professor of Astronomy in the University of
Glasgow, The Observatory, Glasgow, Millbank Terrace, Crieff 45

Beddard, Frank E., M.A. Oxon., D.Sc., F. R.S. , formerly Prosector to the
Zoological Society of London, 20 Sherriff Road, Kilburn, London, N.W. 6
Begg, Ferdinand Faithfull, 46 Saint Aubyns, Hove, Sussex
Bell, John Patrick Fair, F.Z.S. , Springbank, Ayton, Berwickshire

* Bell, Robert John Tainsh, M. A., D.Sc., Professor of Mathematics in the University

of Otago, New Zealand

Bell, Walter Leonard, M.D.Edin., F.S.A.Scot., 123] London Road, North
Lowestoft, Suffolk 50

Berry, Sir George A., M.B., C.M., LL.D., F.R.C.S.E. (Vice-President), 31 f
Drumsheugh Gardens, Edinburgh j

Berry, Richard J. A., M. D., F.R.C.S.E., Professor of Anatomy in the University
of Melbourne, Victoria, Australia

Birch, De Burgh, C.B., M.D. , Emeritus Professor of Physiology in the University
of Leeds

* Black, Frederick Alexander, Solicitor, 59 Academy Street, Inverness

Service on
Council, etc.

1909-12.

1920-

1888-91.

1919-21,

V-P

1921-

1915-18.

1907-09.

V-P

1909-15.

1916-19.

V-P

1919-

1891-94,

1916-18.

Cur.

1906-16.

Black, John S., M.A., LL.D., 125 St James’ Court, London, S.W. 1

55

240

Date oi

Electior

1897

1904

1918

1894

1915

1872

1886

1884

1901

1916

1903

1886

1907

1918

1916

1895

1893

1901

1907

1864

1883

1885

1909

1921

1912

1898

1870

1905

1902

Proceedings of the Royal Society of Edinburgh.

Blaikie, Walter Biggar, LL.D., The Loan, Colinton
*Bles. Edward J. , M.A., D.Sc., Elterholm, Cambridge

* Blight, Francis James, Chairman and Managing Director of Charles Griffin &

Co., Ltd., Publishers, Tregenna, Wembley, Middlesex
Bolton, Herbert, M.Sc., F.G.S., F.Z.S., Director of the Bristol Museum and Art
Gallery, Bristol, 58 Coldharbour Road, Redland, Bristol

* Boon, Alfred Archibald, D.Sc., F.I.C., B.A., Professor of Chemistry, Heriot-Watt

College, Edinburgh 60

Bottomley, J. Thomson, M.A., D.Sc., LL.D., F.R.S., F.C.S., 13 University
Gardens, Glasgow

Bower, Frederick O., M.A., D.Sc., LL.D., F.R.S., F.L.S. (President), Regius
Professor of Botany in the University of Glasgow, 1 St John’s Terrace,
Hillhead, Glasgow

Bowman, Frederick Hungerford, D.Sc., F.C.S. (Lond. and Berk), F.I.C.,
A.Inst.C.E., A.Inst.M.E., M.Inst.E.E., etc., 76 Acomb Street, Whitworth
Park, Manchester

Bradbury, J. B., M.D. , Downing Professor of Medicine, University of Cam-
bridge

Bradley, His Honour Judge (Francis Ernest), M.A., M.Com., LL.D., Barrister-
at-Law, Examiner to the Council of Legal Education, Bank of England
Chambers, Tib Lane, Manchester 65

* Bradley, O. Charnock, M.D. , D.Sc., Principal, Royal Dick Veterinary College, (

Edinburgh, President of the Royal College of Veterinary Surgeons,-!
London (

Bramwell, Byrom, M.D., F.R.C. P.E , LL.D., 23 Drumsheugh Gardens, Edin-
burgh

* Bramwell, Edwin, M.D., F.R.C.P.E., F.R.C.P. Lond., 23 Drumsheugh Gardens,

Edinburgh

* Bremner, Alexander, M.A., D.Sc., Headmaster, Demonstration School, Training

Centre, Aberdeen, 13 Belgrave Terrace, Aberdeen

* Briggs, Henry, D.Sc., A. R.S.M. , Professor of Mining, Heriot-Watt College,

Allermuir, Liberton, Midlothian 70

Bright, Sir Charles, M.Inst.C.E., M.Inst.E.E., F.R.Ae.S., F. Inst. Radio. E.,

F.R.A.S., F.R.G.S., Leigh Grange, Kent, and Athenaeum Club, Pall Mall,
London, S.W.

Brock, G. Sandison, M.D., 6 Corso d’ltalia, Rome, Italy

* Brodie, W. Brodie, M. B. , Camden House, Bletchingley, Surrey

Brown, Alexander, M. A., B.Sc., Professor of Applied Mathematics, The University,
Cape Town

Brown, Alex. Crum, M.A., M.D., D.Sc., F.R.C.P.E., LL.D., F.R.S., Emeritus
Professor of Chemistry in the University of Edinburgh, 8 Belgrave Crescent,"
Edinburgh 75

Brown, J. J. Graham, M. D. , F.R.C.P.E., 3 Chester Street, Edinburgh
Brown, J. Macdonald, M.D., F.R.C.S-, 64 Upper Berkeley Street, Portman
Square, London, W.

* Brownlee, John, M.A., M.D., D.Sc., the National Institute for Medical

Research, Mount Vernon, Hampstead, N.W. 3

* Bruce, Alexander, B.Sc. (Edin.), Government Agricultural Chemist and City

Analyst, Colombo, Ceylon

* Bruce, Alexander Ninian, D.Sc., M. D. , 8 Ainslie Place, Edinburgh 80

* Bryce, T. H., M.A., M.D. (Edin.), Professor of Anatomy in the University of

Glasgow, 2 The University, Glasgow

Buchanan, John Young, M.A., F.R.S., Athenaeum Club, Pall Mall, London,/
S.W. I

Bunting, Thomas Lowe, M.D., 27 Denton Road, Scotswood, Newcastle-on-Tyne

* Burgess, A. G., M.A., Rector of The Academy, Rothesay, Blythswood, Rothesay

Service on
Council, etc.

1914-17.

1887-90,

1893-96,

1907-09,

1917-19

V-P

1910-16.

P

1919-

1907-10,

1915-17.

1890-93.

1865-68,

1869-72,

1873-75,

1876-78,

1911-13.

Sec.

1879-1905.

V-P

1905-11.

1911-14.

1878-81,

1884-86.

Alphabetical List of the Ordinary Fellows of the Society. 241

Date of
Election.

1887

1888

1917
1915

1896

1887

1910

1893

1894
1905

1921

1904

1918

1915

1899

1910

1920

1905
1901

1905

1898

1908

1882

1899

1912

1874

1891

1911

1903

1909

1913

1904

1904

1888

1904
1909

1886

1905

C.

C.

C.

C. N
C.

c.

c.

c.

y. j,
c.

c.

t Burnet, Sir John James, A.R.A., R.S.A., LL.D., Architect, 1 Montague Place,
Bedford Square, London, W.C. 1. 85

Burns, Rev. T., D. D. , J.P., F.S.A. Scot., Minister of Lady Glenorchy’s Parish
Church, Croston Lodge, Chalmers Crescent, Edinburgh

* Burnside, George Barnhill, M.I. Mech.E. , 104 Beechwood Drive, Glasgow, W.

* Butchart, Raymond Keiler, B.Sc., Ph.D., University College, Dundee, 5 Briarwood

Terrace, West Park Road, Dundee
Butters, J. W. , M. A., B.Sc., Rector of Ardrossan Academy

Cadell, Henry Moubray, of Grange, B.Sc., D.L., Linlithgow 90

* Calderwood, Rev. Robert Sibbald, Minister of Cambuslang, The Manse, Cambuslang,

Lanarkshire

Calderwood, W. L. , Inspector of Salmon Fisheries of Scotland, South Bank, Canaan
Lane, Edinburgh

Cameron, James Angus, M.D., Medical Officer of Health, Firhall, Nairn
Cameron, John, M.D., D.Sc., M.R.C.S. Eng., Dalhousie University, Halifax,
Nova Scotia

* Campbell, Andrew, Advisory Chemist, Burmah Oil Co., Ltd., and Anglo-Persian

Oil Co., Ltd. The Coppice, Beckenham, Kent 95

* Campbell, Charles Duff, Scottish Liberal Club, Princes Street, Edinburgh

* Campbell, John Menzies, L.D.S. (Glas.), D.D.S. (Toronto), L.D.S. (Ontario),

14 Buckingham Terrace, Glasgow, W.

* Campbell, Robert, M.A. , D.Sc., F.G.S., Lecturer in Petrology, University of

Edinburgh, 2 Woodhall Road, Colinton

* Carlier, Edmund W. W. , M. D. , M. Sc. , F.E. S. , Professor of Physiology, University,

Birmingham

Carnegie, Col. David, C.B.E., M.Inst.C.E., M. Inst. Mech.E., M.I.S.Inst. ,
“Woodlands,” Beckenham Hill, Kent 100

* Carruthers, R. G., F.G.S., District Geologist, H. M. Geological Survey, High

Barn, Stocksfield-on-Tyne

* Carse, George Alexander M.A. , D.Sc. , Lecturer on Natural Philosophy, University

of Edinburgh, 3 Middleby Street, Edinburgh
Carslaw, H. S. , M.A., D.Sc., Professor of Mathematics in the University of
Sydney, New South Wales

Carter, Joseph Henry, F.R.C.V.S., Avalon, Western Road, Henley-on-Thames
Carus- Wilson, Cecil, F.R.G.S. , F.G.S., Waldegrave Park, Strawberry Hill,
Middlesex, and Sandacres Lodge, Parkstone-on-Sea, Dorset 105

i Cavanagh, Thomas Francis, M. D.. The Hospital, Bella Coola, B.C. , Canada
I Cay, W. Dyce, M.Inst.C.E., Junior Carlton Club, Pall Mall, London, S.W. 1
I Chatham, James, Actuary, c/o Robert Murrie, Esq., 28 St Andrew Square,
Edinburgh

Chaudhuri, Banawari Lai, B. A. (Cal.), B.Sc. (Edin.), Assistant Superintendent,
Natural History Section, Indian Museum, 120 Lower Circular Road, Calcutta,
India

Chieiie, John, C.B., M.D., LL.D., F.R.C S.E. , Emeritus Professor of Surgery in f
the University of Edinburgh, Barn ton Avenue, Davidson’s Mains 1 10 l

Clark, John B., M.A., Head Master of Heriot’s Hospital School, Lauriston,
Garleffin, 146 Craiglea Drive, Edinburgh

* Clark, William Inglis, D.Sc., 22 Buckingham Terrace, Edinburgh

Clarke, William Eagle, I.S.O., LL.D., F. L.S., Honorary Supervisor of the Bird
Collection and formerly Keeper of the Natural History Collections in the Royal
Scottish Museum, Edinburgh. 35 Braid Road, Edinburgh
j Clayton, Thomas Morrison, M. D. , D.Hy., B.Sc., D. P.H., Medical Officer of
Health, Gateshead, 13 The Crescent, Gateshead- on-Tyne

* Cleghorn, Alexander, M.Inst.C.E. , Marine Engineer, 14 Hatfield Drive, Kelvinside,

Glasgow 115

Coker, Ernest George, M.A., D.Sc., Hon. D.Sc. (Sydney), F.R.S., M.Inst.C.E.,
M.Inst.E.E. , Professor of Civil and Mechanical Engineering, University of
London, University College, Gower Street, London, W.C.

Coles, Alfred Charles, M.D. , D.Sc., York House, Poole Road, Bournemouth, W.
Collie, John Norman, Ph.D., D.Sc., LL.D., F.R.S., F.C.S., F.I.C., F.R.G.S.,
Professor of Organic Chemistry in the University College, Gower Street,
London

* Colquhoun, Walter, M.A., M.B., 18 Walmer Crescent, Ibrox, Glasgow

* Comrie, Peter, M.A. , B.Sc., Head Mathematical Master, Boroughmuir Junior

Student Centre, 19 Craighouse Terrace, Edinburgh 120

Connan, Daniel M., M.A.

*Corrie, David, F.C.S., 159 Lauderdale Mansions, MaidaVale, London, W. 9.

VOL. XLI.

Service on
Council, etc.

1919-

1920-

1884-86,

1904-06.

16

242

Proceedings of the Royal Society of Edinburgh.

Date of
Election.

1914

1911

1920

1916

1908

1875

1903

1870

C.

1916
1886

1914

1917

1898

1919

1904

1885

1921

1884

1917

1894

1869

C.

Y. J.

1905

1906
1884

1888

C.

1876

C.

1885

C.

1897

1904

1881

0.

1918

1905

1882 C.
1921 B. C.

*Coutts, William Barron, M.A., B.Sc., Senior Lecturer in Range Finding
and Optics, Artillery College, Red Barracks, Woolwich, S.E. 18.

* Cowan, Alexander, Papermaker, Valleyfield, Penicuik, Midlothian

Craib, William Grant, M.A. (Aberdeen), Regius Professor of Botany in the
University of Aberdeen 125

Craig, E. H. Cunningham, B.A. (Cambridge), Geologist and Mining Engineer,
T'he Dutch House, Beaconsfield

Craig, James Ireland, M.A., B.A., Woolwich House, The Drive, Sydenham,
London, S.E. 26

Craig, William, M.D., F.R.C.S.E., Lecturer on Materia Medica to the College of
Surgeons, 71 Bruntsfield Place, Edinburgh
Crawford, Lawrence, M. A., D.Sc., Professor of Pure Mathematics, The University,
Cape Town

Crichton-Browne, Sir Jas., Kt., M.D., LL.D., D.Sc., F.R.S., Lord Chancellor's
Visitor and Vice-President and Treasurer of the Royal Institution of Great
Britain, 45 Hans Place, S. W., and Royal Courts of Justice, Strand, London 130
*Crombie, James Edward, M.A., LL.D., Millowner, Parkhill House, Dyce,
Aberdeenshire

Groom, Sir John Halliday, Kt., M.D., F.R.C.P.E. , formerly Professor of
Midwifery in the University of Edinburgh, late President, Royal College of
Surgeons, Edinburgh, 25 Charlotte Square, Edinburgh

* Cumming, Alexander Charles, D.Sc., O. B.E. , Roselands, Crescent Road, Blundell

Sands, Liverpool

* Cunningham, Brysson, D.Sc., B.E. , M. Inst.C.E. , Lecturer on Waterways, Har-

bours. and Docks, University College, London, 16 Beechwood Road, Sander-
stead, Surrey

* Currie, James, M.A. Cantab., LL.D. (Treasurer), Larkfield, Goldenacre, Edin-f

burgh 135 \

* Cushny, Arthur Robertson, M. A. , M. D. , LL. D. , F. R. S. , Professor of Materia

Medica and Pharmacology, University, Edinburgh

* Cuthbertson, John, Secretary, West of Scotland Agricultural College, 6 Charles

Street, Kilmarnock

Daniell, Alfred, M.A., LL.B., D.Sc., Advocate, The Athenaeum Club, Pall Mall,
London

* Datta, Rasik Lai, D.Sc., Assistant Professor of Chemistry, University of Calcutta.

78 Manicktola Street, Calcutta, India

Davy, R. , F.R.C.S. Eng., Consulting Surgeon to Westminster Hospital, Burstone
Manor, Bow, North Devon 140

* Day, T. Cuthbert, Partner of the firm of Hislop & Day, 36 Hillside Cres., Edinburgh
Denny, Sir Archibald, Bart., LL.D., Cardross Park, Cardross, Dumbartonshire.

Somerset Lodge, Somerset Road, Wimbledon Common, S.W. 19 (temporary
address)

t Dewar, Sir James, Kt., M.A., LL.D., D.C.L., D.Sc., F.R.S., F.C.S., Jacksonian
Professor of Natural and Experimental Philosophy in the University of
Cambridge, and Fullerian Professor of Chemistry at the Royal Institution of
Great Britain, London

* Dewar, James Campbell, C.A. , 27 Douglas Crescent, Edinburgh

* Dewar, Thomas William, M.D., F.R.C.P., Kincairn, Dunblane 145

Dickson, the Right Hon. Charles Scott, Lord Justice- Clerk, K.C., LL.D., 22

Moray Place, Edinburgh

Dickson, Henry Newton, C. B.E., M.A. , D.Sc., formerly Professor of Geography
at University College, Reading. 18 Bedford Square, London, W.C. 1.
Dickson, J. D. Hamilton, M.A. , Senior Fellow and formerly Tutor, St Peter’s
College, Cambridge

Dixon, James Main, M.A., Litt. Hum. Doctor, Professor of English, University of
Southern California, University Avenue, Los Angeles, California, U.S.A.
Dobbie, James Bell, F.Z.S., 12 South Inverleith Avenue, Edinburgh 150

*Dobbie, Sir James Johnston, Kt., M.A., D.Sc., LL.D., F.R.S., formerly Principal
of the Government Laboratories, London. Fairlie Cottage, Fairlie, Ayrshire
Dobbin, Leonard, Ph.D., Lecturer in Chemistry in the University of Edinburgh, j
6 Wilton Road, Edinburgh \

*Dodd, Alexander Scott, B.Sc., F.I.C., F.C.S., City Analyst for Edinburgh, 20
Stafford Street, Edinburgh

* Donaldson, Rev. Wm. Galloway, J.P., F.R.G.S., F.E.I.S. , The Manse, Forfar

Dott, David B., F.I.C., Memb. Pharm. Soc. , Ravenslea, Musselburgh 155

* Dougall, John, M.A., D.Sc., Publisher’s Reader, 26 Underwood Street, Langside,

Glasgow

Service on
Council, etc.

Treas.

1906-

1919-

1872-74,

1905-08.

1904-07,

1913-16.

Date oi

Electior

1901

&

1918

1910

1908

1901

1917

1921

1904

1903

1892

1906

1893

1904

1904

1875

1913 &

1921

1906

1897

1884

1879

1902

1878

1900

1910

1907

1888

1883

1899

1907

1904

1898

1899

1911

1906

1900

1872

phabetical List of the Ordinary Fellows of the Society. 243

* Douglas, Carstairs Cumming, M.D., D.Sc., Professor of Medical Jurispru-

dence and Hygiene, Anderson’s College, Glasgow, 2 Royal Crescent,
Glasgow

* Douglas, Loudon MacQueen, Author and Lecturer, 29 W. Saville Terrace, Newing-

ton, Edinburgh

Drinkwater, Harry, M.D., M.R.C.S. (Eng.), F.L.S., Lister House, Wrexham,
North Wales

* Drinkwater, Thomas W., L.R.C. P.E., L.R.C.S.E., Chemical Laboratory, Sur-

geons’ Hall, Edinburgh 160

*Dron, Robert W., A.M. Inst. C.E., 11 W. Regent Street, Glasgow

* Drysdale, Charles Vickery, D.Sc. (Lond.), M.I.E.E., F.Inst.P., O.B.E., Super-

intendent of the Admiralty Research Laboratory, Teddington, Middlesex

* Dunlop, William Brown, M. A. , 4a St Andrew Square, Edinburgh
Dunstan, John, M.R. C. V.S., Inversnaid, Liskeard, Cornwall

Dunstan, M. J. R., M. A., F.I. C., F.C.S., Principal, South-Eastern Agricultural
College, Wye, Kent 165

Dyson, Sir Frank Watson, Kt. , M.A., D.Sc., LL.D., F.R.S., Astronomer Royal,
Royal Observatory, Greenwich
Edington, Alexander, M. D. , Howick, Natal

* Edwards, John, LL.D., 4 Great Western Terrace, Kelvinside, Glasgow

* Elder, William, M.D., F.R.C.P.E., 4 John’s Place, Leith

Elliot, Daniel G. , American Museum of Natural History, Central Park West,
New York, N.Y., U.S.A. * 170

* Elliot, George Francis Scutt, M.A. (Cantab.), B.Sc., F.R.G.S., F.L.S., Drum-

whill, Mossdale

* Ellis, David, D.Sc., Ph.D. , Lecturer in Botany and Bacteriology, Royal

Technical College, Glasgow

Erskine- Murray, James Robert, D.Sc., 16Elmlield Road, Bromley, Kent
Evans, William, F.F.A. , 38 Morningside Park, Edinburgh

Ewart, James Cossar, M.D., F.R.C.S.E., F.R.S., F.Z.S., Regius Professor of |
Natural History, University of Edinburgh, Craigybield, Penicuik, Mid-q
lothian 175 ^

*Ewen, John Taylor, B.Sc., M.I.Mech.E., H.M. Inspector of Schools, Clairmont,
54 Albert Drive, Pollokshields, Glasgow

Ewing, Sir James Alfred, K.C.B., M.A., D.Sc., LL.D., M.Inst.C.E., F.R.S., J.P. I
(Vice-President), Principal of the University of Edinburgh, formerly^
Director of Naval Education, Admiralty, 16 Moray Place, Edinburgh

Eyre, John W. H., M. D., M. S. (Dunelm), D. P. H. (Camb.), Professor of
Bacteriology, Guy’s Hospital, London

* Fairgrieve, Mungo M‘Callum, M.A. (Glasg.), M.A. (Cambridge), Master at the

Edinburgh Academy, 37 Queen’s Crescent, Edinburgh
Falconer, John Downie, M.A., D.Sc., F.G.S., Lecturer on Geography, The
University, Glasgow 180

Fawsitt, Charles A., Coney Park, Bridge of Allan

Felkin, Robert W., M.D., F.R.G.S. , Whare Ra, Havelock North, Hawkes Bay,
New Zealand

* Fergus, Andrew Freeland, M.D., LL.D., c/o Messrs. Mackay & Boyd, 50 Wellington

Street, Glasgow

* Fergus, Edward Oswald, c/o 22 Blythswood Square, Glasgow

* Ferguson, James Haig, M.D., F.R.C.P.E., F.R.C.S.E., 7 Coates Crescent,

Edinburgh 185

* Findlay, Sir John R., K.B.E., M.A. Oxon., 3 Rothesay Terrace, Edinburgh

* Finlay, David W., B.A., M.D., LL.D., F.R.C.P., D.P.H., Emeritus Professor of

Medicine in the University of Aberdeen, Honorary Physician to His Majesty
in Scotland, Balgownie, Helensburgh

Fleming, John Arnold, F.C.S., etc., Pottery Manufacturer, Locksley, Helens-
burgh, Dumbartonshire

* Fleming, Robert Alexander, M.A., M.D., F.R.C.P.E., Physician, Royal Infirmary,

10 Chester Street, Edinburgh

* Flett, John S., M.A., D.Sc., LL.D., F.R.S., O.B.E., Director of the Geological

Survey of Great Britain and of the Museum of Practical Geology, London, 28
Jermyn Street, S.W. 1 190

Forbes, George, M.A., M.Inst.C.E., M.Inst.E.E., F.R.S., F.R.A.S., formerly
Professor of Natural Philosophy in Anderson’s College, Glasgow. 11 Little
College Street, Westminster, S.W.

Service on
Council, etc.

1907-10.

1882-85,

1904-07.

V-P

1907-12.

1888-91,

1919- 20.
Y-P

1920-

1916-19.

244

Date of

Election.

1892

1921

1920

1910

1896

1915

1914

1891

1907

1888

1901

1909

1880

1861

1914

1909

1920

1914

1916

1910

1917

1910

1890

1921

1911

1900

1907

1909

1911

1898

Proceedings of the Royal Society of Edinburgh.

Ford, John Simpson, F.C.S., 7 Corrennie Drive, Edinburgh

* Forrest, George Topham, Architect to the London County Council, and Super-

intending Architect of Metropolitan Buildings, New County Hall, West-
minster Bridge, London, S.W.

* Franklin, Thomas Bedford, B.A. (Hons. Mathematics), Cambridge, Stancliffe

Hall, near Matlock, Derb}Tshire

* Fraser, Alexander, Actuary, 15 S. Learmonth Gardens, Edinburgh 195

Fraser, John, M. B., F.R.C.P.E., formerly one of H.M. Commissioners in

Lunacy for Scotland, 54 Great King Street, Edinburgh

* Fraser, Rev. Joseph Robert, U.F. Manse, Kinneff, Bervie

* Fraser, William, Managing Director, Neill & Co., Ltd., Printers, 212 Causeway-

side, Edinburgh

Fulton, T. Wemyss, M.D. , Scientific Superintendent, Scottish Fishery Board,
41 Queen’s Road, Aberdeen

* Galbraith, Alexander, “ Ravenswood,” Dalmuir, Dumbartonshire 200

Galt, Alexander, D.Sc., late Keeper of the Department of Technology, Royal

Scottish Museum, Edinburgh, St Margaret’s, Craiglockhart, Edinburgh
Ganguli, Sanjiban, M.A., Principal, Maharaja’s College, and Director of Public
Instruction, Jaipur State, Jaipur, India

*Geddes, Rt. Hon. Sir Auckland C., K.C.B., M.D., D.C.L., British Ambassador
to the U.S.A., The British Embassy, Washington
Geddes, Patrick, Professor of Botany in University College, Dundee, and Lecturer
on Zoology, Ramsay Garden, University Hall, Edinburgh
Geikie, Sir Archibald, O.M.,K.C.B., D.C.L. Oxf., D.Sc., LL.D., Ph.D., Late\
Pres. R.S., Foreign Member of the Reale Accad. Lincei, Rome, of the National
Acad, of the United States, of the Academies of Stockholm, Christiania,
Gottingen, Corresponding Member of the Institute of France and of the
Academies of Berlin, Vienna, Munich, Turin, Belgium, Philadelphia, New
York, etc., Shepherd’s Down, Haslemere, Surrey 205^

Gemmell, John Edward, M.B., C.M., Hon. Surgeon, Hospital for Women and
Maternity Hospital ; Hon. Gynecologist, Victoria Central Hospital, Liscard,
28 Rodney Street, Liverpool

* Gentle, William, B.Sc., 12 Mayfield Road, Edinburgh

* Ghosh, Sudhamoy, M.Sc. (Cal), D.Sc. (Edin.), F.C.S., Government Research

Chemist, Medical College, Calcutta, 9/1 Rammoban Dutt Road, P>howanipur,
Calcutta, India

* Gibb, Sir Alexander, G.B.E., C.B., formerly Director-General of Civil

Engineering, Ministry of Transport. 91 Victoria Street, Westminster,
London, S.W.

* Gibb, A. W. , D.Sc., Lecturer in Geology, The University, Aberdeen, 1 Belvidere

Street, Aberdeen 210

* Gibb, David, M.A. , B.Sc., Lecturer in Mathematics, Edinburgh University,

15 South Lauder Road, Edinburgh

* Gibson, Alexander, M.B., Ch.B., F.R.C.S. (Eng.), 661 Broadway, Winnipeg,

Canada

* Gibson, Charles Robert, Lynton, Mansewood, by Pollokshaws

Gibson, George A., M.A., LL.D. Professor of Mathematics in the University!
of Glasgow, 10 The University, Glasgow |

* Gibson, Walcot, D.Sc., F.G.S., Assistant Director, H.M. Geological Survey

(Scotland), 33 George Square, Edinburgh 215

Gidney, Henry A. J., L.M. and S. Sects. Ap. (Lond.). F.R.C.S. (Edin.), D.P. H.
(Camb.), D. O. (Oxford), Army Specialist Public Health, c/o Thomas Cook &
Sons, Ludgate Circus, London

Gilchrist, Douglas A., B.Sc., Professor of Agriculture and Rural Economy,
Armstrong College, Newcastle-upon-Tyne
Gilruth, John Anderson, M.R.C.V.S., D.V.Sc. (Melb.), Administrator, Govern-
ment House, Darwin Northern Territory, Australia

* Gladstone, Hugh Steuart, M.A., M.B.O.U., F.Z.S., Capenoch, Thornhill,

Dumfriesshire

Gladstone, Reginald John, M. D. , F.R.C. S. (Eng.), Lecturer and Senior Demon-
strator of Anatomy, King’s College, University of London, 22 Regent’s Park
Terrace, London, N.W. 220

* Glaister, John, M.D., F.R. F.P.S. Glasgow, D.P.H. Camb., Regius Professor of

Forensic Medicine and Public Health in the University of Glasgow,
3 Newton Place, Glasgow

Service on
Council, etc.

1869-72,

1874-76,

1879-82.

1905-08,

1912-13.

V-P-

1917-20.

Date of

Election.

1910

1901

1920

1913

1897

1898

1883

1910

1909

1918

1897

1905

1906

1905

1910

1899

1907

1911

1888

1911

1911

1918

1896

1914

1917

1921

1914

1880

1892

1893

1900

1908

1890

Alphabetical List of the Ordinary Fellows of the Society,

245

c.

c.

c.

c.

c.

c.

c.

c.

0.

c.

c.

c.

c.

c.

Goodall, Joseph Strickland, M.B. (Lond.), M.S.A. (Eng.), Lecturer on Physiology,
Middlesex Hospital, London, Annandale Lodge, Vanbrugh Park, Blackheath,
London, S.E.

Goodwillie, James, M. A., B.Sc., Liberton, Edinburgh

* Gordon, William, B.Sc., A.M.I.Mech.E. , Lecturer in Engineering in the

University of Edinburgh, 3 Wellington Street, Edinburgh

* Gordon, William Thomas, M.A., D.Se. (Edin.), M.A. (Cantab.), Professor of

Geology, University of London, King’s College, Strand, W.C. 225

Gordon-Munn, John Gordon, M. D., Heigham Hall, Norwich
*Gray, Albert A., M.D., 4 Clairmont Gardens, Glasgow

Gray, Andrew, M.A., LL.D., F.R.S., Professor of Natural Philosophy in the)
University of Glasgow |

Gray, Bruce M'Gregor, C.E., A.M. Inst.C.E. , Westbourne Grove, Selby,

Y orkshire

* Gray, James Gordon, D.Sc., Professor of Applied Physics in the University of

Glasgow, 11 The University, Glasgow 230

*Gray, Wm. Forbes, F.S.A. (Scot.), Editor and Author, 8 Mansionhouse Road,
Edinburgh

| Greenlees, Thomas Duncan, M.D. Edin., Viresco, Fordingbridge, Hants

* Gregory, John Walter, D.Sc., F.R.S. (Vice-President), Professor of Geology)

in the University of Glasgow, 4 Park Quadrant, Glasgow 1

Greig, Edward David Wilson, C.I.E., M.D., D. Sc., Lt.-Col., H.M. Indian Medical
Service, Pasteur Institute, Kasauli, India
Greig, Sir Robert Blyth, M.C., LL.D., F.Z. S., Chairman of the Board of
Agriculture for Scotland, 29 St Andrew Square, Edinburgh 235

*Grimshaw, Percy Hall, Assistant Keeper, Natural History Department, The Royal
Scottish Museum, 49 Comiston Drive, Edinburgh

* Guest, Edward Graham, M.A., B.Sc., 5 Newbattle Terrace, Edinburgh

* Gulliver, Gilbert Henry, D.Sc., A.M. I. Mech.E., 99 Southwark Street, London, S.E.

* Gunn, James Andrew, M.A., M.D., D.Sc., Professor of Pharmacology in the Uni-

versity of Oxford

Guppy, Henry Brougham, M.B., Rosario, Salcombe, Devon 240

*Guy, William, F.R.C.S., L.R.C.P., L.D.S.Ed., Consulting Dental Surgeon, Edin-
burgh Royal Infirmary ; Dean, Edinburgh Dental Hospital and School ;
Lecturer on Human and Comparative Dental Anatomy and Physiology, 11
Wemyss Place, Edinburgh

Hall- Kdwards, John Francis, L.R.C.P. (Edin.), Hon. F. R.P.S., Senior Medical
Officer in charge of X-ray Department, General Hospital, Birmingham,
141a and 141b Great Charles Street (Newhall Street), Birmingham
*Hardie, P. S., M.A. , B.Sc., Lecturer in Physics, Sultania Training College,
Cairo, Egypt

Harris, David Fraser, B.Sc. (Lond.), D.Sc. (Birm.), M.D. , F.S.A. Scot., Professor
of Physiology in the Dalhousie University, Halifax, Nova Scotia
Harrison, Edward Philip, Ph. D., Professor of Physics, Presidency College, Uni-
versity of Calcutta, The Observatory, Alipore, Calcutta 245

* Harrison, John, C.B.E., D.L., J.P., LL.D., Chairman of the Edinburgh Public

Library, Rockville, Napier Road, Edinburgh

* Harrison, John William Heslop, D.Sc. (Durham), Lecturer in Genetics, Armstrong

College, Newcastle. The Avenue, Birtley, Co. Durham
Harvey-Gibson, Robert John, C.B.E. , D.L. , J. P., M.A. , Mem. Roy. Dub. Soc. ,
formerly Professor of Botany, University of Liverpool. ‘ ‘ Beckallars ”
Grasmere, Westmorland.

Hay craft, J. Berry, M.D., D.Sc., Professor of Physiology in the University College
of South Wales and Monmouthshire, Cardiff
Heath, Thomas, B.A. , formerly Assistant Astronomer, Royal Observatory, Edin-
burgh, 11 Cluny Drive, Edinburgh 250

Hehir, Sir Patrick, K. C. I.E., C.B. , C.M.G. , M.D., F.R. C.S.E., M.R.C.S.,
L.R.C.P.E., Retired Maj. -General I.M.S., 3 Nelson Terrace, Westward Ho !
N. Devon

Henderson, John, D.Sc., A. Inst. E.E., Kinnoul. Gregory’s Road, Beaconsfield,
Bucks

* Henderson, William Dawson, M.A., B.Sc., Ph.D., Lecturer, Zoological Laboratories,

University, Bristol

I Hepburn, David, C.M.G., M.D., Professor of Anatomy in the University College
of South Wales and Monmouthshire, Cardiff

Service on
Council, etc.

1903-06.

V-P

1906-09.

1913-15.

1908-11.

V-P

1920-

1921

246

Proceedings of the Royal Society of Edinburgh.

Date of
Election.
1881

1916

1894

1902

1904

1885

1911
1920

1881

1896
1904

1897

1912
1893
1883

1910

1916

1911

1887

1908

1920

1912

1904

1917

1914

1875

1889

1901

1912

1906

1900

1 N.

C.

!. N.

Herdman, Sir W. A., Kt., C.B.E., D.Sc., LL.D., F.R.S., Past Pres. L.S., Pres.
Brit. Assoc., Emeritus Professor of Natural History in the University of
Liverpool. Croxteth Lodge, Ullet Road, Liverpool, and Rowany, Port
Erin, I.O.M. 255

* Herring, Percy Theodore, M.D. , F.R.C.P.Ed., Professor of Physiology, University

of St Andrews, Hepburn Gardens, St Andrews
Hill, Alfred, M.D., M.R.C.S., F.I.C., Valentine Mount, Freshwater Bay, Isle of
Wight

Hinxman, Lionel W., B.A., formerly of the Geological Survey of Scotland.
4 Morant Gardens, Ringwood, Hants

Hobday, Major Frederick T. G., C.M.G., F.R.C.V.S., Officier du Merite Agricole,
Cavaliere dei S.S. Maurizio e Lazaro, Hon. Veterinary Surgeon to H.M. the
King, Editor of the Veterinary Journal, 165 Church Street, Kensington,
London, W.

Hodgkinson, W. R., O.B.E., M. A., Ph.D., F.I.C., F.C.S., Professor of Chemistry
and Physics at the Ordnance College, Woolwich, 89 Shooter’s Hill Road,
Blackheath, Kent 260

Holland, William Jacob, LL.D. St Andrews, etc., Director Carnegie Institute,
Pittsburg, Pa., 5545 Forbes Street, Pittsburg, Pa., U.S.A.

* Horne, Alexander Robert, O.B.E., B.Sc., M.I.Mech.E., A.M.I.C.E., Professor

of Engineering, Robert Gordon’s Technical College, Aberdeen, 374 Great
Western Road, Aberdeen

Horne, John, LL.D., F.R.S., F.G.S., formerly Director of the Geological Survey
of Scotland, 20 Merchiston Gardens, Edinburgh

C.

). B.

0.

C.

C.

0.

C.

Horne, J. Fletcher, M. D., F.R.O.S.E., The Poplars, Barnsley

* Horsburgh, Ellice Martin, M.A., D.Sc., Reader in Technical Mathematics,

University of Edinburgh, 11 Granville Terrace, Edinburgh 265

Houston, Sir Alex. Cruikshanks, K.B.E., C.V.O., M.B., C.M., D.Sc., 19 Fairhazel
Gardens, South Hampstead, London, N.W.

*Houstoun, Robert Alexander, M.A., Ph.D., D.Sc., Lecturer in Physical Optics,
University, Glasgow, 45 Kirklee Road, Glasgow
Howden, Robert, M. A. , M. B. , C.M. , D.Sc. , Professor of Anatomy in the University
of Durham, 14 Burdon Terrace, Newcastle-upon-Tyne
Hoyle, William Evans, M.A., D.Sc., M. R.C.S., Director of the Welsh National
Museum : Crowland, Llandaff, Wales

Hume, William Fraser, D.Sc. (Lond. ), Director, Geological Survey of Egypt,
Helwan, Egypt 270

* Hunter, Charles Stewart, L.R.C.P.E., L.R.C.S.E., D.P.H., Walden, Anerley

Road, London, S.E. 20

Hunter, Gilbert Macintyre, M.Inst.C.E., M.Inst.E.S., M. Inst.M.E. , Resident
Engineer, Nitrate Railways, Iquique, Chile, and Maybole, Ayrshire
Hunter, William, M.D., M.R.C.P.L. and E., M.R.C.S., 103 Harley Street, London
Hyslop, TheophilusBulkeley, M.D.,M.R.C.P E., 5 Portland Place, London, W.

* Inglis, James Gall, Publisher and Editor of Educational Works, Edinburgh, 36

Blacket Place, Edinburgh 275

* Inglis, Robert John Mathieson, M.Inst.C.E., District Engineer, North British

Railway. Tantah, Peebles

Innes, R. T. A., Director, Government Observatory, Johannesburg, Transvaal

* Irvine, James Colquhoun, C.B.E., Ph.D., D.Sc., LL.D., F.R.S., Principal of the

University of St Andrews
Jack, John Noble

Jack, William, M.A., LL.D., D.Sc., Emeritus Professor of Mathematics in the
University of Glasgow 280

James, Alexander, M.D., F.R.C.P.E. , 9 Randolph Crescent, Edinburgh
*Jardine, Robert, M.D., M.R.C.S., F.R.F.P.S. Glas., 20 Royal Crescent, Glasgow

* Jeffrey, George Rutherford, M.D. (Glasg.), F.R.C.P. (Edin.), etc., Bootham Park

Private Mental Hospital, York

* Jehu, Thomas John, M.A., M.D., F.G.S., Professor of Geology in the University

of Edinburgh : 35 Great King Street, Edinburgh
*Jerdan, David Smiles, M.A. , D.Sc., Ph.D., 26 Avenue du Chateau d’ Eau,
Saventhem, Belgium 285

Service on
Council, etc.

1917-20.

1902-05,

1906- 07,

1914- 15.
V-P

1907- 13.
P

1915- 19.

1920-

1888-91-

1917-20.

Alphabetical List of the Ordinary Fellows of the Society.

247

Date of
Election.

1895

1903

1874

1888

1915

1912

1909

1908

1891

1913

1908

1886

1907

1880

1918

1878

1901

1907

1880

1921

1920

1878

1910

1885

1894

1921

1910

1905

1910

1903

1910

C.

!. N.

!. K.

Johnston, Col. Henry Halcro, C.B., D.Sc., M.D., F.L.S., late A.M.S., Orphir
House, Kirkwall, Orkney

* Johnston, Thomas Nicol, M. B., C.M., Pogbie, Humbie, East Lothian

Jones, Francis, M.Sc., Lecturer in Chemistry, 17 Whalley Road, Whalley Range,
Manchester

Jones, John Alfred, M.Inst.C.E., Fellow of the University of Madras, Sanitary
Engineer to the Government of Madras, c/o Messrs Parry & Co., 70 Grace-
church Street, London

Kemnal, Sir James Hermann Rosenthal, Managing Director and Engineer-in-
Chief of Babcock & Wilcox, Ltd., Kemnal Manor, Chislehurst, Kent 290
Kennedy, Robert Foster, M.D. (Queen’s Univ., Belfast), M. B., B.Ch. (R.U.I.),
Assistant Professor of Neurology, Cornell University, New York, 20 West !
50th Street, New York, U.S. A.

Kenwood, Henry Richard, M.B. , Chadwick Professor of Hygiene in the University i
of London, 126 Queen’s Road, Finsbury Park, London, N.

* Kerr, Andrew William, F.S.A. Scot., 81 Great King Street, Edinburgh
Kerr, Joshua Law, M.D., 16 High Street, Swindon, Wilts.

* Kerr, Walter Hume, M.A., B. Sc., Lecturer on Engineering Drawing and Structural

Design in the University of Edinburgh 295

Kidd, Walter Aubrey, M.D. , 2 Suffolk Square, Cheltenham

Kidston, Robert, LL.D., D.Sc., F.R.S., F.G.S. , 12 Clarendon Place, Stirling

* King, Archibald, M. A., B.Sc., formerly Rector of the Academy, Castle Douglas ;

H.M. Inspector of Schools, Inverspey, Fochabers, Morayshire
f King, W. F. , Lonend, Russell Place, Trinity, Leith

* Kingon, Rev. John Robert Lewis, M.A. (Edin. and Cape of Good Hope), D.Sc.

(Ghent), F.L.S., U.F. Church of Scotland, Box 17, Port Elizabeth, C.P.,
South Africa 300

Kintore, The Right Hon. the Earl of, P.C., G.C.M.G., M.A. Cantab., LL.D.
Cambridge, Aberdeen, and Adelaide, Keith Hall, Inverurie, Aberdeenshire

* Knight, Rev. G. A. Frank, M.A. , 5 Granby Terrace, Hillhead, Glasgow

* Knight, James, M.A., D.Sc., F.C.S., F.G.S., Head Master, Queen’s Park High

School. Enterkin, Douglas Gardens, Uddingston, by Glasgow

Knott, C. G., D.Sc., LL.D., F.R.S. , Reader in Applied Mathematics in the
University of Edinburgh, formerly Professor of Physics, Imperial University,
Japan (Gen. Secretary), 42 Upper Gray Street, Edinburgh

Service on
Council, etc.

1891-94,

1903-06.

Sec.

1909-16.

V-P

1917-20.

1894-97,

1898-1901,

1902-05.

Sec.

1905-12.

C.

c.

c.

c.

). B.

c.

v.

*Lamb, James Alexander George, Banker, 11 Braid Crescent, Edinburgh 305

* Lamont, John Charles, Lieut. -Col., I.M.S. (retired), C.I.E., M.B., C.M. (Edin.),

M.R.C.S. (Eng.), 7 Merchiston Park, Edinburgh
Lang, Sir P. R. Scott, Kt., M.A., B.Sc., Emeritus Professor of Mathematics, Uni-
versity of St Andrews

* Lauder, Alexander, D.Sc., Lecturer in Agricultural Chemistry, Edinburgh and

East of Scotland College of Agriculture, 13 George Square, Edinburgh
Laurie, A.P., M.A., D.Sc., J.P., Principal of the Heriot-Watt College, Edin- (
burgh 1

Laurie, Malcolm, B.A., D.Sc., F.L.S., 4 Wordsworth Road, Harpenden, Herts 310

* Laurie, The Rev. Albert Ernest, M.C., C.F., Rector of Old St Paul’s, Edinburgh,

and Canon of St Mary’s Cathedral, Edinburgh. Lauder House, Jeffrey
Street, Edinburgh

* Lawson, A. Anstruther, B.Sc. , Ph.D., D.Sc., F.L.S., Professor of Botany, Univer-

sity of Sydney, New South Wales, Australia

* Lawson, David, M.A., M.D., L.R.C.P. and S.E., Druimdarroch , Banchory,

Kincardineshire

* Lee, Gabriel W., D.Sc., Palaeontologist, Geological Survey of Scotland, 33 George

Square, Edinburgh

* Leighton, Gerald Rowley, O. B.E., M.D., Medical Officer, Scottish Board of

Health, 125 George Street, Edinburgh 315

Levie, Alexander, F.R.C.Y.S. , D. V.S.M., Rannock, Carlton Road, Derby

Gen. Sec.
1912-

1917-20.

1908-11,

1913-16.

248

Date of
Election.

1916

1914

1918

1905

1889

1912

1920
1912
1903
1903

1898

1884.

1888

1900

1894

1887

1917

1907

1921

883

1903

1918
1905

1897

1904
1920
1904

1886

1901

1910

1888

1885

1897

1878

1903

1911

Proceedings of the Royal Society of Edinburgh.

c.

). N.

c.

c.

0.

c.

c.

*Lavy, Hyman, M.A. , D.Sc. , Assistant Professor of Mathematics, Imperial
College of Science and Technology, London, S.W. 7, “Eskbank,” 105 Cam-
bridge Road, Teddington, Middlesex

Lewis, Francis John, D.Sc., F.L.S., Professor of Biology, University of Alberta,
Edmonton South, Alberta, Canada

* Lidstone, George James, F.F.A., F.I.A., Manager and Actuary of the Scottish

Widows’ fund Life Assurance Society, 8 Eglinton -Crescent, Edinburgh

* Lightbody, Forrest Hay, 53 Queen Street, Edinburgh 320

Lindsay, Rev. James, M.A., D.U., B.Sc., F.R.S.L., F.G.S., M.R.A.S., Corresponding

Member of the Royal Academy of Sciences, Letters and Arts, of Padua,
Associate of the Philosophical Society of Louvain, Annick Lodge, Irvine

* Lindsay, John George, M.A., B.Sc. (Edin.), Rector of Dunfermline High

School

* Lindsay, Thomas A., M.A. (Hons.), B.Sc., Head Master, Higher Grade School,

Bucksburn, Aberdeenshire

* Linlithgow, The Most Honourable the Marquis of, Hopetoun House, South

Queensferry

t Liston, William Glen, M.D., Lt.-Col. Indian Medical Service, Director Bombay
Bacteriological Laboratory, Paree, Bombay, India 325

* Littlejohn, Henry Harvey, M.A., M.B., B.Sc., F.R.C.S.E., Professor of Forensic

Mediciqe, and late Dean of the Faculty of Medicine in the University of
Edinburgh, 11 Rutland Street, Edinburgh

* Lothian, Alexander Veitch, M.A., B.Sc., Training College, Jordanhill, Glasgow
Low, George M., Actuary, 11 Moray Place, Edinburgh

Lowe, D. F. , M. A., LL.D., formerly Headmaster of Heriot’s Hospital School,
Lauriston, 19 George Square, Edinburgh

t Lusk, Graham, Ph.D., M.A. , Professor of Physiology, Cornell University Medical
College, New York, N.Y., U.S.A. 330

Mabbott, Walter John, M.A., Rector of County High School, Duns, Berwickshire
M‘Aldowie, Alexander M. , M. D., 8 Holland Road, Cheltenham

* Macalister, Sir Donald, K.C.B., M.D., M.A., B.Sc., Principal of the University

of Glasgow, The University, Glasgow

MacAlister, Donald Alexander, A.R.S.M. , F.G.S., 10 St Alban’s Road, Kensing-
ton, London, W. 8

*M‘Arthur, Neil, M.A., B.Sc., Lecturer in Mathematics, Glasgow University,
c/o Mrs Croll, 56 West End Park Street, Glasgow 335

M‘ Bride, P., M.D., F.R.C.P.E., 20 South Drive, Harrogate
M'Cormick, Sir W.S., M.A., LL.D., Chairman of the Advisory Council, Depart-
ment of Scientific and Industrial Research, 16-18 Old Queen Street, West-
minster, S. W. 1

*M‘Culloch, Rev. James David, D.D., 43 Brougham Street, Greenock

* Macdonald, Hector Munro, M.A., F.R.S., Professor of Mathematics, University of

Aberdeen, 52 College Bounds, Aberdeen

Macdonald, James A., M.A., B.Sc., H.M. Inspector of Schools, Stewarton,
Kilmacolm 340

* Macdonald, John A., M.A., B.Sc., King Edward VII School, Johannesburg,

Transvaal

*M ‘Donald, Stuart, M.A. , M.D. , F. R.C.P.E., Professor of Pathology, School of
Medicine, Newcastle-on-Tyne

Macdonald, William, M.S. Agr., Sc.D., Ph.D., D.Sc., Editor, Agricultural Journal
of South Africa, Rand Club, Johannesburg, Transvaal
Macdonald, William J., M.A., LL.D., 15 Comiston Drive, Edinburgh

* MacDougall, R. Stewart, M.A. , D.Sc., Professor of Biology, Royal Veterinary

College, Edinburgh, 9 Dryden Place, Edinburgh 345

Macewen, Hugh Allen, M.B., Ch.B., D.P.H. (Lond. and Camb.), Local
Government Board, Whitehall, London, S. W.

M'Fadyean, Sir John, Kt., M.B., B.Sc., LL.D., Principal, and Professor of
Comparative Pathology in the Royal Veterinary College, Camden Town,
London

Macfarlane, J. M., D.Sc., LL.D., Emeritus Professor of Botany, 4320 Osage
Avenue, Philadelphia, Pennsylvania, U.S.A.

MacGillivray, Angus, C.M., M.D., D.Sc., F.S.A. (Scot.), 23 South Tay Street,
Dundee

M‘Gowan, George, F.I.C. , Ph.D., 21 Montpelier Road, Ealing, London, W. 5 350

*M‘Intosh, Donald C., M.A., D.Sc., Education Offices, Elgin
MTntosh, John William, A.R.C.V.S., Dollis Hill Farm, Cricklewood,
London, N.W. 2

Service on
Council, etc.

1919-

1910-13.

1908-11.

1914-17.

Date of

Election.

1869

1895

1914

1873

1912

1900

1910

1916

1894

1904

1918

1910

1904

1899

1888

1913

1916

1907

1917

1921

1921

1921

1898

1913

1917

1908

1912

1913

1909

1882

1901

Iphabetical List of the Ordinary Fellows of the Society. 249

M'lntosh, William Carmichael, M.D., LL.D., F.R.S., F.L.S., Emeritus Professor of
Natural History in the University of St Andrews, Pres. Ray Society,
2 Abbotsford Crescent, St Andrews
Macintyre, John, M.D., LL.D., 179 Bath Street, Glasgow
* M‘ Kendrick, Archibald, F.R.C.S.E., D.P.H., L.D.S., 12 Rothesay Place, Edin-
burgh 355

M'Kendrick, John G., M.D., F.R.C.P.E., LL.D., F.R.S., Emeritus Professor of
Physiology in the University of Glasgow, Maxieburn, Stonehaven

M'Kendrick, Anderson Gray, M.B., Major, Indian Medical Service, Superinten-
dent, Research Laboratory, Royal College of Physicians, Edinburgh

* M'Kendrick, John Souttar, M.D., F.R.F.P.S.G., 2 Buckingham Terrace, Hill-

head, Glasgow

* Mackenzie, Alister, M.A. , M.D., D.P.H., Principal, College of Hygiene and

Physical Training, Dunfermline

* Mackenzie, .lohn E., D.Sc., Lecturer in Chemistry, University of Edinburgh,

Major- Adjutant, O.T. C., 2a Ramsay Garden, Edinburgh 360

Mackenzie, Robert, M.D., Napier, Nairn

* Mackenzie, Sir W. Leslie, M.A., M.D., D.P.H., LL.D., Medical Member of the

Scottish Board of Health, 14 Belgrave Place, Edinburgh

* Mackie, Wm. , M.A., M.D., D.P H., 13 North Street, Elgin

* MacKinnon, James, M. A., Pli.D. , Professor of Ecclesiastical History, Edinburgh

University, 12 Lygon Road, Edinburgh

| * Mackintosh, Donald James, C.B., M.Y.O., M.B., C.M., LL.D., Supt. Western
Infirmary, Glasgow - . 365

Maclean, Ewan John, M. D. , M.R.C.P. Lond., J.P. , Professor of Obstetrics
and Gynaecology, Welsh National School of Medicine, 12 Park Place,
Cardiff

Maclean, Magnus, M.A., D.Sc., LL.D , M.Inst.C.E., M.I.E.E., Professor of
Electrical Engineering in the Royal Technical College, 51 Kerrsland Terrace,
Hillhead, Glasgow

*M‘Lellan, Dugald, M.Inst.C.E., District Engineer, Caledonian Railway, 20
Kingsburgh Road, Murray-Held, Edinburgh
*M‘Lintock, W. F. P., D.Sc. (Edin.), Museum of Practical Geology, 28 Jermyn
Street, London, S.W. 1

* Macnair, Professor Peter, Curator of the Natural History Collections in the

Glasgow Museums, Kelvingrove Museum, Glasgow 370

*Macpherson, Rev. Hector Copland, M.A. , F.R.A.S. , Guthrie Memorial U. F.
Church. 30 Pilrig Street, Edinburgh

* M'Quistan, Dougald Black, M.A., B.Sc., Head Mathematical Master in Allan

Glen’s School, Glasgow. 29 Viewpark Drive, Rutherglen, near Glasgow

* MacRobert, Thomas Murray, M.A., D.Sc., Lecturer in Mathematics in the

University of Glasgow. 6 Lothian Gardens, Kelvinside, N. , Glasgow
*M‘Whan, John, M.A. (Glasgow), Ph.D. (Gott.), Lecturer in Mathematics in the
University of Glasgow. 59 Greenlees Road, Catnbuslang
Mahalanobis, S. C., B.Sc., Professor of Physiology, Presidency College, Calcutta,
India 375

Majumdar, Tarak Nath, D.P. H. (Cal.), L.M.S., F.C.S., Health Officer, Calcutta,
IV, .37 Lower Chitpore Road, Calcutta, India

* Malcolm, Louis William Gunther, M.A. (Melbourne), Cant. R.G.A., Bristol

Museum and Art Gallery

Mallik, Devendranath, Sc. 1)., B.A., Professor of Mathematics, Astronomical
Observatory, Presidential College, Calcutta, India
Maloney, William Joseph, M.D. (Edin.), Professor of Neurology at Fordham
University, New York City, N.Y. , U.S.A.

Marchant, Rev. Sir James, K.B.E., LL.D., F.R.A.S., F.L.S., Director, National
Council for Promotion of Race- Regeneration, 20 Bedford Square, London,
W.C. 11 380

* Marshall, C. R., M.D., M.A., Professor of Materia Medica, Marischal College,

Aberdeen

Marshall, D. H., M.A., Em. -Professor of Physics, Queen’s University, Elmtree
House, Union Street, W. , Kingston, Ontario, Canada
Marshall, F. H. A., Sc.D., Lecturer on Agricultural Physiology in the Uni-
versity of Cambridge, Christ’s College, Cambridge

Service on
Council, etc.

1885-88.

1875-78,

1885-88,

1893- 94,
1900-02.

V-P

1894- 1900.

1916-19.

1915-18.

250

Date of

Election.

1920

1913

1885

1898

1911

1921

1906

1902

1917

1901

1917

1888

1902

1885

1908

1910

1909

1905

1905

1904

1886

1899

1889

1897

1900

1911

1906

1890

1887

1896

1919

1892

1914

1901

1892

1916

Proceedings of the Royal Society of Edinburgh.

* Marshall, John, M.A., D.Sc. (St Andrews), B.A. (Cantab.), Senior Lecturer in

Mathematics, University College, Swansea
Masson, George Henry, M.D., D.Sc., M. R.C.P.E. , Port of Spain, Trinidad,
British West Indies 385

Masson, Orme, M.A. , D.Sc., F.R.S., Professor of Chemistry in the University of
Melbourne

* Masterman, Arthur Thomas, M.A., D.Sc., F. R. S., formerly Superintending

Inspector, H.M. Board of Agriculture and Fisheries. Mill House, Wooburn
Green, Bucks

Mathews, Gregory Macalister, F.L.S. , F.Z.S., Foulis Court, Fair Oaks, Hants

* Mathieson, John, F.R. S.G.S., late Division Superintendent, Ordnance Survey

(retired), 42 East Claremont Street, Edinburgh ,

* Mathieson, Robert, F.C.S., St Serf’s, Innerleithen 390

Matthews, Ernest Romney, A. M. Inst.C.E., F.G.S., Chadwick Professor of

Municipal Engineering in the University of London, University College,
Gower Street, London, W.C.

* Maylard, A. Ernest, M. B. , B.Sc. (Lond.), F.R.F. P.S. (Glasgow), 1 Windsor

Terrace, W., Great Western Road, Glasgow
Menzies, Alan W. C. , M.A., B.Sc., Ph.D., F.C. S., Professor of Chemistry,
Princeton University, Princeton, New Jersey, U.S.A.

* Merson, George Fowlie, Manufacturing Technical Chemist, 9 Hampton Terrace,

Edinburgh

Methven, Cathcart W., M. Inst.C.E., F.R.I.B.A., Durban, Natal, S. Africa 395
Metzler, William H., A.B., Ph.D., Corresponding Fellow of the Royal Society of
Canada, Professor of Mathematics Syracuse University, Syracuse, N.Y., U.S.A.
Mill, Hugh Robert, D.Sc., LL. D. , Hill Crest, Dorman’s Park, E. Grinstead, London

* Miller, Alexander Cameron, M.D., F.S.A. Scot., Craig Linnhe, Fort-William,

Inverness-shire

* Miller, John, M.A. , D.Sc., Professor of Mathematics, Royal Technical College,

2 North bank Terrace, North Kelvinside, Glasgow
Mills, Bernard Langley, M.D., F.R.C.S.E. , M.R.C.S., D. P.H., Lt.-Col.

R.A.M.C., formerly Army Specialist in Hygiene, c/o National Provincial
Bank, Fargate, Sheffield 400

* Milne, Archibald, M.A., D.Sc., Lecturer on Mathematics and Science, Edinburgh

Provincial Training College, 108 Comiston Drive, Edinburgh

* Milne, C. H. , M. A., Head Master, Daniel Stewart’s College, 19 Merchiston

Gardens, Edinburgh

* Milne, James Robert, D.Sc., Lecturer in Natural Philosophy, University of Edin-

burgh, 17 Manor Place, Edinburgh
Milne, William, M.A. , B.Sc., 70 Beechgrove Terrace, Aberdeen

* Milroy, T. H., M. D., B.Sc. , Professor of Physiology in Queen’s College, Belfast 405
Mitchell, A. Crichton, D.Sc., Hon. Doc. Sc. (Geneve), formerly Director of Public (

Instruction in Travancore, India (Curator of Library and Museum),-!
The Observatory, Eskdalemuir, Langholm, Dumfriesshire ^

f Mitchell, George Arthur, M.A. , 9 Lowther Terrace, Kelvinside, Glasgow

* Mitchell, James, M.A., B.Sc., Monydrain, Lochgilphead

Modi, Edalji Manekji, D.Sc., LL.D., Litt.D., F.C.S., etc., Proprietor and Director
of Arthur Road Chemical Works, Meher Buildings, Tardeo, Bombay, India
Moffat, Rev. Alexander, M.A., B.Sc., Professor of Physical Science, Christian
College, Madras, India 410

Mond, R. L., M.A. Cantab., F.C.S., Combe Bank, near Sevenoaks, Kent
Moos, N. A. F., D.Sc., L.C.E., J. P., Director of Bombay and Alibag Observa-
tories (retired), Gowalia, Tank Road, Bombay, India
Morgan, Alexander, M.A., D.Sc., Principal, Edinburgh Provincial Training
College, 1 Midmar Gardens, Edinburgh

* Morris, Robert Owen, M.A., M.D., C.M. (Edin.), D.P.H. (Liverpool), Tuberculosis

Institute, Newtown, N. Wales

Morrison, J. T. , M.A. , B.Sc., Professor of Physics and Chemistry, University,
Stellenbosch, Cape Colony 415

Mort, Spencer, M.D., Ch.B., F.R.C.S.E., Lieut.-Col., R.A.M.C., North
Middlesex Hospital, Upper Edmonton, London, N. 18.

Moses, O. St John, I.M.S., M.D., D.Sc., F.R.C.S., Lt.-Col. I.M.S., Professor of
Medical Jurisprudence, c/o Messrs King, Hamilton & Co., 4 and 5 Koila Ghat
Street, Calcutta, India

Mossman, R. C., Oficina Meteorologica Argentina, Paseo Colon 974, Buenos Aires
*Muir, Robert, M.A., M.D. , Sc.D. , F.R.S., Professor of Pathology, University of
Glasgow, 16 Victoria Crescent, Dowanhill, Glasgow

Service on
Council, etc.

1902-04.

1915- 16.
Cur.

1916-

Date of
Election.

1874

1888

1907

1887

1894 &
1921

1896

1907

1888

1897

1898

1884

1880

1878

1888

1886

1895

1915

1914

1908
1905
1914

1901

1918

1886

1919

1892

1881

1907

1914

1904

1889

Alphabetical List of the Ordinary Fellows of the Society.

c. K.
y. j.

c.

c.

c.

Muir, Sir Thomas, C.M.G. , M.A.,LL.D., F.R.S. , lately Superintendent-General C
of Education for Cape Colony, Education Office, Cape Town, and Elmcote, -J
Sandown Road, Rondebosch, South Africa 420 f

Muirhead, George, Commissioner to His Grace the Duke of Richmond and Gordon,
K.G. , Speybank, Fochabers

Muirhead, James M. P., J. P., F.R.S.L., F.S.S., c/o Royal Societies Club, St
James’s Street, London, S. W.

Mukhopadhyay, Asutosh, M.A., LL.D., F.R.A.S., M.R.I.A., Professor of Mathe-
matics at the Indian Association for the Cultivation of Science, 77 Russa
Road North, Bhowanipore, Calcutta, India

* Munro, J. M. M., M. Inst.E.E. , Assoc. M. Inst.C.E. , Consulting Electrician and

Engineer, 11 Randolph Place, Edinburgh.

Murray, Alfred A., M.A., LL.B., 20 Warriston Crescent, Edinburgh 425

Musgrove, James, M.D., F.R.C.S. Edin. and Eng., LL.D., Emeritus-Professor
of Anatomy, University of St Andrews, The Swallowgate, St Andrews
Napier, A. D. Leith, M. D., C.M., M.R.C.P., 4 Kent Street, Hawthorn, Unley,
S. Australia

Nash, Hon. Alfred George, M.L.C. , B.Sc. , F. R.G. S. , C.E. , Belretiro, Mandeville,
Jamaica, W.I.

Newman, Sir George, K.C.B. , M.D. , D.C.L. , F.R.C.P., Chief Medical Officer of the
Ministry of Health and the Board of Education, Whitehall, S.W. 1

Nicholson, J. Shield, M.A., D.Sc., Professor of Political Economy in thel
University of Edinburgh, 3 Belford Park, Edinburgh 430 1

Nicol, W. W. J., M.A., D.Sc., 15 Blacket Place, Edinburgh
Norris, Richard, M.D., M.R.C.S. Eng., 3 Walsall Road, Birchfield, Birming-
ham

t Ogilvie, Sir F. Grant, Kt., C.B., M.A., B.Sc., LL.D., Principal Assistant
Secretary, Department of Scientific and Industrial Research, 15 Evelyn
Gardens, London, S.W.

Oliver, James, M.D., F.L.S., Physician to the London Hospital for Women,
123 Harley Street, London, W.

Oliver, Sir Thomas, Kt., M.D. , LL.D., F.R.C.P. , Professor of Physiology in the
University of Durham, 7 Ellison Place, Newcastle-upon-Tyne 435

* Orr, Lewis P. , F.F.A., Manager of Scottish Life Assurance Co., 19 St Andrew

Square, Edinburgh

* Oswald, Alfred, Lecturer in German, Glasgow Provincial Training College,

11 Nelson Terrace, Hillhead, Glasgow

Page, William Davidge, F.C.S., F.G.S., M.Inst.M.E., 10 Clifton Dale,
York

Pallin, Lt.-Col. William Alfred, C.B.E., D.S.O. , F.R.C.Y.S., Headquarters,
Eastern Command, Nainital, India

Pare, John William, M. 1)., C. M., L.D.S. , Lecturer in Dental Anatomy,
National Dental Hospital, 9a Cavendish Square, London, W. 440

* Paterson, David, F.C.S., Lea Bank, Rosslyn, Midlothian

* Paterson, Rev. William Paterson, D.D., LL.D., Professor of Divinity, University,

Edinburgh, 3 Royal Terrace, Edinburgh

C.

Paton, D. Noel, M.D., B.Sc., LL.D., F.R.C.P.E., F.R.S., Professor of
Physiology in the University of Glasgow, University, Glasgow

C.

C. N.

* Patterson, Thomas Stewart, D.Sc. (London and Glasgow), Ph.D. (Heidelberg),

Professor of Organic Chemistry in the University of Glasgow, 10 Oakfield
Terrace, Hillhead, Glasgow

Paulin, Sir David, Actuary; 6 Forres Street, Edinburgh 445

Peach, Benjamin N., LL.D., F.R.S., F. G.S., formerly District Superintendent j
and Acting Palaeontologist of the Geological Survey of Scotland, 72 Granger
Loan, Edinburgh

* Pearce, John Thomson, B.A., B.Sc., School House, Tranent

Pearson, Joseph, D.Sc., F.L.S., Director of the Colombo Museum, and Marine
Biologist to the Ceylon Government, Colombo Museum, Ceylon

* Peck, James Wallace, C. B. , M.A., Scottish Board of Health. 10 South

Learmonth Gardens, Edinburgh

f Peck, Sir William, Kt., F.R.A.S., Town’s Astronomer, City Observatory, Calton
Hill, Edinburgh 450

251

Service on
Council, etc.

1885-88.

y-p

1888-91.

1885-87,

1892-95,

1897-1900.

1901-03.

1894-97,

1904-06,

1909-12.

V-P

1918-21

1905-08,

1911- 12.

y-p

1912- 17.

252

Date of

Election.

1887

1893

1913

1889

1907

1914

1905

1908

1911

1906

1921

1919

1888

1902

1892

1915

1903

1911

1920

1898

1897

1899

1914

1911

1891

1904

1900

1883

1902

1902

1913

1908

1914

1913

Proceedings of the Royal Society of Edinburgh.

Peddie, Wm., D.Sc. (Vice-President), Professor of Natural Philosophy in J
University College, Dundee, The Weisha, Ninewells, Dundee j

Perkin, Arthur George, F. R.S., Grosvenor Lodge, Grosvenor Road, Leeds
| Philip, Alexander, M.A., LL.B., Writer, The Mary Acre, Brechin
Philip, Sir R. W., Kt., M.A., M.D., LL.D., F.R.C.P.E., Professor of Tuber-
culosis, University of Edinburgh, 45 Charlotte Square, Edinburgh
Phillips, Major Charles E. S., O.B.E., Castle House, Shooters Hill, Woolwich,
S.E. 18 455

* Pilkington, Basil Alexander, “ Kambla,” Davidson’s Mains

* Pinkerton, Peter, M.A., D.Sc., Rector, High School, Glasgow, 7 Park Quadrant,

Glasgow, W.

* Pirie, James Hunter Harvey, B.Sc., M.D., F.R.C.P.E., Superintendent of the

Routine Division of The South African Institute for Medical Research, P.O.
Box 1038, Johannesburg, South Africa

* Pirie, James Simpson, M.Inst.C.E., 28 Scotland Street, Edinburgh

Pitchford, Herbert Watkins, C.M.G., F.R.C.V.S., Lt.-Col., Oaklands Drive,
Weybridge, Surrey 460

* Pollard, Sir George Herbert, K.B., M.D., C. M. (Edin.), Barrister-at-Law, Inner

Temple. 79 Albert Road, Southport

* Porritt, B. D. , M.Sc. (Lond. ), F. I.C. , Research Association of British Rubber

and Tyre Manufacturers Chemistry Dept., University College, Gower Street,
London, W.C. 1

Prain, Sir David, Lt.-Col., Indian Medical Service (retired), Kt., C. M.G. , C.I.E.,
M.A., M.B., LL.D., F.L.S., F.R.S., For. Memb. K. Svensk. Vetensk. Akad. ;
Hon. Memb. Soc. Lett, ed Arti d. Zelanti, Acireale ; Pharm. Soc. Gt. Britain ;
Corr. Memb. Bayer Akad. Wiss., etc. ; Director, Royal Botanic Gardens,
Kew, Surrey

* Preller, Charles du Riche, M.A., Ph.D., A. M.Inst.C.E., M.I.E.E., F.G.S.,

61 Melville Street, Edinburgh

Pressland, Arthur J., M.A. Camb., Edinburgh Academy 465

Price, Frederick William, M.D., M.R.C.P. Edin., Physician to the Great Northern
Hospital, London, 3 33 Harley Street, London, W.

* Pullar, Laurence, Dunbarney, Bridge of Earn, Perthshire

Purdy, John Smith, D.S.O., M.D., C.M. (Aberd.), D.P.H. (Camb.), F.R.G.S.,
Town Hall, Sydney, N. S.W., Australia

* Purser, George Leslie, M.A. (Cantab.), Assistant in the Natural History Depart-

ment of the University of Edinburgh, c/o Muir, 21 Buccleuch Place,
Edinburgh

* Purves, John Archibald, D.Sc., 52 Queen Street, Exeter 470

Rainy, Harry, M.A., M.D., F.R.C.P.Ed., 16 Great Stuart Street, Edinburgh

* Ramage, Alexander G., Marchfield, Davidson’s Mains, Midlothian

* Ramsay, Peter, M.A., B.Sc., Head Mathematical Master, George Watson’s

College, 63 Comiston Drive, Edinburgh

* Rankin, Adam A., British Astronomical Association, West of Scotland Branch,

24 Woodend Drive, Jordanhill, Glasgow

Rankine, Sir John, K.C., M.A., LL.D., Professor of the Law of Scotland in the
University of Edinburgh, 23 Ainslie Place, Edinburgh 475

Ratcliffe, Joseph Riley, M.B., C.M., c/o The Librarian, The University,
Birmingham

Raw, Nathan, C.M.G., M.D., M.P., 45 Weymouth Street, Harley Street,

London, W. 1.

Readman, J. B. , D.Sc., F.C.S. , Frankleigh House, Bradford-on- Avon, Wilts
Rees-Roberts, John Vernon, M.D., D.Sc., D.P.H. , 11 Oak Hill Park, Hamp-
stead, London, N. W. 3

Reid, George Archdall O’Brien, M.B., C.M., 9 Victoria Road South, Southsea,
Hants 480

Reid, Harry Avery, O.B.E., F.R.C.V.S., D.V.H., Bacteriologist and Pathologist,
Department of Agriculture, Wellington, New Zealand

* Rennie, John, D.Sc., Lecturer on Parasitology and Experimental Zoology,

University of Aberdeen, 60 Desswood Place, Aberdeen
Renshaw, Graham, M.D. , M. R. C.S., L.R.C.P., L.S.A., Editor of the Avicultural
Magazine , Sale Bridge House, Sale, Manchester

* Richardson, Harry, M.Inst.E.E., M.Inst.M.E., General Manager and Chief

Engineer, Electricity Supply, Dundee and District, Dudhope Crescent Road,
Dundee

Service on
Council, etc.

1904-07,

1908-11.

V-P

1919-

Date of

Election.

1908

1875

1916

1914

1906

1898

1919

1900

1902

1919

1896

1910

1916

1881

1909

1921

1906

1902

1906

1916

1914

1912

1903

1903

1900

1919

1885

1919

1917

1908

1900

1911

phabetical List of the Ordinary Fellows of the Society. 253

Richardson, Linsdall, F.G.S., 10 Oxford Parade, Cheltenham, Glos. 485

Richardson, Ralph, W.S., 29 Eglinton Crescent, Edinburgh

* Ritchie, James, M.A., D.Sc., Keeper of the Natural History Department in the

Royal Scottish Museum, 20 Upper Gray Street, Edinburgh

* Ritchie, James Bonnyman, D.Sc., Headmaster, Academy, Forres

* Ritchie, William Thomas, M.D., F.R.C.P.E., 14 Rothesay Place, Edinburgh

Roberts, Alexander William, D.Sc., F.R.A.S., Lovedale, South Africa 490

* Roberts, Alfred Henry, O. B. E., M.Inst.C.E., Superintendent and Engineer,

Leith Docks, 2 Cargil Terrace, Trinity, Edinburgh

* Robertson, Joseph M‘ Gregor, M.B., C.M., 26 Buckingham Terrace, Glasgow

* Robertson, Robert A., M.A. , B.Sc., Lecturer on Botany in the University of St

Andrews

* Robertson, William Alexander, F.F.A., Century Insurance Co., Ltd., 18

Charlotte Square. 12 Lonsdale Terrace, Edinburgh
Robertson, W. G. Aitchison, D.Sc., M.D. , F.R.C.P.E., The Grange, Ashford,
Middlesex 495

* Robinson, Arthur, M.D., M.R.C.S., Professor of Anatomy, University ofj

Edinburgh, 35 Coates Gardens, Edinburgh 1

* Ronald, David, M.Inst.C.E., Chief Engineer, Scottish Board of Health, 125

George Street, Edinburgh

Rosebery, The Right Hon. the Earl of, K.G., K.T., LL.D., D.C.L. , F.R.S.,
Dalmeny Park, Edinburgh

* Ross, Alex. David, M.A., D.Sc., F.R. A.S., Professor of Mathematics and Physics,

University of Western Australia, Perth, Western Australia

* Ross, Edward Burns, M.A. (Edin. and Camb.), Professor of Mathematics in the

Madras Christian College, Madras 500

* Russell, Alexander Durie, B.Sc. , Mathematical Master, Falkirk High School,

14 Heugh Street, Falkirk

* Russell, James, 22 Glenorchy Terrace, Edinburgh

Saleeby, Caleb William, M.D., 10 Campden Mansions, Kensington, London,
W. 8

* Salvesen, The Hon. Lord, Judge of the Court of Session, Dean Park House,

Edinburgh

* Salvesen, Theodore Emile, 37 Inverleith Place, Edinburgh 505

* Sampson, Ralph Allen, M.A., D.Sc., F.R.S., Astronomer Royal for Scotland, j

Professor of Astronomy, University, Edinburgh, Royal Observatory, 4
Edinburgh I

* Samuel, Sir John S., K.B.E., D. L., J.P., F S.A. (Scot.), 13 Park Circus, Glasgow, W.
*Sarolea, Charles, Ph.D. , D.Litt., Professor of French, University of Edinburgh,

21 Royal Terrace, Edinburgh

* Schafer, Sir Edward Albert Sharpey, M.D., LL.D., D.Sc., F.R.S., Professor

of Physiology in the University of Edinburgh

* Scott, Alexander, M.A., D.Sc., Carnegie Scholar, 1912-14; 1851 Exhibition

Scholar, 1914-16; lectured (temp.) on Petrology, Oxford, 1914-15, and at
Glasgow University, 1917-18 ; Physical Chemist in charge of Radiometric
Laboratory, Glasgow University, 1916-18 ; Chief Assistant to Principal,
Pottery Laboratory, Stoke-on-Trent 510

Scott, Alexander, M.A., D.Sc., F.R.S., 34 Upper Hamilton Terrace, London,
N.W.

* Scott, Alexander Ritchie, B.Sc. (Edin.), D.Sc. (Lond.), Principal London County

Council, Beaufoy Institute, Prince’s Road, Yauxhall Street, London, S.E. 11

* Scott, Henry Harold, M.D., M.R.C.P., L.R.C.P. (London), M.R.C.S. (Eng.),

D.P.H. , Bacteriologist and Pathologist to the Government of Hong Kong

* Simpson, George Freeland Barbour, M.D., F.R.C.P.E., F.R.C.S.E., 43 Manor

Place, Edinburgh

* Simpson, James Young, M.A., D.Sc., Professor of Natural Science in the New

College, Edinburgh. 25 Chester Street, Edinburgh 515

Simpson, Sutherland, M. D., D.Sc. (Edin.), Professor of Physiology, Medical
College, Cornell University, Ithaca, N.Y. , U.S.A., 118 Eddy Street, Ithaca,
N.Y., U.S.A.

Service on
Council, etc

1921-

1910-12.

Sec.

1912-18.

V-P

1918-21.

1920-

1912-15,

1919-21.

Y-P

1915-18.

1900-03,

1906-09,

1918-19.

V-P

1913-17.

254

Proceedings of the Royal Society of Edinburgh.

Date of |
Election.

1900
1903

1901
1920

1891

1882

1915

1921

1921

1911

1907

1880

1919

1899

1880

1910

1889

1911

1882

1896

1906

1891

1885
&

1915
1912

1910

1916

1921

1886
1884
1919
1888

1902

1889

!. K.
C.

c.

c.

!. K.

C.

c.

c.

Sinhjee, Sir Bhagvat, G.C.I.E., M.D., LL.D. Edin., H.H. the Thakur Sahib
of Gondal, Gondal, Kathiawar, Bombay, India

* Skinner, Robert Taylor, M. A., J.P., Head Master, Donaldson’s Hospital, Edin-

burgh

* Smart, Edward, B.A., B.Sc., Tillyloss, Tullylumb Terrace, Perth

* Smellie, William Robert, M.A. , B.Sc., D.Sc., Geologist on the Staff of the Anglo-

Persian Oil Company, Mayfield, Mossend, near Glasgow 520

Smith, Alexander, B.Sc., Ph. D. , LL.D., Department of Chemistry, Columbia Uni-
versity, New York, N.Y., U.S.A.

Smith, C. Michie, C.I.E., B.Sc., F.R.A.S., formerly Director of the Kodaikanal and
Madras Observatories, Winsford, Kodaikanal, South India, c/o Messrs H. S.
King & Co., 9 Pall Mall, London, S.W. 1

* Smith, James Lorrain, M.A., M.D., F.R.S., Professor of Pathology, University

of Edinburgh, 9 Carlton Terrace, Edinburgh

* Smith, The Right Hon. James Parker, P.C., M.A. (Camb.), 41 Drumsheugh

Gardens, Edinburgh

* Smith, Norman Kemp, M.A., D.Phil. , Professor of Logic and Metaphysics,

University of Edinburgh 525

* Smith, Stephen, B.Sc., Engineer, 31 Grange Loan, Edinburgh

Smith, William Ramsay, D.Sc., M. D., C.M., Permanent Head of the Health
Department, South Australia, Belair, South Australia
Smith, Sir William (Robert), M.D., D.Sc., LL.D., Principal of The Royal
Institute of Public Health, Em. -Professor of Forensic Medicine and Toxi-
cology in King’s College, University of London, 36 Russell Square, London,
W.C. 1

* Smith, William Wright, M.A. (Edin.), Assistant Keeper, Royal Botanic Garden,

Edinburgh, 6 Lennox Row, Trinity, Edinburgh
Snell, Ernest Hugh, M.D., B.Sc., D.P.H. Camb., Medical Officer of Health,
Coventry 530

Sollas, W. J. , M.A. , D.Sc., LL.D., F.R.S., Fellow of University College,
Oxford, and Professor of Geology and Palamntology in the University of
Oxford

* Somerville, Robert, B.Sc., Science Master, High School, Dunfermline, 31 Cameron

Street, Dunfermline

Somerville, Wm., M.A. , D.Sc., D.Oec., Sibthorpian Professor of Rural Economy
and Fellow of St John’s College in the University of Oxford, 121 Banbury
Road, Oxford

* Sommerville, Duncan M‘Laren Young, M.A., D.Sc., Professor of Pure and

Applied Mathematics, Victoria College, Wellington, New Zealand
Sorley, James, 73 Onslow Square, London, S.W. 7 535

Spence, Frank, M.A., B.Sc., 25 Craiglea Drive, Edinburgh
Squance, Major Thomas Coke, M.D., M.S., F.R.M.S., F.S.A.Scot., Physician and
Pathologist in the Sunderland Infirmary, President. Sunderland Antiquarian
Society, Sunderland Naturalists’ Association, The Cottage, Newbiggin,
Aysgarth, S.O.

Stanfield, Richard, Professor of Mechanics and Engineering in the Heriot-Watt
College, Edinburgh

* Steggall, John Edward Aloysius, M.A., Professor of Mathematics at University

College, Dundee (St Andrews University), Woodend, Perth Road,
Dundee

t Stephenson, John, M.B., D.Sc. (Lond.), Lt.-Col. I.M.S., Zoological Depart-
ment, University, Edinburgh 540

* Stephenson, Thomas, F.C.S. , Editor of the Prescribes, Examiner to the Pharma-

ceutical Society, 6 South Charlotte Street, Edinburgh
*Steuart, D. R., F. I.C., Chemist to the Broxburn Oil Company, 20 Hillview,
Blackball, Midlothian »

* Stewart, Ian Struthers, M.D. (Edin.), Nordrach-on-Dee, Banchory
Stevenson, Charles A., B.Sc., M.Inst.C.E., 28 Douglas Crescent, Edinburgh
Stevenson, David Alan, B.Sc., M.Inst.C.E., 84 George Street, Edinburgh 545

* Stevenson, David Alan, B.Sc., A. M.Inst.C.E., 28 Douglas Crescent, Edinburgh
Stewart, Charles Hunter, D.Sc., M.B., C.M., Professor of Public Health in the

University of Edinburgh, Usher Institute of Public Health, Warrender
Park Road, Edinburgh

* Stockdale, Herbert Fitton, LL. D. , Director of the Royal Technical College, Glasgow,

Clairinch, Upper Helensburgh, Dumbartonshire
Stockman, Ralph, M. D. , F. R.C. P. E. , F. F. P S. G. , Professor of Materia Medica and
Therapeutics in the U niversity of Glasgow

Service tm
Council, etc.

1918-21.

1903-05.

Date of

Election.

1906

1907

1903

1905

1912

1885

1917

1904

1898

1895

1890

1870

1899

1917

1892

1885

1917

1905

1887

1896

1903

1906

1887

1906

1880

1899

1912

1870

1882

1876

1917

1920

1917

1914

1915

phabetical List of the Ordinary Fellows of the Society.

Story, Fraser, formerly Professor of Forestry, University College, Bangor, North
Wales. 4k Artillery Mansions, Victoria Street, London, S.W. 1 550

* Strong, John, C.B.E., M.A., LL.D., Professor of Education in the University of

Sutherland, David W., M.D., M.R.C.P., C.I.E., Lt.-Col. I.M.S., Principal and
1 ’rofessor of Medicine, Medical College, Lahore, India
Swithinbank, Commander Harold William, Crag Head, Bournemouth, Hants

* Syme, William Smith, M.D. (Edin. ), 11 Lynedoch Crescent, Glasgow
Symington, Johnson, M.D. , LL.D., F.R.C.S., F.R.S., formerly Professor of

Anatomy in the Queen’s University, Belfast. Towercliffe Private Hotel,
West Cliff, Bournemouth 555

*Tait, John, D.Sc., M.D. , Professor of Physiology, M'Gill University, Montreal,
Canada

* Tait, John W. , B.Sc., Rector of Leith Academy, 18 Netherby Road, Leith

Tait, William Archer, D.Sc., M.Inst.C.E. (Vice-President), 72a George Street, J
Edinburgh (Society’s Representative on George Heriot’s Trust) J

fTalmage, James Edward, D.Sc., Ph.D., F.R.M.S., F.G.S., formerly Professor of
Geology, University of Utah, 47 East S. Temple Street, Salt Lake City,
Utah, U.S.A.

Tanakadate, Aikitu, Professor of Natural Philosophy in the Imperial University
of Japan, Tokyo, Japan 560

Tatlock, Robert R., F.C.S., City Analyst’s Office, 156 Bath Street, Glasgow

* Taylor, James, M. A. , Mathematical Master in the Edinburgh Academy

* Taylor, William White, M.A., D.Sc., Lecturer on Chemical Physiology,

University, Edinburgh, Park Villa, Liberton, Edinburgh
Thackwell, J. B., M.B., C.M., D.P.H., Carlton House, 1 Prince of Wales Road,
Battersea Park, London, S.W.

Thompson, D’Arcy W., C.B., D.Litt., F.R.S., Professor of Natural History, J
University, St Andrews, 44 South Street, St Andrews 565 j

* Thompson, John M'Lean, M.A., D.Sc., F.L.S., Professor of Botany, University

of Liverpool

* Thoms, Alexander, 7 Playfair Terrace, St Andrews

Thomson, Andrew, M.A., D.Sc., F.I.C., 145 Bruntsfield Place, Edinburgh
Thomson, George Ritchie, C.M.G., M.B., C.M., Professor of Surgery, University
College, Johannesburg, Transvaal

Thomson, GeorgeS., F.C.S., Ferma Albion, Marculesci, Roumania 570

* Thomson, Gilbert, M.Inst.C.E., 164 Bath Street, Glasgow

Thomson, J. Arthur, M.A., LL.D., Regius Professor of Natural History in the/
University of Aberdeen \

Thomson, James Stuart, M.Sc. , Ph.D., Zoological Department, University,
Manchester

Thomson, John Millar, LL.D., F.R.S. , Em. -Professor of Chemistry in King’s
College, London, 55 Bedford Gardens, Kensington, London, W. 8

* Thomson, R. Tatlock, F.C.S., 156 Bath Street, Glasgow 575

Thomson, Robert Black, M.B. Edin,, Professor of Anatomy, The University,

Cape Town

Thomson, Spencer C., Actuary, 10 Eglinton Crescent, Edinburgh
Thomson, Win., M. A. , B.Sc., LL.D., Registrar, University of South Africa,
Somerset House, Vermeulen Street, Pretoria
Thomson, William, Royal Institution, Manchester

* Thorn ey croft, Wallace, J. P., Coal and Iron Master, Plean House, Plean,

Stirling ' 580

* Todd, John Barber, B.Sc., A.M. I.Mech.E., Lecturer in Engineering in the

University of Edinburgh. 39 Warrender Park Terrace, Edinburgh

* Tovey, Donald Francis, B. A., Professor of Music, University, Edinburgh, 2 St

Margaret’s Road, Edinburgh

f Tredgold, Alfred Frank, M.D. (Durham), M.R.C.P., Lecturer on Mental Deficiency
at London University, and Bethlem Royal Hospital, “ St Martins,” Guildford

* Trotter, George Clark, M.D. , Ch.B. Edin. , D.P.H. (Aberdeen), Medical Officer of

Health, Metropolitan Borough, Islington. Public Health Department, 20
Compton Terrace, Upper Street, Islington, London, N. 1

255

Service on
Council, etc.

1892-93.

1914-17,

1918-21.

V-P

1921-

1892-95,

1896-99,

1907-10,

1912-15.

V-P

1916-19.

1906-08,

1920-

256

Date of

Election.

1905

1906

1895

1898

1918

1910

1891

1902

1886

1898

1891

1920

1901

1911

1900

1907

1911

1911

1896

1907

1903

1904

1896

1916

1896

1911

1912

1918

1918

1879

1908

1910

1900

1911

1902

1895

Proceedings of the Royal Society of Edinburgh.

* Turner, Arthur Logan, M. D., F.R. C.S.E., 27 Walker Street, Edinburgh 585

* Turner, Dawson F. D. , B.A. , M.D., F.R.C.P.E., M.R.C.P., Lecturer on Medical

Physics, Surgeons’ Hall, Physician in charge of Kadium Treatment, Royal
Infirmary, Edinburgh, 37 George Square, Edinburgh
Turton, Albert H., M.I.M.M., 233 George Road, Erdington, Birmingham

* Tweed ie, Charles, M.A. , B. Sc., formerly Lecturer on Mathematics in the Uni-

versity of Edinburgh. Marine View, Belhaven, Dunbar

* Tyrrell, G. W., A.R.C.Sc., F.G.S., Chief Assistant and Lecturer in Petrology,

Geological Department, University, Glasgow
Vincent, Swale, M.D. Lond. , D.Sc. Edin., etc. , Professor of Physiology in the
University of London, Physiological Laboratory, Middlesex Hospital Medical
School, Berners Street, London, W. 1 590

Walker, Sir James, Kt., D.Sc., Ph.D., LL.D., F.R.S., Professor of Chemistry!
in the University of Edinburgh, 5 Wester Coates Read, Edinburgh |

* Wallace, Alexander G., M.A., 56 Fonthill Road, Aberdeen

Wallace, R. , M. A. , F. L. S. , Professor of Agriculture and Rural Economy in the Uni-
versity of Edinburgh

Wallace, Wm., M. A. , Belvedere, Alberta, Canada

Walmsley, R. Mullineux, D.Sc., Principal of the Northampton Institute, Clerken-
well, London 595

* Walmsley, Thomas, M.D. (Glasgow), Professor of Anatomy in the University of

Belfast, 59 South Street, Greenock

* Waterston, David, M.A., M. D., F.R. C.S.E., Professor of Anatomy, University,

St Andrews

* Watson, James A. S., B.Sc., etc., Lecturer in Agriculture, University of Edin-

burgh, 30 Mayfield Terrace, Edinburgh

* Watson, Thomas P., M.A.., B.Sc., Principal, Keighley Institute, Keighley

* Watt, Andrew, M.A. , 10 Rothesay Place. 6 Woodburn Terrace, Edinburgh 600
t Watt, James, W.S . F. F. A. , Craiglockhart House, Slateford, Edinburgh

* Watt, Rev. Lauchlan Maclean, D.D. , Minister of St Stephen’s Parish, 7 Royal

Circus, Edinburgh

Webster, John Clarence, B.A., M.D., F.R.C.P.E., Professor of Obstetrics and
Gy n {ecology, Rush Medical College, Shediac, N.B. , Canada

* Wedderburn, Ernest Maclagan, M.A., LL.B., W.S., D.Sc., 6 Succoth Gardens,/

Edinburgh \

* Wedderburn, J. H. Maclagan, M.A., D.Sc., P.O. Box 53, Princeton, N.J.,

U.S.A. 605

Wedderspoon, William Gibson, M.A., LL.D., Indian Educational Service, Senior
Inspector of Schools, Burma, The Education Office, Rangoon, Burma
Wenley, Robert Mark, M.A., D.Sc., D.Phil., Litt.D., LL.D., D.C.L., Professor
of Philosophy in the University of Michigan, Ann Arbor, U.S.A.

* White, J. Martin, Esq. , of Balruddery, Balruddery, near Dundee

White, Philip J., M. B. , Professor of Zoology in University College, Bangor, North
Wales

* Whittaker, Charles Richard, F.R.C.S. (Edin.), F.S.A. (Scot.), Lynwood, Hatton

Place, Edinburgh 610

* Whittaker, Edmund Taylor, Sc. D. , F.R.S., Professor of Mathematics in thef

University of Edinburgh (Secretary), 35 George Square, Edinburgh |

* Whyte, Rev. Charles, M.A., LL.D., F.R.A.S., U.F. Church Manse, Kingswells,

Aberdeen

* Wight, John Thomas, General Manager, Hydraulic Gears, Ltd., Beavor Lane,

Hammersmith, London, W. 6 ; Dai’tbeigh, Ascot, Berks.

Will, John Charles Ogilvie, of Newton of Pitfodels, M.D., 17 Bon-Accord Square,
Aberdeen

* Williamson, Henry Charles, M.A. , D.Sc., Naturalist to the Fishery Board for

Scotland, Marine Laboratory, Aberdeen 615

* Williamson, William, F. L.S. , 79 Morningside Drive, Edinburgh
Wilson, Alfred C. , F.C.S., Yoewood Croft, Stockton-on-Tees

* Wilson, Andrew, M.Inst.C.E., 66 Netherby Road, Trinity, Edinburgh

* Wilson, Charles T. R., M.A., F. R.S., 14 Cranmer Road, Cambridge, Sidney

Sussex College, Cambridge

Wilson -Barker, Sir David, Kt., R.N.R., F.R.G.S., late Captain- Superintendent
Thames Nautical Training College, H.M.S. “Worcester,” off Greenhithe,
Kent, Flimwell Grange, near Hawkhurst, Kent 620

Service on
Council, etc.

1903-05,

1910-13.

Y-P

1916-19.

1916-19.

1912-14.

1913-16.

1921-

1912-15.

c .
1916-

Date of
Election.
1882
1920

1908

1911

1890

1896

1882

1892

1896

1904

Alphabetical List of the Ordinary Fellows of the Society.

c.

Wilson, George, M. A., M.B., LL. D.

* Wilson, Malcolm, D.Sc. (London), Lecturer in Mycology and Bacteriology in the

University of Edinburgh. Royal Botanic Garden, Edinburgh

* Wood, Thomas, M.D., Eastwood, 182 Ferry Road, Bonnington, Leith

* Wrigley, Ruric Whitehead, B.A. (Cantab.), Assistant Astronomer, Royal Observa-

tory, Edinburgh

Wright, Johnstone Christie, Conservative Club, Edinburgh 625

Wright, Sir Robert Patrick, LL.D., formerly Chairman of the Board of Agri-
culture for Scotland. Kin garth, Colin ton, Midlothian
Young, Frank W. , F.C.S., Scottish Education Department (Ex-Service Student’s
Branch), 3 Parliament Square, Edinburgh
Young, George, Ph.D., “Bradda,” Church Crescent, Church End, Finchley,
London, N.

Young, James Buchanan, M.B., D.Sc., Dalveen, Braeside, Liberton
Young, R. B., M.A., D.Sc., F.G.S. , Professor of Geology and Mineralogy
in the South African School of Mines and Technology, Johannesburg,
Transvaal 630

257

Service on
Council, etc.

VOL. XLI

17

LIST OF HONORARY FELLOWS OF THE SOCIETY

At January 31, 1922.

HIS MOST EXCELLENT MAJESTY THE KING.

HIS ROYAL HIGHNESS THE PRINCE OF WALES.

Foreigners (limited to thirty-six by Law I).

Elected

1916 Charles Barrois, Professor of Geology and Mineralogy, 'Universite, Lille, France: 37 rue
Pascal, Lille.

1905 Waldemar Christofer Brogger, Professor of Mineralogy and Geology, K. Frederiks Universitet,
Christiania, Norway.

1916 Douglas Houghton Campbell, Professor of Botany, Leland Stanford Junior University,
California, U.S.A.

1920 William Wallace Campbell, Director of the Lick Observatory, Mt. Hamilton, California,

U.S.A.

1921 Reginald Aldworth Daly, Professor of Geology, Harvard University, Cambridge, Mass.

1910 Hugo de Vries, Professor of Plant Anatomy and Physiology, Lunteren, Holland.

1916 Marcel Eugene Emile Gley, Professor of Biology, College de France, Paris, Membre de
l’Academie de Medecine, Paris : 14, rue Monsieur le Prince, Paris.

1910 Karl F. von Goebel, Professor of Botany, Universitat, Miinchen, Germany.

1916 Camillo Golgi, Professor of Pathology, Universita, Pavia, Italy.

1916 Gio. Battista Grassi, Professor of Comparative Anatomy, Regia Uhiversita, Roma, Italy :
Via Agostino Depretis N. 91, Rome.

1905 Paul Heinrich von Groth, Professor of Mineralogy, Universitat, Miinchen, Germany.

1313 George Ellery Hale, Director of Mount Wilson Solar Observatory (Carnegie Institution of
Washington), Pasadena, California, U.S.A.

1921 Johan Hjort, Director of Norwegian Fisheries, Bergen.

1910 James Cornelius Kapteyn, Professor of Astronomy, Universiteit, Groningen, Holland.

1921 Charles Louis Alphonse Laveran, Nobel Laureate, Medicine, 1907. Rue du Montparnasse
25, Paris.

1920 Hendrik Antoon Lorentz, Nobel Laureate, Physics, 1902, Professor of Physics, Leiden

University.

1910 Albert Abraham Michelson, Nobel Laureate, Physics, 1907, Professor of Physics, University,
Chicago, U.S.A.

1897 Fridtjof Nansen, Professor of Oceanography, K. Frederiks Universitet, Christiania, Norway.

1921 Heike Kamerlingh Onnes, Nobel Laureate, Physics, 1913, Universiteit, Leiden, Holland.
1908 Henry Fairfield Osborn, Professor of Zoology, Columbia University and American Museum

of Natural History, New York, N.Y. , U.S.A.

1908 Ivan Petrovitch Pavlov, Emeritus Professor of Physiology, Kais.Inst. Exper. Med., Petrograd :
Wedenskaja Strasse 4, Petrograd, Russia.

1920 Ch. Emile Picard, Perpetual Secretary, Academy of Sciences, Paris.

1921 Salvatore Pincherle, Professor of Mathematics in the University of Bologna.

1889 Georg Hermann Quincke, Emeritus Professor of Physics, Bergstrasse 41, Heidelberg, Germany.
1913 Santiago Ramon y Cajal, Nobel Laureate, Medicine, 1906, Professor of Histology and
Pathological Anatomy, Universidad, Madrid, Spain.

1920 Charles Richet, Professor of Physiology, Faculty of Medicine, Paris.

1920 Georg Ossian Sars, formerly Professor of Zoology, Christiania, and Director of Norwegian
Fisheries.

1913 Vito Volterra, Professor of Mathematical Physics, Regia Universita, Rome, Italy.

1916 Eugenius Warming, Emeritus Professor of Botany at the University of Copenhagen and
Director of the Botanical Garden : Bjerregaardsvej 5, Copenhagen, Valby.

Total, 29.

British Subjects (limited to twenty by Law I).

1916 Sir Francis Darwin, Kt. , D.Sc., M.B., F.R.S., Hon. Fellow, Christ’s College, Cambridge, 10
Madingley Road, Cambridge,.

1900 Sir David Ferrier, Kt. , M.A., M.D. , LL. D., F. R.S., Emer. -Professor of Neuro-Pathology,
King’s College, London, 34 Cavendish Square, London, W.

258

List of Honorary Fellows, etc.

259

Elected

1900 Andrew Russell Forsyth, M.A., Sc.D., LL.D., Math.D., F.R.S,, Chief Professor of
Mathematics in the Imperial College of Science and Technology, London, formerly
Sadleirian Professor of Pure Mathematics in the University of Cambridge, Imperial
College of Science and Technology, London, S. W.

1910 Sir James George Frazer, D. C.L., LL.D., Litt. D., F. R. S., Fellow of Trinity College, Cam-
bridge, 1 Brick Court, London, E.C. 4.

1916 James Whitbread Lee Glaisher, M.A., Sc.D., F.R.S., Fellow of Trinity College, Cambridge.

1908 Sir Alexander B. W. Kennedy, Kt., LL.D., F.R.S., Past Pres. Inst. C.E., A7, Albany,
Piccadilly, London, W.

1913 Horace Lamb, M.A., Sc.D., D.Sc., LL.D., F.R.S., lately Professor of Mathematics in the
University of Manchester. 65 Grange Road, Cambridge.

1916 John Newport Langley, Sc.D., LL.D., F.R.S., Fellow of Trinity College, Professor of
Physiology in the University of Cambridge, Hedgerley Lodge, Madingley Road,
Cambridge.

1908 Sir Edwin Ray Lankester, K.C.B , D.Sc., LL.D., F.R.S., 44 Oakley Street, Chelsea,
London, S.W. 3.

1910 Sir Joseph Larmor, Kt., M.A., D.Sc., LL.D., D.C.L., F.R.S., M.P. University of Cambridge
since 1911, Lucasian Professor of Mathematics in the University of Cambridge, St John’s
College, Cambridge.

1900 Archibald Liversidge, M.A., LL.D., F.R.S. , Emer.-Professor of Chemistry in the University
of Sydney, Fieldhead, Coombe Warren, Kingston, Surrey.

1921 William Henry Perkin, M.A., Ph.D., Sc.D., LL.D., F.R.S., Waynflete Professor of Chemistry
in the University of Oxford.

1921 Sir Ronald Ross, K.C.B., K.C.M.G., F.R.S., Consultant in Malaria, Ministry of Pensions,
London, 36 Harley House, Regent’s Park, N. W. 1.

1921 Sir Ernest Rutherford, Kt., M.A., D.Sc., B.A. , LL.D., F.R.S., Nobel Laureate, Chemistry,
1908, Cavendish Professor of Experimental Physics in the University of Cambridge.

1916 Sir Arthur Schuster, Kt., Ph.D., D.Sc., LL.D., D. es Sc. Geneva, Foreign Secretary of the
Royal Society, Honorary Professor of Physics in the University of Manchester, Yeldall,
Twyford, Berks.

1908 Sir Charles Scott Sherrington, G.B.E., M.A., M.D.. LL.D., P.R.S., Waynfle'te Professor of
Physiology in the University of Oxford, Physiological Laboratory, Oxford.

1921 Sir Jethro J. H. Teall, Kt., M.A., Sc.D,, LL.D., F.G.S., F.R.S. , lately Director of the
Geological Survey of Great Britain and of the Museum of Practical Geology.

1913 Sir William Turner Thiselton-Dyer, K.C.M.G., C.I.E., M.A., LL.D., F.R.S., formerly
Director of the Royal Botanic Gardens, Kew : The Ferns, Witcombe, Gloucester.

1905 Sir Joseph John Thomson, Kt., O.M., D.Sc., LL.D., Past Pres.R.S., Nobel Laureate,
Physics, 1906, lately Cavendish Professor of Experimental Physics, University of
Cambridge, Trinity College, Cambridge.

1900 Sir Thomas Edward Thorpe, Kt., C.B., D.Sc., LL.D., F.R.S., formerly Principal of the
Government Laboratories, Emeritus- Professor of Chemistry, Imperial College of Science
and Technology, South Kensington, London, S.W. Whinfield, Salcombe, South Devon.

Total, 20.

CHANGES IN FELLOWSHIP DURING SESSION 1920-1921.

ORDINARY FELLOWS OF THE SOCIETY ELECTED.

NELSON ANNANDALE.
WILLIAM ARTHUR.

BEVAN BRAITHWAITE BAKER.
ARCHIBALD BARR.

JOHN BARTHOLOMEW.
ALEXANDER BRUCE.

ANDREW CAMPBELL.

RASIK LAL DATTA.

JOHN DOUCALL.

CHARLES YICKERY DRYSDALE.
GEORGE TOPHAM FORREST.
WALCOT GIBSON.

JOHN WM. HESLOP HARRISON.

JAMES ALEX. GEORGE LAMB.
Rev. ALBERT ERNEST LAURIE.
NEIL M ‘ARTHUR.

DOUGALD BLACK MeQUISTAN.
THOMAS MURRAY MACROBERT.
JOHN MAVHAN.

JOHN MATHIESON.

Sir GEO. HERBERT POLLARD.
EDWARD BURNS ROSS.'

Rt. Hon JAMES PARKER SMITH.
NORMAN KEMP SMITH.

IAN STRUTHERS STEWART.

HONORARY FELLOWS ELECTED.

BRITISH.

WILLIAM HENRY PERKIN.
Sir RONALD ROSS.

Sir ERNEST RUTHERFORD.
Sir JETHRO J. H. TEALL.

4 th July 1921.

FOREIGN.

REGINALD ALDWORTH DALY, Cam-
bridge, Mass,

JOHAN HJORT, Bergen.

CHARLES LOUIS ALPHONSE LAVERAN,
Paris.

HEIKE KAMERLINGH ONNES, Leiden.
SALVATORE PINCHERLE, Bologna.

ORDINARY FELLOWS DECEASED.

ROBERT GERYASE ALFORD.

Sir R. ROWAND ANDERSON.
HENRY BARNES.

Sir J. H. MEIRING BECK (died 1919).
ADOLPHUS EDWARD BRIDGER.
DAVID BROWN.

DAVID RAINY BROWN.

WM. ALLAN CARTER.

WM. JOHN DUNDAS.

T. LINDSAY GALLOWAY.

T. E. GATEHOUSE.

GEO. RITCHIE GILRUTH.
T. ARTHUR HELME.
JAMES HUNTER.

Sir T. CARLAW7 MARTIN.
Rev. R. S. MYLNE.

JAMES OLIPHANT.

E. W. PREVOST.

D. LLOYD ROBERTS.
THOMAS BOND SPRAGUE.
ROBERT WALKER.

G. A. WOODS.

HONORARY FELLOWS DECEASED.

JULIUS VON HANN. i CARL MENGER.

GABRIEL LIPPMAN. | ALFRED G. NATHORST.

ORDINARY FELLOWS RESIGNED.

Sir DUNCAN A. JOHNSTON. I Sir GEO. ADAM SMITH.

G. C. PRINGLE. I

260

Additions to Library by Gift or Purchase.

261

List of Additions to Library by Gift or Purchase.

Bergen’s Museum, 1825-1900. En Historisk Fremmstilling a£ Dr J.
Brunchorst. 8vo. Bergen, 1900. (Pr esented by Mr Wm. Williamson.)

Bhattacharyya, D. Vector Calculus. 8vo. Calcutta, 1920. ( Presented

by Calcutta University.)

Bibliographie Scientifique Franyaise. (Presented by Ministere de V Instruc-
tion Publique.)

Bright, Sir Charles. Inter-Imperial Communication through Cable, Wire-
less, and Air. 8vo. London, 1919. ( Presented by the Author.)

British (Terra Nova) Antarctic Expedition, 1910-1913: Meteorology.
Vols. I and II. 4to. 1919. ( Presented .)

Terrestrial Magnetism. By Charles Chree. 4to. London, 1921.

Calcutta, University of: Journal of the Department of Letters. Vol. I-
8vo. Calcutta, 1920. (Univ. Studies Series.)

Campbell, Andrew. Petroleum Refining. 8vo. London, 1918. ( Presented

by the Author.)

Catalogue of Scientific Papers. (Royal Society of London.) Fourth
Series, 1884-1900. Vol. XVII (Marc-P). 4to. Cambridge, 1921.
(Purchased.)

Cavendish, Henry, The Scientific Papers of.

Vol. I. The Electrical Researches. Edited by James Clerk Maxwell,
Revised by Sir Joseph Larmor. 4to. Cambridge, 1921.

Vol. II. Chemical and Dynamical. Edited by Sir Edward Thorpe.
4 to. Cambridge, 1921. (Purchased.)

Constantinesco, George. Theory of Wave Transmission. (Theory of
Sonics.) A Treatise on Transmission of Power by Vibrations. Vol.
I. 8vo. London, 1920. (Presented by Walter Haddon.)

Cotton Research Board (Ministry of Agriculture, Egypt). Annual Report,
1920. La. 8vo. Cairo, 1921. (Presented.)

Cushman, Allerton S. Chemistry and Civilisation. 8vo. Boston, 1921.
(Presented by Wagner Free Institute.)

Granton, Edinburgh, Marine Station for Scientific Research. 8vo. Edin-
burgh, 1884.

Scottish Marine Station for Scientific Research : its Work and

Prospects. 8vo. Edinburgh, 1885. (Presented by Mr Wm,
Williamson.)

Gribble, J. D. B. (see Hehir, Patrick).

Gude, G. K. The Fauna of British India: Mollusca. Vol. Ill: Land
Operculates. 8vo. London, 1921. (Presented by the Under Secretary
of State for India.)

Hehir, Patrick. Prophylaxis of Malaria in India. 8vo. Allahabad, 1910.

Prevention of Disease and Inefficiency, with Special Reference to

Indian Frontier Warfare. 2nd edition. 8vo, Allahabad, 1911.

262

Proceedings of the Royal Society of Edinburgh. [Sess.

Hehir, Patrick. The March : Its Mechanism, Effects, and Hygiene. 8vo.
Calcutta, 1912.

Hygiene and Diseases of India. A Popular Handbook. 3rd

edition. 8vo. Madras, 1913. ( Presented by Sir Patrick Hehir.)

Hehir, Patrick, and J. D. B. Gribble. Outlines of Medical Jurisprudence
for India. 5th edition. 8vo. Madras, 1908. ( Presented by Sir

Patrick Hehir.)

Herdman, W. A. Reports of the Grain Pests (War) Committee. No. 10.
(R.S.L.) 8 vo. London, 1921. ( Presented by the Author.)

Horsburgh, E. M. Calculating Machines. (Inst. Engineers and Ship-
builders in Scotland.) 8vo. Glasgow, 1920.

Howard, William Trevis, Jr. The Natural History of Typhoid Fever in
Baltimore, 1851-1919. (Reprinted from the Johns Hopkins Hospital
Bulletin, Yol. XXXI, Nos. 354-355, 1920.) 8vo. Baltimore, 1920.
(. Presented by Raymond Pearl.)

Huygens, Christiaan. (Euvres Completes publiees par la Societe Holland-
aise des Sciences. Vol. XIII, fasc. 1 and 2, and Vol. XIY. 4to. La
Haye, 1916 and 1920. (Presented by the Societe Hollandaise des
Sciences de Harlem.)

Kanthack, R. Tables of Refractive Indices. Yol. I. — Essential Oils. Yol.
II. — Oils, Fats, and Waxes. Edited by J. N. Goldsmith. 8vo.
London, 1918 and 1921. ( Presented by Adam Hilger, Ltd.)

Kaploun, Albert. Psychologie Generale tiree de l’Etude du Reve. 8vo.
Lausanne, 1919.

Kidd, Walter. Initiative in Evolution. 8vo. London, 1920. ( Presented

by the Author.)

Lancashire and Cheshire Fauna Committee. Sixth Annual Report and
Report of the Recorder for 1919. 8vo. Manchester, 1920.

Lister, Lord, Photograph of. ( Presented by Lady Lister and Sir R. J.
Godlee , Bt.)

Lowell, J. Reed. The Mathematics of Biometry. (Reprinted from the
American Mathematical Monthly, Yol. XXYII, November 1920.)
8 vo. Baltimore, 1920. ( Presented by Raymond Pearl.)

Macgillivray, Angus. A Bacteriological and Clinical Study of the External
Diseases of the Eye. 8vo. London, 1916. (Presented by the Author.)

Manchester University Publications.

Historical Series—

Tout, T. F., and Tait, James. Historical Essays. 8vo. 1907.

Petit-Dutaillis, Charles. Studies and Notes Supplementary to Stubb’s
Constitutional History. Yols. I and II. 8vo. 1911.

Clemesha, H. W. A History of Preston in Amounderness. 8vo. 1912.
Holden, Joshua. A Short History of Todmorden. 8vo. 1912.

Gill, Conrad. The Naval Mutinies of 1797. 8vo. 1913.

Tait, James. Chronica Johannis de Reading et Anonymi Cantu-
ariensis, 1346-1367. 8vo. 1914.

263

1920-21.] Additions to Library by Gift or Purchase.

Manchester University Publications — Historical Series — continued.

Tout, T. F. The Place of the Reign of Edward II in English History.
8vo. 1914.

Deansley, Margaret. The Incendium Amoris of Richard Rolle of
Hampole. 8vo. 1915.

Pirenne, Henri. Belgian Democracy : its Early History. Translated
by J. V. Saunders. 8vo. 1915.

Tout, T. F. Germany in the Nineteenth Century. 8vo. 1915.

Muir, Ramsay. The Making of British India, 1756-1858. 8vo. 1917.

Little, A. G. Studies in English Franciscan History. 8vo. 1917.

Hovell, the late Mark. The Chartist Movement. Edited and com-
pleted, with a Memoir, by Prof. T. F. Tout. 8vo. 1918.

Unwin, George. Finance and Trade under Edward III. 8vo. 1918.

M‘Lauchlan, H. The Methodist Unitarian Movement. 8vo. 1919.

Tout, T. F. Chapters in the Administrative History of Mediaeval
England. Two vols. 8vo. 1920.

Daniels, George W. The Early English Cotton Industry. 8vo. 1920.

Lecture Series —

Neville, Ralph. Garden Cities. (Warburton Lecture.) 8vo. 1904.

Thomson, J. J. On the Light Thrown by Recent Investigations on
Electricity on the Relation between Matter and Ether. (Adamson
Lecture.) 8vo. 1908.

Thorburn, William. The Evolution of Surgery. 8vo. 1910.

Ward, A. W. Leibniz as a Politician. (Adamson Lecture.)

Waterhouse, Paul, and Raymond Unwin. Old Towns and New
Needs : also the Town Extension Plan. (Warburton Lectures.)
4to. 1912,

Wilkinson, Henry S. Learners as Leaders. 8vo. 1918.

Hart, Bernard. The Modern Treatment of Mental and Nervous Dis-
orders. 8vo. 1918.

Celtic Series —

Lewis, Timothy. A Glossary of Mediaeval Welsh Law. 8vo. 1913.

Classical Series —

Norwood, Gilbert. The Riddle of the Bacchae. 8vo. 1908.

Economic Series —

Dehn, R. M. R. The German Cotton Industry. (A Report.) 8vo.
1913.

Ethnological Series —

Jackson, J. Wilfrid. Shells as Evidence of the Migrations of Early
Culture. 8vo. 1917.

Miscellaneous {Botanical Section ) —

Weiss, F. E., A. D. Imms, and Wilfrid Robinson. Plants in Health
and Disease. 8vo. 1916.

264 Proceedings of the Royal Society of Edinburgh.

Manchester University Publications — Miscellaneous — continued.
Calendar, 1920-1921. 8vo. 1920.

Journal of the Manchester Egyptian and Oriental Society, 1911 ;
1912-13; 1913-14; 1914-15; 1915-16; 1916-17; 1917-18; 1918
-19; 1920 (No. 9).

Maxwell, J. Clerk. Matter and Motion. Reprinted : with Notes and
Appendices by Sir Joseph Larmor. (Society for Promoting Christian
Knowledge.) 8vo. London.

Mindeskrift i Anledning af 100-aaret for J. Steenstrups Fodsel. Two
vols. 4to. Kobenhavn, 1914. (From the Royal Danish Society of
Sciences.)

Munro, Robert, Autobiographic Sketch of. 8vo. Glasgow, 1921. ( Pre-

sented by Mr Hugh Munro and the Misses Munro.)

Natal (Province) Descriptive Guide and Official Handbook. La. 8vo.
Durban, Natal, 1911. ( Presented by High Commissioner , Union of
South Africa.)

Norman Lockyer Observatory. Handbook to the Norman Lockyer Ob-
servatory. Compiled by Major William J. S. Lockyer. Sm. 8vo.
London, 1921.

Director’s Annual Report, 1921. 4to. London, 1921. ( Presented .)

Pearl, Raymond. Some Landmarks in the History of Vital Statistics.
(Reprinted from Quarterly Publications of the American Statistical
Association, June 1920.) 8vo. Baltimore, 1920. (. Presented by the

Author.)

The Relative Influence of the Constitutional Factor in the Etiology

of Tuberculosis. (Reprinted from the American Review of Tubercu-
losis, Vol. IV, No. 9, November 1920.) 8vo. Baltimore, 1920. ( Pre-

sented by the Author.)

Quincke, G. Spaltung und Erwarmung von Metalldrahten und isolierenden
Staben durch elektrische Longitudinalschwingungen. (Sitz. Heidel-
berger Akad. Wissenschaftlichen, Math.-Nat. Kl.) 8vo. Heidelberg,

1920.

Radium (a Monthly Magazine). Edited by Charles H. Viol, Ph.D., and
William H. Cameron, M.D. Vol. XVII- . 8vo. Pittsburgh, Pa., 1921.

(. Presented by Watson & Sons (Electro- Medical) Ltd., King sway , W.C. 2.)

Rayleigh, Baron. Scientific Papers. Vol. VI. 1911-1919. 4to. Cam-
bridge, 1920. (Purchased.)

Report of the Third Entomological Meeting (Pusa). In three vols. Edited
by T. Bainbrigge Fletcher. La. 8vo. Calcutta, 1920.

Salter, M. de Carle S. The Rainfall of the British Isles. 8vo. London,

1921. (Presented by the University of London Press.)

Spiller, G. A New System of Scientific Procedure. 8vo. London, 1921.

(Presented.)

Sweden : Historical and Statistical Handbook. Edited by J. Guinchard.
Two vols. 2nd edition. English issue. 8vo. Stockholm, 1914.
(Presented by the Royal University of Upsala.)

LAWS OF THE SOCIETY.

Adopted July 3, 1916 ; amended December 18, 1916.

(Laws VIII, IX, and XIII amended May 3, 1920. Law VI amended February 7, 1921.)

I.

THE ROYAL SOCIETY OF EDINBURGH, which was instituted by Royal
Charter in 1783 for the promotion of Science and Literature, shall consist of
Ordinary Fellows (hereinafter to be termed Fellows) and Honorary Fellows.
The number of Honorary Fellows shall not exceed fifty-six, of whom not more
than twenty may be British subjects, and not more than thirty-six subjects of
Foreign States.

Fellows only shall be eligible to hold office or to vote at any Meeting of the
Society.

ELECTION OF FELLOWS.

II.

Each Candidate for admission as a Fellow shall be proposed by at least four
Fellows, two of whom must certify from personal knowledge. The Official
Certificate shall specify the name, rank, profession, place of residence, and the
qualifications of the Candidate. The Certificate shall be delivered to the General
Secretary before the 30th of November, and, subject to the approval of the
Council, shall be exhibited in the Society’s House during the month of January
following. All Certificates so exhibited shall be considered by the Council at its
first meeting in February, and a list of the Candidates approved by the Council
for election shall be issued to the Fellows not later than the 21st of February.

III.

The election of Fellows shall be by Ballot, and shall take place at the first
Ordinary Meeting in March. Only Candidates approved by the Council shall be
eligible for election. A Candidate shall be held not elected, unless he is supported
by a majority of two-thirds of the Fellows present and voting.

IY.

On the day of election of Fellows two scrutineers, nominated by the President,
shall examine the votes and hand their report to the President, who shall declare
the result.

265

266 Proceedings of the Royal Society of Edinburgh.

Y.

Each Fellow, after his election, is expected to attend an Ordinary Meeting,
and sign the Roll of Fellows, he having first made the payments required by
Law VI. He shall be introduced to the President, who shall address him in
these words :

In the name and by the authority of THE ROYAL SOCIETY OF
EDINBURGH , I admit you a Fellow thereof.

PAYMENTS BY FELLOWS.

VI.

Each Fellow shall, before he is admitted to the privileges of Fellowship,
pay an admission fee of three guineas, and a subscription of three guineas
for the year of election. He shall continue to pay a subscription of three
guineas at the beginning of each session so long as he remains a Fellow.

Each Fellow who was elected subsequent to December 1916 and previous
to December 1920 shall also pay a subscription of three guineas at the
beginning of each session so long as he remains a Fellow.

Each Fellow who was elected previous to December 1916, and who has not
completed his twenty-five annual payments,* shall, at the beginning of each
session, pay three guineas or four guineas according as he has or has not made
ten annual payments as reckoned from the year of election. Each Fellow who
has completed or shall complete his payments shall be invited to contribute
one guinea per annum or to pay a single sum of ten guineas.

A Fellow may compound for the annual subscriptions by a single pay-
ment of fifty guineas, or on such other terms as the Council may from time
to time fix.

VII.

A Fellow who, after application made by the Treasurer, fails to pay any
contribution due by him, shall be reported to the Council, and, if the Council
see fit, shall be declared no longer a Fellow. Notwithstanding such declaration
all arrears of contributions shall remain exigible.

* The following is an extract from the previous law affecting Annual Subscribers elected
prior to December 1916: — “Every Ordinary Fellow, within three months after his election,
shall pay Two Guineas as the fee of admission, and Three Guineas as his contribution for the
Session in which he has been elected ; and annually at the commencement of every Session,
Three Guineas into the hands of the Treasurer. This annual contribution shall continue for ten
years after his admission, and it shall be limited to Two Guineas for fifteen years thereafter.”

Laws of the Society.

267

ELECTION OF HONORARY FELLOWS.

VIII.

Honorary Fellows shall be persons eminently distinguished in Science or
Literature. They shall not be liable to contribute to the Society’s Funds.
Personages of the Blood Royal may be elected Honorary Fellows at any time on
the nomination of the Council, and without regard to the limitation of numbers
specified in Law I.

IX.

Honorary Fellows shall be proposed by the Council. The nominations shall
be announced from the Chair at the First Ordinary Meeting after their selection.
The names shall be printed in the circular for the last Ordinary Meeting of the
Session, when the election shall be by Ballot, after the manner prescribed in
Laws III and IV for the Election of Fellows.

EXPULSION OF FELLOWS.

X.

If, in the opinion of the Council, the conduct of any Fellow is injurious to
the character or interests of the Society, the Council may, by registered letter,
request him to resign. If he fail to do so within one month of such request,
the Council shall call a Special Meeting of the Society to consider the matter.
If a majority consisting of not less than two -thirds of the Fellows present and
voting decide for expulsion, he shall be expelled by declaration from the Chair,
his name shall be erased from the Roll, and he shall forfeit all right or claim in
or to the property of the Society.

XI.

It shall be competent for the Council to remove any person from the Roll
of Honorary Fellows if, in their opinion, his remaining on the Roll would be
injurious to the character or interests of the Society. Reasonable notice of such
proposal shall be given to each member of the Council, and, if possible, to the
Honorary Fellow himself. Thereafter the decision on the question shall not be
taken until the matter has been discussed at two Meetings of Council, separated
by an interval of not less than fourteen days. A majority of two-thirds of the
members present and voting shall be required for such removal.

268 Proceedings of the Royal Society of Edinburgh.

MEETINGS OF THE SOCIETY.

XII.

A Statutory Meeting for the election of Council and Office-Bearers, for the
presentation of the Annual Reports, and for such other business as may be
arranged by the Council, shall be held on the fourth Monday of October. Each
Session of the Society shall begin at the date of the Statutory Meeting.

XIII.

Meetings for reading and discussing communications and for general business,
herein termed Ordinary Meetings, shall be held, when convenient, on the first and
third Mondays of each month from November to July inclusive, with the excep-
tion that in January the meetings shall be held on the second and fourth
Mondays.

XIV.

A Special Meeting of the Society may be called at any time by direction of
the Council, or on a requisition to the Council signed by not fewer than six
Fellows. The date and hour of such Meeting shall be determined by the
Council, who shall give not less than seven days’ notice of such Meeting. The
notice shall state the purpose for which the Special Meeting is summoned ; no
other business shall be transacted.

PUBLICATION OF PAPERS.

XV.

The Society shall publish Transactions and Proceedings. The consideration
of the acceptance, reading, and publication of papers is vested in the Council,
whose decision shall be final. Acceptance for reading shall not necessarily imply
acceptance for publication.

DISTRIBUTION OF PUBLICATIONS.

XVI.

Fellows who are not in arrear with their Annual Subscriptions and all
Honorary Fellows shall be entitled gratis to copies of the Parts of the Trans-
actions and the Proceedings published subsequently to their admission.

Copies of the Parts of the Proceedings shall be distributed by post or
otherwise, as soon as may be convenient after publication ; copies of the Transac-
tions or Parts thereof shall be obtainable upon application, either personally or

269

Laws of the Society.

by an authorised agent, to the Librarian, provided the application is made
within five years after the date of publication.

CONSTITUTION OF COUNCIL.

XVII.

The Council shall consist of a President, six Vice-Presidents, a Treasurer,
a General Secretary, two Secretaries to the Ordinary Meetings (the one repre-
senting the Biological group and the other the Physical group of Sciences),* a
Curator of the Library and Museum, and twelve ordinary members of Council.

ELECTION OF COUNCIL.

XVIII.

The election of the Council and Office-Bearers for the ensuing Session shall
be held at the Statutory Meeting on the fourth Monday of October. The list of
the names recommended by the Council shall be issued to the Fellows not less
than one week before the Meeting. The election shall be by Ballot, and shall
be determined by a majority of the Fellows present and voting. Scrutineers
shall be nominated as in Law IV.

XIX.

The President may hold office for a period not exceeding five consecutive
years ; the Vice-Presidents, not exceeding three ; the Secretaries to the Ordinary
Meetings, not exceeding five ; the General Secretary, the Treasurer, and the
Curator of the Library and Museum, not exceeding ten ; and ordinary members
of Council, not exceeding three consecutive years.

XX.

In the event of a vacancy arising in the Council or in any of the offices
enumerated in Law XVII, the Council shall proceed, as soon as convenient, to
elect a Fellow to fill such vacancy for the period up to the next Statutory
Meeting.

* The Biological group includes Anatomy, Anthropology, Botany, Geology, Pathology,
Physiology, Zoology ; the Physical group includes Astronomy, Chemistry, Mathematics,
Metallurgy, Meteorology, Physics.

270 Proceedings of the Royal Society of Edinburgh.

POWERS OF THE COUNCIL.

XXL

The Council shall have the following powers : — (1) To manage all business
concerning the affairs of the Society. (2) To decide what papers shall be
accepted for communication to the Society, and what papers shall be printed
in whole or in part in the Transactions and Proceedings. (3) To appoint
Committees. (4) To appoint employees and determine their remuneration.
(5) To award the various prizes vested in the Society, in accordance with the
terms of the respective deeds of gift, provided that no member of the existing
Council shall be eligible for any such award. (6) To make from time to time
Standing Orders for the regulation of the affairs of the Society. (7) To control
the investment or expenditure of the Funds of the Society.

At Meetings of the Council the President or Chairman shall have a casting
as well as a deliberative vote.

DUTIES OF PRESIDENT AND VICE-PRESIDENTS.

XXII.

The President shall take the Chair at Meetings of Council and of the Fellows.
It shall be his duty to see that the business is conducted in accordance with the
Charter and Laws of the Society. When unable to be present at any Meetings or
attend to current business, he shall give notice to the General Secretary, in order
that his place may be supplied. In the absence of the President his duties shall
be discharged by one of the Vice-Presidents.

DUTIES OF THE TREASURER.

XXIII.

The Treasurer shall receive the monies due to the Society and shall make
payments authorised by the Council. He shall lay before the Council a list of
arrears in accordance with Rule VII. He shall keep accounts of all receipts
and payments, and at the Statutory Meeting shall present the accounts for
the preceding Session, balanced to the 30th of September, and audited by a
professional accountant appointed annually by the Society.

DUTIES OF THE GENERAL SECRETARY.

XXIV.

The General Secretary shall be responsible to the Council for the conduct of
the Society’s correspondence, publications, and all other business except that
which relates to finance. He shall keep Minutes of the Statutory and Special

Laws of the Society.

271

Meetings of the Society and Minutes of the Meetings of Council. He shall
superintend, with the aid of the Assistant Secretary, the publication of the
Transactions and Proceedings. He shall supervise the employees in the
discharge of their duties.

DUTIES OF SECRETARIES TO ORDINARY MEETINGS.

XX Y.

The Secretaries to Ordinary Meetings shall keep Minutes of the Ordinary
Meetings. They shall assist the General Secretary, when necessary, in superin-
tending the publication of the Transactions and Proceedings. In his absence,
one of them shall perform his duties.

DUTIES OF CURATOR OF LIBRARY AND MUSEUM.

XXYI.

The Curator of the Library and Museum shall have charge of the Books,
Manuscripts, Maps, and other articles belonging to the Society. He shall keep
the Card Catalogue up to date. He shall purchase Books sanctioned by the
Council.

ASSISTANT-SECRETARY AND LIBRARIAN.

XXVII.

The Council shall appoint an Assistant-Secretary and Librarian, who shall
hold office during the pleasure of the Council. He shall give all his time, during
prescribed hours, to the work of the Society, and shall be paid according to the
determination of the Council. When necessary he shall act under the Treasurer
in receiving subscriptions, giving out receipts, and paying employees.

ALTERATION OF LAWS.

XXVIII.

Any proposed alteration in the Laws shall be considered by the Council,
due notice having been given to each member of Council. Such alteration, if
approved by the Council, shall be proposed from the Chair at the next Ordinary
Meeting of the Society, and, in accordance with the Charter, shall be considered
and voted upon at a Meeting held at least one month after that at which the
motion for alteration shall have been proposed.

INDEX.

Absorption of Carbon Dioxide by Solid Caustic
Soda, by Miss E. Gilchrist, 128-135.
Accounts of the Society, Session 1920-21, 230.
Additions to Library by Gift or Purchase, 261,
Adsorption of Gas under Pressure, by H. Briggs
and W. Cooper, 119-127.

./Ether and the Quantum Theory, by H. S.
Allen, 34-43.

Aitken (John), Obituary Notice of, by C. G.
Knott, 177-181.

Alford (Robert Gervase), Obituary Notice of,

197.

Allen (H. S.). ./Ether and the Quantum Theory,
34-43.

Anderson (Sir R. Rowand), Obituary Notice of,
197-198.

Ashworth (J. H.). Obituary Notice of Yves
Delage, 182-183.

Associate Membership. Question of J unior Grade
of Membership of R.S.E., 220.

Awards of Prizes, 224.

Barnes (Henry). Obituary Notice of E. W.
Prevost, 184-185.

Obituary Notice of, by Miss E. Barnes,

195-196.

Barnes (Miss E.). Obituary Notice of Henry
Barnes, 195-196.

Bartholomew (J. G.), Obituary Notice of, by
G. G. Chisholm, 170-176.

Beck (Hon. Sir J. H. M.), Obituary Notice of,

198.

Binding in Library, Carnegie U. K. Trust Grant
of £3000 nearly expended, 219.

Bower (F. O.). Size, a Neglected Factor in Stelar
Morphology. President’s Address, 1-25.
Bridger (A. E. ), Obituary Notice of, 199.

Briggs (Henry). An Experimental Analysis of
the Losses by Evaporation of Liquid Air con-
tained in Vacuum Flasks, 97-110.

and W. Cooper. Adsorption of Gas

under Pressure, 119-127.

British Association Meeting in Edinburgh,
September 1921, 219.

Brown (David), Obituary Notice of, 199.

Brown (David Rainy), Obituary Notice of, 200.

Carbon Dioxide, Absorption of, by Solid Caustic
Soda, by Miss E. Gilchrist, 128-135.

Carnegie U.K. Trust. Grant of £3000 for
Library Binding. Work nearly completed,
219.

Carter (Wm. Allan), Obituary Notice of, 200.

Caustic Soda, Solid, Absorption of Carbon
Dioxide by, by Miss E. Gilchrist, 128-135.

Cayley’s, a Continuant of, of the Year 1874, by
Sir Thomas Muir, 111-116.

Chisholm (G. G. ). Obituary Notice of J. G.
Bartholomew, 170-176.

Colloids in Soil, Relation to Thermal Conduc-
tivity, by T. B. Franklin, 61-67.

Conjoint Board of Scientific Societies. Question
of Government Aid to Societies, 219.

Continuant of Cayley’s of the Year 1874, by
Sir Thomas Muir, 111-116.

Contributions, Voluntary, List of, 236.

Cooper ( W. ). See Briggs (Henry).

Council, List of, at October 1920 and October
1921, 212, 220, 237.

Crombie (D. M. R. ). See Turner (Dawson).

Delage, Yves, Obituary Notice of, by J. H.
Ashworth, 182-183.

Dinner, Royal Societies’, B.A. Meeting, Sep-
tember 1921, 219.

Dracaena fruticosa, Koch, Interruption of En-
dodermis in, by Annette G. Mann, 50-59.

Dundas (William John), Obituary Notice of,

200.

Dynamics of a Particle, Generalised, by J. H. M.
Wedderburn, 26-33.

Endodermis, Interruption of, in Dracaena fruti-
cosa, Koch, by Annette G. Mann, 50-59.

Equations of Motion of a Single Particle, by
J. H. M. Wedderburn, 26-33.

Eye, Self- Luminosity of the : Fechner’s Law.
(Abstract), by W. Peddie, 60.

Fairgrieve (M. M'Callum). The Annual In-
cidence of Intelligence, and its Measurement
by the American Army Tests, 150-153.

Fechner’s Law and the Self- Luminosity of the
Eye. (Abstract), by W. Peddie, 60.

Fellows, Honorary, 217, 258.

Obituary Notices, 158-207.

List of Ordinary, 238.

Deceased and resigned in 1920-21, 260.

Elected in 1920-21, 215, 260.

Fluid Flow in Uniform Channel, Stability of,
by H. Levy, 136-147.

Franklin (T. B.). The Relation of the Soil
Colloids to the Thermal Conductivity of the
Soil, 61-67.

Fraser (Sir Thomas R. ), Obituary Notice of, by
Harry Rainy, 186-192.

272

Index.

273

Functions, Confluent Hypergeometric, of Two
Variables, by P. Humbert, 73-96.

Galloway (T. Lindsay), Obituary Notice of, by
W. P Ker, 193-194.

Gas under Pressure, Adsorption of, by H. Briggs
and W. Cooper, 119-127.

Gatehouse (Tom Ernest), Obituary Notice of,

201.

George Heriot’s Trust, Representative on, 220.

Gilchrist (Elizabeth). Utilisation of Solid
Caustic Soda in the Absorption of Carbon
Dioxide, 128-135.

Gilruth (Geo. Ritchie), Obituary Notice of, 202.

Government Assistance Conjoint Board of
Scientific Societies, 219.

Gregory (J. W.). Supplementary Note on the
Geology of Benguella in relation to its
Cephalopods and the History of the South
Atlantic. ( Title only — published in Trans-
actions), 213.

Gunning Victoria Jubilee Prize to Mr C. T. R.
Wilson, 217, 219, 229.

Harvey (Elsie J.) and P. Bruce White. See
Rennie, John.

Helme (Thomas Arthur), Obituary Notice of,
202.

Honorary Fellows, elected and deceased 1920-21,
217, 260.

List of, 258.

Horne (Alex. R.). On a Graphical Method of
determining Shear Influence Lines and Dia-
grams of Maximum Shearing Force for a
Beam subjected to a Series of Concentrated
Rolling Loads, 68-72.

Humbert (Pierre). The Confluent Hypergeo-
metric Functions of Two Variables, 73-96.

Hunter (James), Obituary Notice of, 202.

Hypergeometric Functions, Confluent, of Two

. Variables, by P. Humbert, 73-96.

Index of Papers published in Transactions ,
1920-21, 275.

Influence Lines, Shear, by A. R. Horne, 68-72.

Intelligence, Annual Incidence, by M. M‘Callum
Fairgrieve, 150-153.

Ionised Atmosphere, Electrified Pith Ball in,
by Dawson Turner and D. M. R. Crombie,
154-157.

Ker (W. P. ). Obituary Notice of T. Lindsay
Galloway, 193-194.

Kidston (R. ) and W. H. Lang. On Old Red
Sandstone Plants showing Structure, from the
Rhynie Chert Bed, Aberdeenshire, Parts IV
and V. (Abstract — full papers in Trans-

actions), 117-118.

Knott ( C. G. ) . Obituary N otice of J ohn Aitken,
177-181.

Lamont (Augusta). Development of the
Feathers of the liuck during the Incubation
Period. {Title only), 218.

Lang(W. H.). See Kidston (R.).

Laplace’s Equation in n Dimensions, Solution of,
by P. Humbert, 73-96.

Law VI, Changes in, 214, 219.

VOL. XLI,

Laws, 265.

Changes in, 214, 219.

Levy (H.). Criterion for Stable Flow of Fluid
in a Uniform Channel, 136-147.

Library, Additions to, 261.

— t Binding in, Grant from Carnegie U.K.

Trust, 219.

Liquid Air, Analysis of Losses by Evaporation
of, by H. Briggs, 97-110.

Liston (Lt.-Col. W. G.). Plague and Rats.
{Title only), 216.

Luminosity, Self-, of the Eye: Fechner’s Law.
(Abstract), by W. Peddie, 60.

Macdonald (George). Obituary Notice of Robert
Munro, 158-169.

Macnair (P. ) and Colin M. Leitch. The Genus
Clisiophyllum. {Title only), 216.

Magnetic Tubes of Induction as Quanta, by H.
S. Allen, 34-43.

Makdougall- Brisbane Prize awarded to Prof. J.
H. M. Wedderburn, 218, 219, 227.

Mann (Annette G.). Observations on the In-
terruption of the Endodermis in a Secondarily
Thickened Root of Dracaena fruticosa, Koch,
50-59.

Marshall (John). A Generalisation of Lagrange’s
Equations of Motion and their Hamiltonian
Forms. {Title only), 215.

Martin, (SirT. Carlaw), Obituary Notice of, 203.

Meetings of the Society, Proceedings of Ordinary,
213.

Proceedings of Statutory, 211, 219.

Membership, Question of Junior Grade of, 220.

Metals, Transverse Effects in, by F. Unwin,
44-49.

Mirage, Note on Conditions for, by A. G.
Ramage, 148-149.

Muir (Sir Thomas). Note on a Continuant of
Cayley’s of the Year 1874, 111-116.

Munro (Robert), Obituary Notice of, by George
Macdonald, 158-169.

Mylne (Rev. R. S.), Obituary Notice of, 203.

Obituary Notices of Fellows, 158-207.

Oliphant (James), Obituary Notice of, 203.

Ordinary Meetings, Proceedings of, 213.

Papers read during 1920-21, 213.

Particle, Single : Equations of Motion of, by
J. H. M. Wedderburn, 26-33.

Peddie (W.). On Fechner’s Law and the Self-
Luminosity of the Eye. (Abstract), 60.

The Avoidance of Relativity which is

not of the Galileo-Newtonian Type. {Title
only), 214.

Pith Ball, Electrified, in an Ionised Atmosphere,
by Dawson Turner and D. M. R. Crombie,
154-157.

President’s Address. Size, a Neglected Factor
in Stelar Morphology, by F. O. Bower, 1-25.

Prevost(E. W.), Obituary Notice of, by Henry
Barnes, 184-185.

Prizes, Rules, and List of Awards, 221-229.

Proceedings of Ordinary Meetings, 213.

of Statutory Meetings, 211, 219.

18

274 Proceedings of the Royal Society of Edinburgh.

Quantum Theory, iEther and the, by H. S.
Allen, 34-43.

Queensferry Road, Note on Conditions for
Mirage on, by A. G. Ramage, 148-149.

Rainy (Harry). Obituary Notice of Sir Thomas
R. Fraser, 186-192.

Ramage (A. G.). Note on Conditions for Mirage
on the Queensferry Road, 148-149.

Rennie (John), Elsie J. Harvey, and P. Bruce
White. Isle of Wight Disease in Bees. ( Title
only — published in Transactions), 213.

Reports of General Secretary and Treasurer, 219.

Rliynie Chert Bed, Aberdeenshire, Old Red
Sandstone Plants from, by R. Kidston and
W. H. Lang, 117-118.

Roberts (David Lloyd), Obituary Notice of, 204.

!

Secretary’s Reports, 1920-21, 219.

Shearing Force Diagrams, Maximum, for Con-
centrated Rolling Loads, by A. R. Horne,
68-72.

Size, a Neglected Factor in Stelar Morphology.
President’s Address, by F. 0. Bower, 1-25.

Soil Colloids, Relation to Thermal Conductivity
of the Soil, by T. B. Franklin, 61-67.

Spath (L. F. ). Cretaceous Ammonoidea from
Angola, collected by Prof. J. W. Gregory,
F.R.S. ( Title only — published in Transac-
tions), 213.

Sprague (Thomas Bond), Obituary Notice of,
204-206.

Spring-born Boys’ Intelligence, by M. M‘Callum
Fairgrieve, 150-153.

Stability of Fluid Flow in Uniform Channel, by
H. Levy, 136-147.

Statutory Meetings, Proceedings of, October
1920 and October 1921, 211, 219.

Stelar Morphology : Size, a Neglected Factor
in. President’s Address, by F. O. Bower,
1-25.

Stewart (E. M.), appointed Assistant- Librarian,
219.

(Geo. A.), Assistant Secretary. Obitu-
ary Notices of Fellows, 197-207.

Subscriptions, Annual, etc., Increase of, 214,
219.

Thompson, (J. M‘L). Studies in Floral Mor-
phology : No. II. Staminal Zygomorphy of
Couroupita guianensis, Aubl. ( Title only —
published in Transactions), 215.

Transactions Papers, Index of, 1920-21, 275.

Turner (Dawson) and D. M. R. Crombie.
Experiments with an Electrified Pith Bail
in an Ionised Atmosphere, 154-157.

Unwin (F. ). On the Transverse Galvano-

magnetic and Therm omagnetic Effects in
several Metals, 44-49.

Vacuum Flasks, Evaporation of Liquid Air in,
by H. Briggs, 97-110.

Voluntary Contributors, List of, under third
paragraph of Law VI, 236.

Walker (Robert), Obituary Notice of, 206.

Wedderburn (J. H. M.). On the Equations of
Motion of a Single Particle, 26-33.

Awarded Makdougall-Brisbane Prize,

218, 219, 227.

White (P. Bruce) and Elsie J. Harvey. See
Rennie, John.

Wilson (C. T. R. ). Awarded Gunning Prize,
217, 219, 229.

Address : Some Recent Work on Light-
ning and Thunderstorms. {Title only), 218.

Woods (Geo. Arthur), Obituary Notice of, 207.

Wordie (J. M. ). Shackleton Antarctic Ex-
pedition, 1914-17. {Titles only) — Papers on
Weddell Sea — -published in Transactions),
215, 216.

Index of Papers published in the “ Transactions ”
during Session 1920-21.

(Arranged under the Authors’ Names.)

Harvey (Elsie J.) and White (P. Bruce). See
Rennie (John).

Kidston (R.)and Lang (W. H.). On Old Red
Sandstone Plants showing Structure, from
the Rhynie Chert Bed, Aberdeenshire. Part
IV : Restorations of Vascular Cryptogams,
and Discussion of their Bearing on the
General Morphology of the Pteridophyta and
the Origin of the Organisation of Land Plants,
vol. lii, Ho. 32, 1921, pp. 831-854.

Lang (W. H.). See Kidston (R.).

Rennie (John), Harvey (Elsie J. ), and White (P.
Bruce). Isle of Wight Disease in Hive Bees,
vol. lii, No. 29, 1921, pp. 737-779.

Thompson (J. M‘L.). Studies in Floral Mor-
phology : No. II. The Staminal Zygomorphy
of Couroupita guianensis, Aubl., vol. liii,
No. 1, 1921, pp. 1-15.

White (P. Bruce) and Harvey (Elsie J.). See
Rennie (John).

Wordie (J. M.). Shackleton Antarctic Ex-
pedition, 1914-17 ; Depths and Deposits of
the Weddell Sea, vol. lii, No. 30, 1921, pp.
781-793.

Shackleton Antarctic Expedition, 1914-

17 : The Natural History of Pack Ice as
observed in the Weddell Sea, vol. lii, No. 31,
1921, pp. 795-829.

PRINTED IN GREAT BRITAIN BY NEILL AND CO., DTD., EDINBURGH.

INSTRUCTIONS TO AUTHORS.

The ‘ copy 5 should be written on large sheets of paper, on one side only,
and the pages should be clearly numbered. The MS. must be easily legible,
preferably typewritten, and must be absolutely in its final form for printing.
All tables of contents, references to plates, or illustrations in the text, etc.,
must be in their proper places, with the page numbers left blank; and
spaces must be indicated for the insertion of illustrations that are to appear
in the text.

Illustrations. — All illustrations must be drawn in a form im-
mediately suitable for reproduction ; and such illustrations as can be
reproduced by photographic processes should, so far as possible, be
preferred. Drawings to be reproduced as line blocks should be made with
Indian ink (deadened with yellow if of bluish tone), preferably on fine
white bristol board, free from folds or creases ; smooth, clean lines, or
sharp dots, but no washes or colours, should be used. If the drawings are
done on a large scale, to be afterwards reduced by photography, any
lettering or other legend must be on a corresponding scale.

If an author finds it inconvenient to furnish the drawings according to
these regulations, the Society will have the figures re-drawn and the letter-
ing entered at his expense ; but this will cause delay.

When the illustrations are to form plates, a scheme for the arrangement
of the figures (in quarto plates for the Transactions, in octavo for the
Proceedings) must be given, and numbering and lettering indicated.

Proofs. — A first proof and, if desired, a revise of each paper will be
sent to the author, whose address should be indicated on the MS. Expenses
for proof correction should not exceed 10 per cent, of the printers’ charges
on the setting and printing of each paper. Any excess will be charged
against the author.

All proofs must, if possible, be returned within one week, addressed to
The Secretary , Royal Society, 22-24 George Street, Edinburgh, and not to
the printer. To prevent delay, authors residing abroad should appoint
someone residing in this country to correct their proofs.

The author receives fifty of the reprints free, and may have any
reasonable number of additional copies at a fixed scale of prices which
will be furnished by the printer, who will charge him with the cost. To
prevent disappointment, especially if the paper contains plates, the author
should, as soon as possible, notify to the Secretary the number of additional
copies required, and should also repeat the notification on the first proof
returned.

Index Slips. — In order to facilitate the compilation of Subject
Indices, and to secure that due attention to the important points in a
paper shall be given in General Catalogues of Scientific Literature and
in Abstracts by Periodicals, every author is requested to return to the
Secretary, along with the proof of his paper, a brief index (on the model
given below) of the points in it which he considers new or important. These
indices will be edited by the Secretary, and incorporated in Separate Index
Slips, to be issued with each part of the Proceedings and Transactions.

MODEL INDEX.

Schafer, E. A. — On the Existence within the Liver Cells of Channels which can be. directly
injected from the Blood-vessels. Proc. Roy. Soc. Edin., vol. 1902, pp.

Cells, Liver, — Intra-cellular Canaliculi in.

E. A. Schafer. Proc. Roy. Soc. Edin., vol.

Liver, — Injection within Cells of.

E. A. Schafer. Proc. Roy. Soc. Edin., vol.

, 1902, pp.
, 1902, pp.

iv CONTENTS.

No. PAQR

XYII. The Annual Incidence of Intelligence, and its Measurement
by the American Army Tests. By M. M‘Callum Fair-
GRIEYE, M.A., 150

(Issued separately December 13, 1921.)

XVIII. Experiments with an Electrified Pith Ball in an Ionised
Atmosphere. By Dr Dawson Turner and Mr D. M. R.
Crombie 154

( Issued separately December 13, 1921.)

Obituary Notices —

Robert Munro,M.A.,M.D.,LL.D. By Dr George Macdonald, C.B.,
John George Bartholomew, LL.D. (Edin.), F.R.G.S., Geographer
and Cartographer to the King. By Geo. G. Chisholm,
M.A., B.Sc., Reader in Geography, Edinburgh University,
Secretary to the Royal Scottish Geographical Society,
John Aitken, LL.D., F.R.S. By C. G. Knott, D.Sc., LL.D., F.R.S.,
Yves Delage. By Professor J. H. Ashworth, F.R.S.,

Edward William Prevost, Pb.D., F.I.C. By Dr Henry Barnes,

O.B.E., M.D.,

Sir Thomas R. Fraser. By Harry Rainy, M.A., M.D..

F.R.C.P. Ed., . . . .

T. Lindsay Galloway, M.A., F.G.S., A.M.Inst.C.E., M.Inst.M.E.
By Professor W. P. Ker, F.B.A., M.A., .....

Henry Barnes, O.B.E., M.D., LL.D. Contributed by his
daughter, Miss E. Barnes, .......

Obituary Notices of Fellows. By Mr George A. Stewart,
Assistant Secretary, ........

Appendix —

Proceedings of the Statutory General Meeting, October 1920,
Proceedings of the Ordinary Meetings, Session 1920-1921, .
Proceedings of the Statutory General Meeting, October 1921,

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

Awards of the Keith, Makdougall-Brisbane, Neill, and Gunning
Prizes, ...........

Accounts of the Society, Session 1920-1921, .

Voluntary Contributors under Law VI (end of para. 3),

The Council of the Society at October 1921,

Alphabetical List of the Ordinary Fellows of the Society, .

List of Honorary Fellows of the Society, .....

List of Honorary and Ordinary Fellows of the Society elected

during Session 1920-1921,

Changes in Fellowship during Session 1920-1921,

Additions to Library by Gift or Purchase, .....

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

Index, ............

Index, under Authors’ Names, of Papers published in Transactions ,

158

170

177

182

184

186

193

195

197

211

213

219

221

224

230

236

237

238
258

260

260

261

265

272

275

The Papers published in this part of the Proceedings may be
had separately, on application to the Publishers, at the follow-
ing Prices : —

No. X .
No. XI .
No. XII .
No. XIII
No. XIV

. Price Is. 8d.
„ Is. Od.

,, Is. Od.

. „ Is. Od.

„ Is. Od.

No. XV .
No. XVI
No. XVII
No. XVIII

. Price Is. 4d.
„ Is. Od.
„ Is. Od.
,, Is. Od.