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MONOGRAPHS ON PHYSICS

EDITED BY

Sir J. J. THOMSON, O.M., F.R.S.

CAVENDISH PROFESSOR OF EXPERIMENTAL PHYSICS, CAMBRIDGE
AND

FRANK HORTON, Sc.D.

PROFESSOR OF PHYSICS IN THE UNIVERSITY OF LONDON

MONOGRAPHS ON PHYSICS.

Edited by Sir J. J. THOMSON, O.M., F.R.S.,

Cavendish Professor of Experimental Physics, Cambridge;

and FRANK HORTON, Sc.D.,

Professor of Physics in the University of London.

8vo,

RAYS OF POSITIVE ELECTRICITY AND THEIR APPLI-
CATION TO CHEMICAL ANALYSIS, By Sir J. J.
Thomson, O.M., F.R.S., Cavendish Professor of Experimental
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RELATIVITY AND THE ELECTRON THEORY. By E.
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THE EMISSION OF ELECTRICITY FROM HOT BODIES.
By O. W. Richardson, F.R.S., Wheatstone Professor of
Physics, King's College, London. With 35 Diagrams,
gs. net.

ELECTRIC WAVES. By G. W. Pierce, Professor of Physics,
Harvard University. [/« preparation.

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Professor of Physics, The University, Toronto.

[/» preparation.

LONGMANS, GREEN AND CO.

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Elect

^ THE

EMISSION OF ELECTRICITY
FROM HOT BODIES

O. W. RICHARDSON, F.R.S.

WH8AT8TONB PROFESSOR OF PHYSICS, KINO'S COLLEGE, LONDON

WITH DIAGRAMS

LONGMANS, GREEN AND CO
39 PATERNOSTER ROW, LONDON

FOURTH AVENUE & 30th STREET, NEW YORK

BOMBAY, CALCUTTA, AND MADRAS

I916

PREFACE.

It will be seen from the following pages that the subject of
the emission of electricity from hot bodies is one which has
made rapid strides in recent years. It will also be clear that
this field of inquiry still suggests for investigation many in-
teresting questions which are either of theoretical or of prac-
tical importance. In dealing with the theory of the emission
of electrons, one feels continually handicapped by the absence
of a satisfactory and comprehensive theory of conduction for
conductors of the metallic type. For this reason I have tried
to make the treatment of this part of the subject as general as
possible, and to reduce the part played by special theories to
a minimum. Another difficulty lies in the interpretation of
the facts bearing on the true nature of the contact potential
difference between metals. In spite of a conflict lasting over
a century, there still seems to be much room for difference of
opinion here. This question is of fundamental importance in
the interpretation of the theory of the emission of electricity
from hot bodies.

It has seemed undesirable to include in the book an ac-
count of the numerous and important technical developments
of the subject. Readers who are interested in these may,
however, find useful the following list of references, arranged
according to subjects: — Wireless Telegraphy and Telephony:
Fleming, " Instrument for converting alternating currents into
continuous currents," British Patent, No. 803,684, 7 November,
1905; De Forest, "The audion detector and amplifier,"
"Electrician," Vol. LXXII, p. 285 (1913); Reisz, "A new

VI PREFACE

method of magnifying electric currents," ibid., Vol. LXXII, p.
726 (1914); Langmuir, "The pure electron discharge and its
applications in radio-telegraphy and telephony," ibid., Vol.
LXXV, p. 240 (191 5); Armstrong, "Some recent develop-
ments in the audion receiver," ibid., Vol. LXXVI, p. 798
(19 1 6). Production of X-Rays : Coolidge, "A powerful
Roentgen ray tube with a pure electron discharge," " Phys.
Rev.," Vol. II, p. 409 (191 3). Rectification of Alternating
Currents: Langmuir, loc. cit. ; Hull, "A powerful source of
constant high potential," "Phys. Rev.," Vol. VII, p. 405
(191 6). The Electric Arc : MacKay and Ferguson, " Arcs in
gases between non-vaporizing electrodes," ibid.^ Vol. VII, p.
410 (1916).

In the last chapter I have included a brief account of the
results of some experiments I have recently made on the
electrons liberated by chemical action. Part of the cost of
this investigation has been defrayed by a Government grant
through the Royal Society.

For permission to publish certain of the figures I am in-
debted to the Royal Society, to the Cambridge Philosophical
Society, to the American Physical Society, and to the Pub-
lishers of the " Philosophical Magazine ".

Finally, I wish to express my thanks to Professor Newall
for information bearing on the question of solar electricity
considered on page 47, and to my wife and to Professor
Horton for assistance with the proofs.

O. W. RICHARDSON.

King's College, London,
I May, 19 16.

CONTENTS.

CHAP. PAGE

Preface v

I. Mainly Considerations of a General Character . i.

II. Theory of the Emission of Electrons from Hot

Bodies 27

III. Temperature Variation of Electron Emission . 54

IV. The Effect of Gases on the Emission of Electrons . 102
V. Energetics of Electron Emission . . . .139

VI, The Emission of Positive Ions by Hot Metals. . 179

VII. The Effect of Gases on the Liberation of Positive

Ions by Hot Metals 209

VIII. The Emission of Ions by Heated Salts . . . 234

IX. Ionization and Chemical Action 283

Index of Names 300

Subject Index 302

CHAPTER 1.
mainly considerations of a general character.

Nature of the Phenomena.

It is not intended in this book to give an account of all the
electrical properties of bodies which depend upon temperature.
In fact, the scope of the book is almost restricted to those
phenomena which I have ventured to describe by the term
thermionic. As is well known, all substances become con-
ductors of electricity at sufficiently high temperatures. Not
only is this the case, but solid and liquid substances have the
power of conferring the property of electrical conductivity on
the space which surrounds them. In other words, a charge of
electricity tends to leak away from the surfaces of bodies at
high temperatures. In general this happens in a vacuum as
well as when the bodies are surrounded by a gaseous atmos-
phere. The study of these thermionic effects has led to many
results of an interesting character, as we shall see. In prac-
tice it is often wellnigh impossible to separate the purely
thermal effects from those caused indirectly by other actions
which are conditioned by temperature. In this category
effects due to chemical action are conspicuous. Chiefly for
this reason I have added a chapter on Ionization by Chemical
Action. At the same time I have omitted to describe the
interesting electrical properties of flames, a subject which
might perhaps have been expected to fall within the scope
of the book. Those who are interested in flames will find
an excellent account of their electrical properties in a recent
work by H. A. Wilson.^

^ " Electrical Properties of Flames and of Incandescent Sglids," by H. A,
Wilson (London Uiiiversity Press, 1912).

2 EMISSION OF ELECTRICITY FROM HOT BODIES

Early Experiments.

The subject under consideration is not entirely of recent
origin. In fact, it has been known for nearly 200 years that
air in the neighbourhood of hot solids has the power of con-
ducting electricity. Experiments on the subject were made
by a number of physicists of the seventeenth century, includ-
ing Du Fay,^ Du Tour,^ Watson,^ Canton,* Priestley,* and
Cavallo.** The phenomena appear to have attracted little
further attention until the middle of the nineteenth century,
when Becquerel ^ showed that air at a white heat was unable
to insulate under a potential difference of a few volts. Some-
what later Blondlot ® showed that the same was true even
with a potential difference of O'ooi volt ; he also found that
the currents did not obey Ohm's law. An important dis-
covery was made by Guthrie,^ who showed that a red-hot
iron ball in air could retain a negative charge but could not
retain a positive charge. At higher temperatures this differ-
ence disappeared, electrifications of either sign being con-
ducted away rapidly. This difference in the character of the
discharge, according to the sign of the electrification, is some-
times described by the term unipolar and is of fundamental
importance.

A systematic investigation of the electrical effects produced
by incandescent solids was begun by Elster and Geitel ^'^ about
1880. Their method consisted in heating various metal wires
by means of an electric current and examining the potential
acquired by a neighbouring electrode under different circum-
stances. The hot wire was as a rule connected to the earthed

^ " M ^moires de I'Acad." (1733).

* " M6m. de Math, et de Physique," XI, p. 246 (1755).
« '* Phil. Trans.," abridge. Vol. X, p. 296 (1746).
«76td., Vol. LII, p. 457 (1762).

* " History of Electricity," p. 579.

* " Treatise on Electricity," Vol. I, p. 324.

' "Ann. de Chimie et de Physique," Hi. Vol. XXXIX, p. 355 (1853).

" '« C. R.," Vol. XCII, p. 870 (1881) ; Vol. CIV, p. 283 (1887).

» " Phil. Mag.," iv. Vol. XLVI, p. 257 (1873).

10 "Ann. der Phys.," Vol. XVI, p. 193 (1882) ; Vol. XIX, p. 588 (1883) ; Vol.
XXII, p. 123 (1884); Vol. XXVI, p. I (1885); Vol. XXXI, p. log (1887); Vol.
XXXVII, p. 315 (1889) ; "Wien. Ber.," Vol. XCVII, p. 1175 (1889).

CONSIDERATIONS OF A GENERAL CHARACTER 3

pair of quadrants of an electrometer, the other pair being con-
nected to the electrode. Let us suppose that the wire Is
maintained at a constant potential, and that all the quadrants
of the electrometer are connected together initially. In
general, an electric current is then flowing either from the
hot wire to the electrode or vice versa, and when the quadrants
are separated this current will give rise to a deflection of the
electrometer. The deflection will not increase indefinitely,
however, since the charging up of the electrode gives rise to
a back electromotive force which tends to stop the current.
Ultimately a limiting potential is reached which is sufficient
either completely to stop the current or to stop so much of it
that the rest just makes up for any small losses which may
arise from faulty insulation. The determination of this limit-
ing potential under a great variety of conditions was the chief
object of most of Elster and Geitel's experiments. They
found that the magnitude and sign of the limiting potential
varied greatly in different circumstances. With a platinum
wire in air at atmospheric pressure this potential was positive
at low temperatures and increased in magnitude as the tem-
perature was raised to a red heat, when a maximum value
was reached. After passing this point the potential fell al-
most to zero at a white heat. At lower pressures the results
were similar, except that the limiting potential, after passing
the temperature at which it reached zero, was found to change
sign and to acquire progressively increasing negative values as
higher temperatures were reached. The wires thus behaved
as though they had a tendency to give off positive electricity
at low temperatures and negative at high temperatures. At
some intermediate temperature equal amounts of each sign
would be given off; so that the potential acquired by the
electrode would be the same as that of the hot wire. The
temperature at which the change from positive to negative
took place was higher the higher the pressure of the air, and
it was also higher for new wires than for wires which had
been heated for a long time. It depended also on the nature
of the gas and on the material of the wire. With platinum
wires the phenomena in water vapoqr and the vapours of

I *

4 EMISSION OF ELECTRICITY FROM HOT BODIES

sulphur and phosphorus were similar to those in air, but
in hydrogen the electrode acquired a negative charge at all
pressures up to and including atmospheric. With a copper
wire in hydrogen, on the other hand, the electrode received
a positive charge except when the pressure was quite low.
Carbon filaments apparently gave riSe to negative potentials
under all circumstances.

Branly ^ used a method which is in some ways the opposite
of that of Elster and Geitel. He measured the rate of leakage
of electricity from an insulated conductor when placed in the
neighbourhood of a hot body. In this way he obtained results
in confirmation of those given by Elster and Geitel for pla-
tinum. He also found that the oxides of lead, aluminium,
and bismuth, exhibited the opposite behaviour to that of
various metals which had been tested; since in air at a red
heat they lost a negative charge but not a positive charge.

An effect which occurs in electric lamps and was first
observed by Edison is related to these phenomena. If an
independent electrode is mounted in an incandescent lamp
and arranged so that it can be connected through a galvano-
meter to either of the outside terminals of the lamp, a current
is found to flow through the galvanometer when the connexion
is made to the positive terminal but not when it is made to
the negative terminal. A large number of experiments bear-
ing on the question were made by Preece^ and Fleming.^
Fleming showed that the effects could be explained on the
view that there was a vigorous emission of electricity from
the negative end of a carbon filament even in the best possible
vacuum. This conclusion was also in agreement with the
earlier observations made by Elster and Geitel in their ex-
periments on carbon filaments.

The Theory of Ions.

During the period which has just been under consideration
the development of the subject was seriously handicapped by

1 " C. R.," Vol. CXIV, p. 1531 {1892).

2" Roy. Soc. Proc," Vol. XXXVHI, p. 219 {1885).

?/6fd., Vol. XLVn, p. ii8 (1890) ; " Phjl. Mag.," Vol. XLU, p. 52 (1896),

CONSIDERATIONS OF A GENERAL CHARACTER 5

the absence of any satisfactory theory to indicate the im-
portant lines of experimental investigation. This want was
partially met, at the close of the nineteenth century, by the
hypothesis which attributed the conduction of electricity by
gases to the motion, under the influence of the electric field,
of minute electrically charged particles or ions. Stimulated
by the discovery of the Roentgen and Becquerel rays this
hypothesis in the hands of Sir J. J. Thomson rapidly de-
veloped into a coherent theory capable of embracing all the
known facts of gaseous discharges and of predicting many new
phenomena hitherto unsuspected. Those who had studied
the question felt that there was a definite connexion between
the phenomena exhibited by gases when ionized, or made
to conduct, under the influence of the Roentgen rays and
other agencies, on the one hand, and the effects described in
the last section on the other. In fact, the view of those
effects which seems to have received most support at this
time was somewhat as follows : It was supposed that there
was some kind of interaction between the metal and the sur-
rounding gas which resulted in the ionization of the latter.
The unipolarity of the currents was explicable as arising
either from the difference in velocity of the ions of opposite
sign or from a difference in their chemical affinity for the hot
metal or, possibly, from a combination of these causes. On
such a view the detailed investigation of the mechanism of the
electrical conductivity and the determination of the nature of
the ions became of the utmost importance.

Properties of the Gases Drawn Away from the
Neighbourhood of Incandescent Bodies.

The nature of the electrical conductivity exhibited by gases
drawn from the neighbourhood of hot wires was investigated
by McClelland.^ In many respects the phenomena were found
to be similar to those exhibited by gases which had been
exposed to the action of Roentgen or Becquerel rays. Thus,
in examining the relation between the current and the applied

i"PhiI. Mag.," Vol. XLVI, p. 29 (1899); " Camb. Phil. Proc.." Vol. X,
p. 241 (1899) ; Vol. II, p. 296 (1902).

6 EMISSION OF ELECTRICITY FROM HOT BODIES

electromotive force, between suitable electrodes immersed in
such gases, McClelland found that for sufficiently small dif-
ferences of potential the currents were proportional to the
applied potential differences. As the potential differences
increased, the rate of increase of the current fell off until finally
a stage was reached when the current acquired a constant
maximum value independent of further increase in the potential
difference. In these experiments the gases were allowed to
stream at a constant rate through the testing vessel, and the
maximum or saturation current was interpreted as indicat-
ing that all the ions present in the gas at entering the vessel
were drawn to the electrodes by the electric field. This in-
ference was established by allowing the gas to pass into a
second testing vessel, when its conductivity was found to have
disappeared. In these respects the gases resembled those
which had been exposed to Roentgen rays and other ionizing
agents. There were, however, important differences. For
example, the properties of the gas depended to a very large
extent on the temperature of the hot wire. With the wire
at a dull red heat the gas drawn away would discharge a
negatively charged conductor but not one which was positively
charged. At sufficiently high temperatures charges of either
sign were discharged with about equal facility. It thus
appears that at low temperatures the ions drawn away from
the hot metal are all positive, whereas at higher temperatures
ions of both signs are present in amounts which, if not equal,
are at any rate comparable with one another. These observa-
tions are at once seen to be in agreement with those recorded
by Elster and Geitel. McClelland observed the excess of
positive ionization at low temperatures with wires of platinum,
iron, German silver, and brass, and with carbon dioxide as
well as air.

McClelland also measured the mobility of the ions, i.e.
their velocity of drift under a unit electric field. The gas
was allowed to flow at a known rate down the annular region
between two coaxial circular cylinders maintained at a given
difference of potential. The fraction of the total number of ions
present collected by a known length of one of the cylinders was

CONSIDERATIONS OF A GENERAL CHARACTER 7

measured From a knowledge of this fraction, which obviously
increases with the mobility of the ions, the value of the mo-
bility can be deduced. It was found to be about 20 per cent
greater for the negative than for the positive ions. The abso-
lute values were comparable with "04 cm. per sec. per volt/cm.,
and were thus much smaller than those for the ions generated
by Roentgen rays (about i '5 cm. sec, ~ ^ per volt cm. " ^).
Moreover, they were not constant but diminished as the dis-
tance travelled by the gas from the hot body increased ; that
is to say, the mobilities diminished with lapse of time and as
the gas became cooler. The mobilities were also found to be
diminished when the temperature of the wire was increased.
The last effect is usually attributed to the loading up of the
ions by the particles sputtered from the hot metal, as sputter-
ing is known to increase rapidly with rising temperature.
Cooling the gas will tend to facilitate the condensation of
vapours on the ions, if any vapours are present, and lapse
of time will diminish the average mobility of the ions owing
to recombination, since the slower ions also recombine more
slowly.

These experiments showed that the currents through gases
drawn away from the neighbourhood of hot bodies were
carried by ions. They did not, however, throw much light
on the processes by which the ions originated in the first
instance, nor, since the properties of the ions under examina-
tion were clearly changing as they were carried away from the
hot body, could the nature of the ions first formed easily be
inferred from those of the ions under investigation. These
problems were solved by experiments of a different character.

The Specific Charge (e/w) of the Ions.

The nature of the negative ions emitted by hot bodies in a
gas at a low pressure was discovered by J. J. Thomson,^ who
measured the ratio ejm of their electric charge e to their mass
m. Thomson's experiments were made with carbon filaments
and the method employed was as follows : A straight filament
arranged to be heated by an electric current was mounted
" Phil. Mag.," Vol. XLVIII, p. 547(1899).

8 EMISSION OF ELECTRICITY FROM HOT BODIES

parallel to and immediately in front of a metal plate A with
which one end of the filament was electrically connected. A
second insulated plate B was mounted parallel to A and was
connected to the insulated quadrants of an electrometer. The
filament was thus in the space between the two plates, which
were maintained at a difference of potential V = Xdf, where
X is the electric intensity and d the distance between the
plates. The plates and filament were enclosed in a glass tube
which was exhausted until the pressure of the enclosed gas
was so low that the mean free path of the gas molecules was
greater than the distance between the plates. Under these
conditions the influence of the gas molecules on the motion of
the ions can be disregarded. The tube was placed between
coils carrying an electric current, so that the plates lay in a
uniform magnetic field H whose direction was parallel to that
of the length of the filament. The ions starting from the
filament were thus subjected to the action of a uniform electric
field perpendicular to the plates, and of a uniform magnetic
field parallel to the length of the filament. If the plate A lies
in the plane x = o and the axis of z is taken to be parallel to
the magnetic intensity H, then Thomson^ showed that the
X and y co-ordinates at time t of an electrified particle, start-
ing with zero velocity from the plane .«• = o at the instant
/ = o, would be given by

'«^p{.-cos(lH.)} . . (.)

where m is the mass and e the charge of one of the particles.
By eliminating t the equation to the path can be obtained. It
is found to be a cycloid in the plane perpendicular to the
magnetic force. The greatest distance d which the particles
are able to travel from the plane .«• = o is determined by the
equation

^ = 2 - -^2 • • . . (3)

^ Cf. J. J. Thomson, "Conduction of Electricity through Gases," p. ii2.
Second edition.

^ - c H-

CONSIDERATIONS OF A GENERAL CHARACTER 9

Under these conditions, i.e. if the wire is taken to be coinci-
dent with the front of the plate A, the current received by the
plate B will depend on the value of Y.\W. If X/H* is less
than edjinty none of the ions emitted by the filament will
reach the plate B, whereas if X/H^ exceeds €dl2m all of
them will arrive at B. There is thus a critical value of
X/H'"^ for which the current from A to B jumps from zero to
the maximum value. If (X/H^y denotes this critical value
evidently

^rlin^i- ■ • • (4)

In actual practice the current does not jump with the
suddenness required by this theory. With very small values
of X/H^ the current is practically zero. In fact, recent ex-
periments by Owen and Halsall ^ and by the writer ^ show
that with a number of metals and under the best conditions
the current at this stage is well under one-thousandth part of
the maximum value. This state of affairs persists until at a
certain stage the value of the current begins to rise with in-
creasing X/H^. The rate of increase of the current is small
at first, rapidly becomes greater, and then falls off again ; so
that ultimately the current exhibits a slow asymptotic ap-
proach to the final maximum value appropriate to large
values of X/H^ This divergence between theory and ex-
periment is probably to be attributed to the fact that the
ions do not set out from the hot body with zero velocity.
We shall see later that at the moment of liberation the dif-
ferent ions set out with velocities which extend over a wide
range of values.

Although this lack of sharpness rather restricts the ac-
curacy of this method of measuring e/m, the values given
by it were quite exact enough to settle the nature of the
negative ions. The value given by Thomson's experiments
was c/m = 87 X 10' in E.M. units. This number agreed
quite well with the values which had been obtained shortly

» " Phil. Mag.," Vol. XXV, p. 735 (1913).
^Ibid., Vol. XXVI, p. 458 (1913).

lo EMISSION OF ELECTRICITY FROM HOT BODIES

before by Thomson and by Wiechert for the cathode rays,
by Lenard for the Lenard rays, and by Thomson for the
negative ions liberated from metals by the action of ultra-
violet light. Before these experiments were made, the
greatest value of ejm with which we were familiar was that
for hydrogen, the lightest chemical atom, in electrolysis. The
value for hydrogen is 9*649 x 10^ in E.M. units. The value
found for the negative ions coming from the carbon filament
was thus about 900 times as large. The importance of these
experiments can hardly be over-estimated. Taken in con-
junction with other experiments which served to establish the
view that the charge e carried by these ions was the same as
that carried by a monovalent atom in electrolysis, they showed
that the negative ions now under consideration were particles
of much smaller mass than the chemical atoms. In other
words, they proved that the carriers of negative electricity
from hot bodies were the negative electrons which are now
believed to form an important part of the structure of all
chemical atoms.

Later experiments have confirmed these conclusions and
extended the list of substances investigated. Owen^ using
a method similar to Thomson's found the value elm = 5 '65
X 10^ for the negative ions coming from a Nernst filament.
Wehnelt^ found that for the negative ions emitted by a
speck of lime on a hot platinum cathode the value of elm
was 1-4 X lo'^. His method was different from Thomson's.
He showed that when a speck of lime was placed on a hot
platinum cathode it formed the source of an intense beam of
negative ions. The path of this beam was made visible by
the luminosity it caused in the surrounding gas. The ex-
periment was arranged so that practically all the fall of po-
tential in the tube occurred close to the cathode, the rest of
the track of the ions being almost free from the influence of
the electric field. A uniform magnetic field H was then ap-
plied, so that the lines of force were parallel to the surface of
the cathode and thus perpendicular to the direction of pro-

J " Phil. Mag.," vi. Vol. VIII, p. 230 (1904).
2 " Ann. der Phys.," Vol. XIV, p. 425 (1904).

CONSIDERATIONS OF A GENERAL CHARACTER ii

jection of the ions. Under these conditions the path of the
ions is a circle of radius

m V
--TH • • ■ • (5)

in a plane perpendicular to the magnetic intensity, v the
velocity of projection of the ions is given by the equation
^mv^ = Ve, where V is the applied potential difference ; so
that

«/ 2V*

, ... (6)

The radius r of the path of the ions was measured by photo-
graphing the luminous track. The writer/ using a method
which will be described later,'^ found the following values of
ejm for the negative ions emitted by hot bodies : for platinum
I '45 X 10^ and for carbon 1-49 x 10^. It is probable that
the differences between the values of e/w found by all the
foregoing observers are due to errors of experiment and that
all the values are too low.

More recently a very accurate investigation has been
published by Bestelmeyer,' who used an improved form of
Wehnelt's method. He found elm = 1766 x 10^ E.M. units.
This result is to be regarded as of a far higher order of ac-
curacy than any of the preceding ones. It is unlikely to be
in error by as much as 0*5 per cent. An entirely different
method which preliminary experiments indicate to be capable
of high accuracy has recently been developed by Langmuir
and Dushman.*

The value of elm for the positive ions emitted by hot
bodies also was first measured by Thomson.^ The results
of the researches in this direction will be considered at length
later. ** At present we shall content ourselves with the general
statement that for the positive ions the values of elm have

1 " Phil. Mag.," vi. Vol. XVI, p. 740 (1908). ' P. 196, chap. vi.

» "Ann. der Physik," iv. Vol. XXXV, p. 909 (1911).
* " Phys. Rev.," ii. Vol. Ill, p. 65 (1914)-

' '• Conduction of Electricity through Gases," p. 217. Second edition
(Cambridge, 1906).

^ Chap. VI. p. 194 ; chap. viii. p. 261.

12 EMISSION OF ELECTRICITY FROM HOT BODIES

always been found to be as small as those occurring in elec-
trolysis. This shows that the positive ions liberated by hot
bodies are invariably structures of atomic or molecular di-
mensions.

General Experimental Methods.

The methods used in investigating the dependence of
thermionic currents on various physical conditions, such as
the temperature of the hot body, and the pressure and nature
of the surrounding gaseous atmosphere, naturally depend to a
considerable extent on the properties of the substance under
examination. For those substances which are available in the
form of wires or filaments, and which conduct electricity, as
well as for numerous other substances which, owing to the
magnitude of the effects to which they give rise, can be tested
in the presence of a hot metal on whose surface they are de-
posited, an electrical method of heating is most convenient.
Numerous experiments made on different substances, and by
various investigators, show that there is no considerable differ-
ence in the observed effects which arise from the employment
of an electric current as the heating agent, as compared with
those which arise when other methods of heating are used ;
provided the same temperature is attained, and the other
physical conditions are identical. Perhaps the most convincing
evidence in this connexion is furnished by some experiments
made with lime-covered cathodes by Fredenhagen,^ who, after
setting out to prove the contrary proposition, finally concluded
that the method of heating made no difference. No doubt the
electric and magnetic fields due to the heating current do influ-
ence the motion of the ions to some extent, but the effects
thereby arising are usually not of serious importance unless
very large currents are employed.^

The essential features of the type of apparatus most gener-
ally serviceable are exhibited in Fig. i. The filament A to be
tested is welded to stouter leads B and C. These in turn are

^ " Phys. Zeits.," Jahrg. 13, p. 539 (1912) ; " Leipzige. Ber.," Vol. LXV,

P- 55 (1913)-

^See, however, p. 61.

CONSIDERATIONS OF A GENERAL CHARACTER 13

welded or hard soldered to platinum wires sealed into the
glass bulb D. A lies on the axis of a cylindrical electrode E
of metal foil, or, preferably, gauze supported by the sealed-in
lead F. The tube H enables the bulb to be exhausted and
sealed off or connected to the apparatus for supplying various
gases, measuring the pressure, etc. The precise construction
of such a bulb depends on the nature of the substance A ex-
perimented with. If A is a platinum wire then all the metal
parts inside the bulb are best made entirely of platinum. The
whole apparatus can then be thoroughly cleaned with boiling
nitric acid and distilled water. Tungsten
filaments require to be electrically welded,
in an atmosphere of hydrogen, to the stout
leads which may be of iron or copper.
Carbon filaments have to be joined with
paste as in constructing incandescent lamps.
Most other materials are to be welded to
the supports if possible, otherwise hard
soldering may be employed. In experi-
ments of this character it is often of the
utmost importance not merely to secure
the chemical purity of the materials used,
but to make sure that not even the smallest
traces of gases are liberated in the bulb
during the course of the experiments. The
best way of accomplishing this is to heat the
tube D to a high temperature whilst it is exhausted by a
Gaede pump, assisted by a liquid air and charcoal condenser.
Meanwhile the wire A is glowed out electrically, and, in order
to drive every trace of gas out of the cylindrical electrode E,
it is desirable that this should be heavily bombarded by
cathode rays, obtained by applying a high negative potential
to A. To maintain the tube D at a high temperature without
its collapsing under the external pressure during the exhaustion,
it should be heated in a vacuum furnace. A suitable form of
furnace may be constructed with a heavy water jacketed brass
base provided with holes for the tube H and the leads B, C,
and F. The holes can be mad^ airtight with glass and seal-

Fio. I.

14 EMISSION OF ELECTRICITY FROM HOT BODIES

ing-wax, and an additional hole for the insertion of a
platinum thermometer or thermocouple is desirable. On the
base rests a large cylindrical brass bell jar, the line of contact
being made airtight with a rubber gasket. The brass cylinder
is balanced by weights attached to ropes passing over pulleys
so that it can easily be moved up and down. The furnace
itself is inside the brass cylinder, and rigidly attached to it.
It consists, starting from the inside, of a vertical cylinder of
some non-oxidizable metal such as monel metal or nickel ;
this is insulated by a layer of mica, over which is a winding
of nichrome strip having a suitable resistance and current-
carrying capacity. Between the nichrome winding and the
outer brass cylinder is a thick packing of fireclay and asbestos.
The leads to the nichrome strip and the exhaust can be let
in through the cover of the brass cylinder. This, as well as
the brass base, should be water cooled. With such an arrange-
ment, with the furnace exhausted to a pressure of about i cm.,
the experimental bulbs can be exhausted for several days at a
temperature of about 570° C. without collapsing. A vacuum
furnace of this type in actual operation is shown in Fig. 2.

Many experiments can be made without taking these
elaborate precautions, but we shall see later 1 that if we wish
to be sure of obtaining the effects which are characteristic
of the pure metals in the absence of a gaseous atmosphere we
cannot afford to dispense with the manipulation just described.

Almost all the phenomena under consideration are very
sensitive to small changes in temperature ; so that even when
it is not necessary to know the actual temperature of the
filament A it is essential that it should not vary. A very
sensitive temperature control is provided by a method which
involves the measurement of the resistance of the filament.
For this purpose, in carrying out the experiments, the filament
is made to form one arm of a Wheatstone's bridge which is
actuated by the battery supplying the heating current. The
arrangement of apparatus for measuring the thermionic current
which flows from the filament A to the cylinder E is shown
diagrammatically in Fig. 3. K, L, and M are the three other
^ See chaps, in. and iv.

CONSIDERATIONS OF A GENERAL CHARACTER 15
resistances which form the arms of the Wheatstone's bridge,

Fig. 2.

the bridge galvanometer G being provided with the key N.

U-=-

[-■■■ mvww ^^rmvvwK \ "T"

Vhvvwvw V

Fig. 3.

The main heating current is supplied by the battery P and

1 6 EMISSION OF ELECTRICITY FROM HOT BODIES

regulated by the system of rheostats Q, R, S. In these ex-
periments a very fine adjustment of the current is necessary.
This is supplied by placing two of the rheostats R and S in
parallel. Then if, for example, the total resistance of R is
very much larger than that of S a displacement of the slide
wire of R will make very little difference to the total resistance
of the combination R, S. In this way any degree of fineness
of regulation is obtainable. Since A is to be heated to a high
temperature it is necessary that a large current should flow
through it. Thus M must be a resistance comparable in
magnitude with A, and capable of carrying a large current
without heating. If then K and L are both large compared
with M and A, practically all the current will flow down the
arms M, A, and the arms K, L will not be in danger of over-
heating even when the bridge is adjusted. Although there
is a great disparity in the resistances of adjacent arms of
the bridge this arrangement is a very sensitive tempera-
ture indicator on account of the very large currents which
flow down the arms A, M. In making observations at a
constant temperature the bridge is adjusted initially and the
galvanometer spot is kept on the zero subsequently by altering
the controlling resistances Q, R, S. It is desirable to provide
a shunt for the bridge galvanometer G as the currents through
it may be quite large before the final adjustments are made.

In order to measure the thermionic current the cylinder E
is connected to a point V in the heating circuit through the
battery U, the switch T, and the current-measuring instrument
C. The battery U is required, in general, to drive the ions
across the gap AE. The nature of C depends on the mag-
nitude of the currents to be measured. If these are large an
ordinary galvanometer or even a millammeter may be used,
but for the small currents obtainable at low temperatures an
electrometer has to be employed. The writer has found ^ a
very convenient and universal arrangement to consist of a
quadrant electrometer set up so that various capacities or
resistances can be thrown in across the quadrants. For the
smaller currents the time rate of deflections are th^n measured
i« Phil. Mag.," Vol, XXII, p. 675 (igii),

CONSIDERATIONS OF A GENERAL CHARACTER 17

either with or without additional capacity across the quadrants.
For the larger currents the steady deflections across the re-
sistance are observed.

For measuring the temperatures of the filaments various
methods have been employed. For those materials, such as
platinum and tungsten, whose resistance as a function of
temperature is known with sufficient accuracy it is most con-
venient to deduce the temperatures directly from the measured
values of the resistance. For exact work it is necessary to
take account of the fact that the temperature falls off towards
the ends of the filament, and is uniform only in the middle.
This difficulty can be overcome if the cylinder E is divided by
horizontal sections into three separate parts, the upper and
lower cylinders then functioning as guard rings. It is also
important that the resistance-temperature calibration should
be made under the conditions of temperature distribution
obtaining in the experiments. This can be secured by placing
minute fragments of salts of known melting-point on the
central portion of the wire or filament after it has been removed
from the experimental tube. The wire is then heated electri-
cally in a suitable atmosphere and the resistance at which the
salts melt determined. The observation of the melting of the
salts is made with a low-power microscope. It is desirable
that some of the salts chosen should have their melting-points
in the temperature region under investigation. The pieces of
salt should be very minute, otherwise their temperature will
not be the same as that of the filament on which they are
placed. In some cases small bits of fine metal wire or foil can
be used instead of salts. A list of fixed temperatures which
are often useful in this kind of work is given in the following
table. The melting-point of tungsten is the result of an ac-
curate determination by Langmuir.^ The remaining tempera-
tures above the melting-point of iron (1503° C.) are taken
from the "Recueil de Constantes Physiques," published by
the French Physical Society in 191 3, the others are taken
from a list of reliable fixed points supplied by Dr. J. A.
Harker to the Cambridge Scientific Instrument Company : —

1 •• Phys. Rev.," Vol. VI, p. 138 (1915).
2

1 8 EMISSION OF ELECTRICITY FROM HOT BODIES

Temperature of— Degrees Centigrade.

Liquid hydrogen - 253

„ oxygen - 182

Melting ice o

Boiling-point of water at 760 mms. pressure . . 100

„ of naphthalene at 760 mms. pressure . 220

Melting-point of tin . » 23a

,, of lead ...... 327

,, of zinc ...... 419

Boiling-point of sulphur at 760 mms. pressure . . 445

Melting-point of aluminium 657

,, of sodium chloride .... 800

„ of silver (in air) 955

„ of silver (in reducing atmosphere) . 962

„ of gold 1064

„ of K2SO4 1070

„ of nickel ...... 1427

„ of iron 1503

„ of palladium 1542

„ of platinum 1755

„ of zirconium 2350

„ of iridium 2360

„ of tantalum 2798

„ of tungsten 3267 + 30

The resistance method of deducing the temperature has
the advantage that it does not introduce any complications
into the experimental bulbs. On the other hand, it often
involves a separate research into the resistance-temperature
relations of each substance investigated, and moreover, the
resistance of some substances is not a sufficiently definite
or sensitive function of temperature. The method of most
general applicability is the thermocouple, but this is difficult
to employ in the case of fine filaments on account of the local
reduction of temperature caused by its presence. In any
event the thermocouple should be made of very fine wire,
and a calibration under conditions as near as possible to the
experimental should be carried out, as with the resistance
method. The couple should be welded to the centre of the
hot wire if this is possible, or it may be cemented with pla-
tinum chloride solution, afterwards converted into platinum
by heating.^ For temperatures up to about 1500° C. couples
of platinum and the alloy 90 per cent platinum +10 per cent

^ Deininger, " Ann. der Phys.," iv. Vol. XXV, p. 292 (1908).

CONSIDERATIONS OF A GENERAL CHARACTER 19

rhodium are satisfactory. For still higher temperatures it is
probable that tungsten-molybdenum couples could be used.

Where these electrical devices are inapplicable, optical
methods may be employed. The easiest of these methods
is to compare the intrinsic brightness of the filament with
that of a second filament, used as an intermediate standard,
whose brightness is regulated by controlling the power sup-
plied to it. The intermediate standard is finally calibrated
against a surface of the same material heated in a furnace
to known temperatures. Up to the present optical methods
have not been much used in this kind of work.

The writer ^ has pointed out that some of the thermionic
properties of bodies are well adapted for development into
thermometric methods at high temperatures, but the de-
velopment of the technique has not been sufficiently rapid
for such methods to be considered practical at the present
time.

As an illustration of the application of the thermocouple
method reference may be made to an apparatus used by Dein-
inger.^ This apparatus represents several variations from
Fig. I, which are of advantage for special purposes. The
upper lead B of Fig. i is bent round inside the bulb so as
to pass downwards outside the cylinder E and come out of
the bottom of the bulb alongside C. The two leads of the
thermocouple are also brought down to the bottom of the
bulb. All four leads are mounted in a stopper which is
fitted to the bulb by a mercury-sealed ground glass joint.
The cylinder E is provided with a vertical slit through which
the wire A can pass. Thus the whole system of filament
and thermocouple can be withdrawn from the apparatus.
In order readily to interchange the filaments the welded
joints between A and B and A and C respectively are
replaced by small screw clamps. This type of arrangement
has obvious advantages where it is desired rapidly to change
the material under investigation. On the other hand, it has
not been found feasible, up to the present time, completely

1 " Phys. Rev.," i. Vol. XXVII, p. 183 (1908).
« "Ann. der Phys.," iv. Vol. XXV, p. 288 (1908).
2 *

20 EMISSION OF ELECTRICITY FROM HOT BODIES

to eliminate traces of gas from apparatus containing ground
glass joints ; so that this type of apparatus is useful only
when the effects of such traces of gas are relatively un-
important.

A convenient arrangement for making rapid qualitative
tests of the sign of the ions emitted by hot wires has re-
cently been described by Hopwood.^ This consists in bring-
ing an electrically -charged rod near a long loop of the
electrically-heated wire which is connected to earth. The
loop will only be deflected provided it does not emit ions
of the sign opposite to the charge on the rod.

Relation between the Currents and Electro-motive
Force and Gas Pressure.

The first experimental investigation of this question was
made by McClelland ^ with an arrangement similar to Fig. i
in its main features. In all these experiments the tempera-
ture of the filament is kept constant and the general character
of the results to be described is independent of the nature of
the material used, provided that the filaments have been
heated for a considerable length of time (see pp. 60 and 182).
At pressures comparable with atmospheric the relation between
the current and the difference of potential maintained be-
tween the filament and the cylinder is similar to the left-hand
half of the curve shown in Fig. 4, although this figure actu-
ally refers to another case. With low voltages the current
is proportional to the applied potential difference, but as the
potential difference increases, the rate of increase of the
current gradually falls off until finally saturation is attained.
There is thus a definite limit to the number of ions liberated
by the glowing filament in unit time. In air at low tempera-
tures this description applies only when the filament is posi-
tively charged ; there is no appreciable current when the wire
is charged negatively. At higher temperatures similar results
are obtained whether the filament is charged positively or ne-

1 " Phil. Mag.," Vol. XXIX, p. 362 (1915).

2 " Camb. Phil. Proc," Vol. XVI, p. 296 (igoi).

CONSIDERATIONS OF A GENERAL CHARACTER 21

gatively, the ratio between the saturation current with the wire
negative and that with the wire positive increasing continuously
with rising temperature. In these respects the observations
agree with the earlier experiments described on page 3.

With pressures of the order of i millimetre of mercury the
current-E.M.F. curves were found to be entirely different.
With the filament negatively charged there was no indication
of saturation. The current in general increased more rapidly
than the first power of the potential difference. The effects
observed with a positively charged wire at these pressures are
exhibited in Fig. 4, which actually refers to this case. At
intermediate voltages there is evidence of saturation, but this

100
00

I h- ] — VA — I — I I I I M — I— H — \-hn-\ — 1 70

O I 1 1 1 1 1 1 1 1 1 1 1 M^-1 **H 1 1 160

MO wT"^ tit »• 5w
VoVtt.
Fio. 4.

stage is succeeded by a stage in which the current again in-
creases with rising potential difference.

McClelland showed that these phenomena could be ex-
plained in a general way on the hypothesis that the ions
liberated at or near the surface of the filament were able,
under the accelerating influence of the electric field, to produce
new ions by impact with the neutral molecules with which
they collided. In the case of the positive ions this increase
in the current due to ionization by impact did not begin to
make itself felt, in the example shown in Fig. 4, until there
was a difference of potential of over 200 volts between the
electrodes. The existence of saturation with lower potentials
showed that all the ions initially liberated were being collected
by the cylinder, and, as the current was independent of the

(

i —

"Tl

2 2 EMISSION OF ELECTRICITY FROM HOT BODIES

electromotive force in this region, there was no additional
current depending on the energy of the impacts. The absence
of saturation with the currents from the negatively charged
wire makes it necessary to suppose that ionization by col-
lision sets in before the stage at which saturation is reached.
Thus the part <«, b of the curve in Fig. 4 is missing when the
wires are charged negatively. Another consequence of this
interpretation is that ionization by impact is effective with a
smaller fall of potential for negative than for positive ions.
The hypothesis of ionization by impact had previously been
put forward by Townsend and J. J. Thomson to account for
somewhat similar phenomena exhibited by other sources of
ionization. McClelland's experiments seem, however, to have
first indicated definitely that positive ions could give rise to
new ions by collision.

A more detailed examination of the relation between cur-
rent, pressure, and electromotive force with negatively charged
wires has been made by H. A. Wilson. ^ Some of the results
obtained by Wilson at pressures ranging from 0'0036 mm. to
760 mm. are shown in Figs. 5 and 6, If the increase of cur-
rent beyond the horizontal line corresponding to the lowest
pressure (0'0036 mm.) is due to ionization by collision, Wil-
son showed that, according to Townsend's theory,

Y r _ (NE/>a/V)log''/a _ (NE/)6/V)log''/a\

provided WjpaXog Va is greater than 200. In this equation
«6 is the number of negative ions which reach the cylinder in
unit time, «« is the number emitted by the hot wire (of circular
section) in the same time, V is the applied potential difference,
p the gas pressure, b the radius of the cylinder, a that of the
wire, N the number of ionizing impacts per moving ion per
cm., and E the potential fall necessary to acquire the ionizing
energy (ionizing potential). This formula was found to re-
present the experimental results satisfactorily, with N = 3 04
and E = 177 (volts). The values of the constants are in
satisfactory agreement with those deduced by Townsend from

I " Phil. Trans., A.," Vol. CCII, p. 243 (1903).

CONSIDERATIONS OF A GENERAL CHARACTER 23

experiments with ionized air at ordinary temperatures, when
allowance is made for the difference in the number of mole-

1/m.ts
Fig. 5.

cules in unit volume of a gas at a definite pressure due to
change in temperature. The results point to the rather im-

I50r

I/O ITS,

Fig. 6.

portant conclusion that ionization by impact depends solely
on the nature of the molecules, and their distance apart, and
has nothing directly to do with the temperature of the gas.

24 EMISSION OF ELECTRICITY FROM HOT BODIES

Referring to Figs. 5 and 6, we see that both at very high
and at very low pressures the current is independent of the
electromotive force except at the lowest voltages. In the
former case the molecules are so crowded together that the
ions never move freely long enough to acquire the energy
necessary for impact ionization : in the latter case there are no
molecules to collide with. Thus ionization by collision will
occur only over an intermediate range of pressures whose ex-
tent is determined by the magnitude of the applied potential
difference. In fact, if we maintain a constant potential on the
filament, and gradually increase the pressure, starting from
zero, the current will increase to a maximum value, and then
fall off again. This experiment was made by Wilson, who
showed that the pressure for the maximum current agreed
with the value calculated from equation (7).

A series of observations of the relation between the currents,
with the wire positively charged, and the electromotive force, at
different pressures, was made by the writer,^ using a platinum
wire in an atmosphere of oxygen. The curves are similar to
those shown in Figs. 5 and 6, except that, at a given pressure,
the potential difference at which ionization by collision begins
to make itself felt is much higher than when the wire is charged
negatively. The increase of the current to a maximum
value at intermediate pressures when the applied potential dif-
ference was kept constant was also observed when the wire
was charged positively. These results could be explained by
the theory of ionization by collisions on the assumption that
positive ions, as well as negative, were effective, and led to an
estimate of the magnitude of the ionizing energy for the posi-
tive ions from hot bodies similar to that which had been de-
duced by Townsend for the positive ions set free in gases by
other agencies.

Recent experiments by Pawlow ^ and by E. v. Bahr and
J. Franck,^ using a more direct method, have led to more de-
finite information as to the impact ionization caused by the

1 " Phil. Trans., A.," Vol. CCVII, p. 8 (1906).
''"Roy. Soc. Proc, A.," Vol. XC, p. 398 {1914).
*" Verb, der Deutsch. Physik. Ges. Jahrg.," 1914.

CONSIDERATIONS OF A GENERAL CHARACTER 25

positive ions from hot bodies. These researches show that
ionization by impact sets in at ionizing potentials which are
practically the same both for positive and negative ions. At
these low potentials, however, the positive ions are compara-
tively inefficient, and their ionizing power only becomes com-
parable with that possessed by the negative ions at much
higher potentials. It is this last-named property which ac-
counts for the observations recorded by McClelland and the
writer.

The Electron Theory.

We have seen that in 1 899 Thomson showed that the
negative ions liberated from a hot carbon filament at a low
pressure were electrons. About that time a considerable
amount of evidence had been accumulated which indicated that
with progressively increasing temperatures and diminishing
pressures, the proportion of the number of negative to the
number of positive ions liberated at the surface of hot metals
became increasingly greater. McClelland^ showed further
that at fairly low pressures the currents from a negatively
charged platinum wire were influenced little, if at all, by
changes in the nature and pressure of the surrounding gas.
At the same time the electron theory of metallic conduction
had made considerable advances owing to the researches of
Thomson,^ Riecke,^ and Drude.* According to this theory the
conductivity of metals arises from the presence in them of an
atmosphere of electrons. These are supposed to be in violent
motion like the molecules of a gas according to the kinetic
theory of gases. The effect of an applied electric field is to
superpose on the haphazard heat motion of these electrons a
definite average velocity of drift in the direction of the electric
potential gradient. This drifting of the electrons constitutes
the electric current. The energy of the heat motion of these

»"Camb. Phil. Proc," Vol, X, p. 241 (1900).

* " Applications of Dynamics to Physics and Chemistry," p. 296. London
(1888) ; Congris Int. de Physique, Paris (1900); " Rapports," Vol. Ill, p. 138.

»" Ann. der Phys.," Vol. LXVI, pp. 353, 545, 1199 (1898); Vol. II, p. 835
(1900).

*/6trf.. Vol. I, p. 566 ; Vol. Ill, p. 369 (1900).

2 6 EMISSION OF ELECTRICITY FROM HOT BODIES

internal "free electrons," as they are often called, will increase
with rising temperature ; and one might expect that at suffi-
ciently high temperatures this energy would be great enough
to carry them out through the surface of the hot body. Under
these conditions the body would be capable of discharging
negative but not positive electricity and the expected pheno-
mena would be similar to those which appeared to characterize
the discharge of negative electricity from hot bodies, so far as
they were then known. The probability of such a view ulti-
mately proving correct was pointed out by Thomson ^ in 1 900.
From this standpoint the escape of negative electricity from
hot bodies is closely analogous to the escape of the molecules
of a vapour from a solid or liquid during evaporation. It is,
in fact, a kind of evaporation of electricity. The first calcula-
tions of the thermionic currents to be expected at different
temperatures, on the view that the discharge from a negatively
charged conductor was carried by electrons shot out owing to
the vigour of their heat motions, were given by the writer,^
who also adduced fresh experimental evidence in support of
his conclusions. The theory of these effects will be considered
at length in the next chapter ; but for the sake of brevity and
clearness the historical order of development will no longer be
strictly followed.

1 " Paris Rapports," Vol. Ill, p. 148.

> " Camb. Phil. Proc," Vol. II, p. 286 (1901) ; " Phil. Trans., A.," Vol. CCI,
p. 497 (1903).

CHAPTER II.

theory of the emission of electrons from hot bodies.

Thermodynamical Considerations.

The experiments recorded in the last chapter, and others to
be described later, show that electrons are continually being
emitted by hot solids even in a good vacuum. Consider the
case of a hot solid or liquid, whose vapour pressure is negli-
gible, contained in an exhausted vessel whose walls are in-
sulators of electricity, the whole system being maintained at a
uniform temperature T. Then there will be an accumulation
of electrons in the vacuous space arising from the emission re-
ferred to. This accumulation will not go on indefinitely be-
cause some of the electrons, on account of their heat motion,
will always be returning to the hot body from which they
started. In consequence of these two processes a balance will
ultimately be established when as many electrons return to the
hot body as are emitted from it in any given interval. In this
steady state there will be a definite number n per unit volume,
on the average, in the vacuous enclosure, and they will exert
a definite pressure /. If the enclosure is provided with a
cylindrical extension in which an insulating piston can move
backwards and forwards, this pressure/ can be made to do
work against an external force. For simplicity we may sup-
pose that the walls of the enclosure and the cylinder and
piston do not emit any appreciable number of electrons at the
temperature under consideration. They are to be regarded
simply as geometrical boundaries impervious to electrons.

The relation between the pressure of these electrons and
the temperature of the enclosure can be found by an applica-
tion of the second law of thermodynamics. The advantages

28 EMISSION OF ELECTRICITY FROM HOT BODIES

of this method are that the results are independent of any
suppositions about the condition of the electrons inside the
hot body, and that the conclusions arrived at will possess a
degree of certainty attainable in no other way, inasmuch as
the second law of thermodynamics is one of the very few
principles in physics to which there are no exceptions.

We know that it follows from the second law of thermo-
dynamics that the entropy S of any system is a complete dif-
ferential when T and / or T and v, where v is the volume of
the system, are taken, respectively, as pairs of independent
variables. For our present purpose a knowledge of the total
entropy S of the system is not required. All we need is an
expression for dS, the increment in the entropy caused by a
motion of the piston. If </> is the change in the energy of the
system which accompanies the transference of each electron
from the hot body to the surrounding enclosure, then

^S = = I dinv<^) + pdv \
Thus 0, = (,.,*.. »^)/t ...(.)

S\ V 'd(n(f))

:dTJ^ T ^T

(3)

^2g

By equating the values of ^-tj given by (2) and (3), we find

T^ =/+«</> . . . (4)

since -y^ = 0 unless the piston is quite close to the emitting

surface. Now the pressure / exerted by the electrons
on the piston will be the same as that exerted at the
same temperature by a perfect gas having the same number of
molecules in unit volume. In the case that we are considering
it is to be remembered that the concentration n is so small that

EMISSION OF ELECTRONS FROM HOT BODIES 29

effects arising from the mutual repulsions of the electrons are
negligible. Thus

p= nkT . . . . (5)
where k is the gas constant reckoned for a single electron. By
substituting the value (5) in (4) we find

^-,4^^T ..... (6)

/_i_ ^T .... (7)
or « = A^j ^T

where A is independent of T. We have thus found a relation
between the number, per unit volume, of the electrons which
are in equilibrium with the hot body at a point not too near
its surface, and the change of energy which occurs when an
electron is emitted by the hot body.

In the experiments on thermionic currents we do not
measure the number n of electrons in equilibrium with a hot
body but the number N emitted by unit area of its surface in
unit time. There is, however, a simple relation between these
two quantities. We shall assume as a sufficiently close ap-
proximation to the truth for our present purpose that all the
electrons which return to the hot body from the surrounding
space are absorbed by it. The limitations thus introduced
will be considered later. ^ According to the principles of the
kinetic theory of gases, which there is every reason to believe
will apply with exactness to the behaviour of the external
atmosphere of electrons, the number N' which reach unit area
in unit time is

I'kT

N' = «V . . . . (8)

where m is the mass of an electron. But in the state of
equilibrium contemplated the number of electrons emitted by
the hot body in unit time is equal to the number which return
to it. Thus

N = N'

2Trm

Jj—ThJ kT"^.- . (9)
\ 2'rrm

1 Cf. p. 48.

30 EMISSION OF ELECTRICITY FROM HOT BODIES

If e is the electronic charge, the saturation current i per
unit area of the hot body is

/ = Ne . . . . (lo)

So that if we knew the relation between ^ and T, equation
(9) would completely determine the relation between the
saturation current and the temperature at all temperatures if
its value at a single temperature were given.

The Relation between <f> and T.

An approximate idea of the way in which ^ varies with T
may be obtained by a rather different thermodynamic argu-
ment. We consider ^ two conductors A and A' of the same
material, each of sufficiently large size. A and A' are main-
tained respectively at the temperatures T and T' and are con-
nected by a thin conductor of the same substance covered with
an insulating material impervious to electrons. Each con-
ductor is surrounded by an evacuated chamber with insulating
walls, and by means of a suitable arrangement of pistons and
cylinders electrons can be transferred reversibly from one
chamber to another in the manner described below.

In general, although the parts A and A' are connected by
a conductor their surfaces will not necessarily be at the same
potential on account of the difference of temperature. Such
a difference of potential may arise, for example, if the contact
difference of potential of metals depends upon temperature.
Let us suppose that the potentials of A and A' when connected
together are V and V respectively, and that V is greater than
v. Surround A by a surface maintained at the potential V.
The effect of this will be to reduce the pressure of the electrons
from the equilibrium value/ characteristic of A at temperature
T to the value /<, outside the equipotential surface referred to,

where

<V' - V)
log/, = log/ - ^^ . . (II)

Equation (11) follows from the supposition that the pres-

1 Cf. O. W. Richardson, " Phil. Mag.," Vol. XXIII, p. 602 (1912) ; " Electron
Theory of Matter," p. 448. Cambridge (1914).

EMISSION OF ELECTRONS FROM HOT BODIES 31

sure of the electrons obeys the law of a perfect gas / -» nkT.
No work against the electrical forces will now be done if we
remove some of the electrons which have passed through the
equipotential surface from the chamber surrounding A to that
surrounding A'.

Now suppose that N^ electrons are taken out of A (Fig. 7)
by means of the piston and cylinder working in the walls of
the surrounding chamber, at temperature T, potential V, and
pressure /<,• They are then caused to expand adiabatically
to the temperature T'. The expansion is continued iso-
thermally at T' to the pressure /', which is the equilibrium
pressure of the electrons outside A'. They are then allowed

'•xya^ma.v.wMKMmM,-}

■y/^//.',y.'^./,vmnrff.

vv,-ir;?mm.-v»w/.-rm)/f/frrMMMWJJ7m

/>'

Fig. 7.

to condense in A' and finally to run down the connecting
conductor to A, Since the conductor varies in temperature
from point to point they will absorb heat in it to the amount

Noel (jdY, where a is the quantity of heat liberated when
Jt'

unit quantity of electricity flows down unit difference of tem-
perature under these conditions. If we apply the equation

fz/O

I -::^ = o to this reversible cycle, we find after calculating the

amount of work in each of the processes already indicated^
and substituting from (i i), that, if y is the ratio of the specific
heats of the electrons at constant pressure and at constant
volume,

32 EMISSION OF ELECTRICITY FROM HOT BODIES
^-:^,+ k[ log/ - log/ - ^^ (logT - log T)

+ e/r,Y'^T = 0 . . . (12)

or log/ - -^ logT + ^ + Ul^dT = A . (13)

where A is independent of T. Differentiating this equation
by T and substituting from (5) we find

I'bn _ II ^ ^^ t^ (ia\

« yr ~ ^f^i T "^ It ^ " >^ ^T ~ /^ f ' ^ ^^

But from (6)

I Dw <^

«yr " /^

hence ^-| - ^^— -^ - 60- . . . (15)

The value of a in these expressions will not in general be
quite the same thing as the specific heat of electricity measured
with voltaic currents. The reason for this is that j> refers to a
virtual displacement of the electrons, and the conditions of
motion affecting such a virtual displacement will not in general
be the same as those for a steady flow.^ However, the dif-
ferences arising in this way are negligible unless the conditions
affecting the motion of the electrons vary very rapidly with
temperature, and, in any event, there are good reasons for
believing that such differences are only capable of giving rise
at the most to effects of the sameiorder of magnitude as those
arising from the specific heat of electricity. Without being able
to enter into the details of the conditions, about which nothing
is known definitely, affecting the motion of the electrons inside
the conductor, we may conclude that a- is a quantity com-
parable with the measured value o-q of the specific heat of
electricity.

Among the substances where Thomson effects have been
investigated the value of o-q is greatest for bismuth.^ For this
substance the value of ea^ is about one-tenth of /^/(y - i), if

1 Cf. N. Bohr, " Phil. Mag.," Vol. XXIII, p. 984 (1912).

EMISSION OF ELECTRONS FROM HOT BODIES 33

we take 7 = 5/3. As regards the other metals <t^ is positive for
some and negative for others. It is evident that ea will in
general be much less than kl{^ - i) ; so that the greater part
of the variation of <^ with T will be determined by the first
term on the right-hand side of (15). As a first approximation
then we may put e<r = o and

d<^

nt*

J)T

7 -

\j\

»<^o

• . (16)

To this degree of approximation we see from (9) that

/= Ne = AT2^-*o/*T . . . (17)

where both A and <^o are independent of T.

The first application of the principles of thermodynamics
to the formation of ions by hot bodies was made by H. A.
Wilson^ in 1901. Later developments are given in papers by
Wilson ^ and the writer.^

The Classical Kinetic Theory.

According to a well-known theorem of the kinetic theory
of gases, there is a simple relation between the number of
molecules per unit volume at any two points of a system at
a uniform temperature and the work required to displace a
molecule from one point to the other. Applying this theorem
to the case now under consideration, it follows that if n^ is the
number of free electrons in unit volume of the interior of the
hot body, the notation being otherwise as before,

n = «i^-*/" .... (18)

Combining this result with the relation already obtained be-
tween the number N emitted in unit time and the number n
in unit volume of the space outside the hot body in the state

1 " Phil. Trans., A.," Vol. CXCVII, p. 429 (1901).

«/6t</., Vol. ecu, p. 258 (1903) ; " Phil. Mag.," Vol. XXIV, p. 196 (1912).

* " Jahrbuch der Radioaktivitaet," Vol. I, p. 302 (1904) ; *' Phil. Mag.," Vol.
XXIII, pp. 601, 619 (1912) ; ihid.. Vol. XXIV, p. 740 (1912) ; ihid.. Vol. XXVIII,
p. 633 (1914).

34 EMISSION OF ELECTRICITY FROM HOT BODIES
of equilibrium, the saturation current per unit area is given by

If «i and ^ are independent of T this is of the form

? = AiT»^-v*T, . . . (20)
and if n^ is proportional to T^'* and ^ is independent of T,

i = K^H-i>^m . . . (21)

In these equations A^ Ag and ^^ are, under the suppositions
named, independent of T. Equation (21) is of the same form
as (17). Equation (19) can readily be deduced ^ by a direct
calculation of the number of electrons which escape from unit
area of a metal in unit time, under the supposition that the n^
free electrons present in unit volume of the interior have a
velocity distribution in accordance with Maxwell's law, and
that each has to do an amount of work ^ before it can escape
from the surface.

The various calculations which have been referred to in
this section all assume that the behaviour of the electrons in
metals is governed by the laws of the classical dynamics.
This assumption is found to lead to difficulties in other ap-
plications of the electron theory of metallic conduction. For
example, the optical properties of metals lead us to conclude
that the number of free electrons present in them is quite large,
and if this large number of electrons possessed the kinetic
energy which the classical dynamics endows them with, the
specific heats of metals would be very much larger than those
actually observed. The general course of the specific heats of
metals quite precludes the view that there is any considerable
number of free electrons present if the behaviour of the elec-
trons is governed by the laws of the classical dynamics. These
are only a few of the difficulties presented by the application
of the classical dynamics in this field. It would take us too
much out of our course to discuss this question at all fully.
But it appears that a way of escape from most, if not all, of
these difficulties opens up if we reject the classical dynamics

10. W. Richardson, " Camb. Phil. Proc.," Vol. XI, p. 286 (1901).

EMISSION OF ELECTRONS FROM HOT BODIES 35

and substitute for it the group of hypotheses, conveniently
termed the quantum theory, which has recently been so suc-
cessful in connexion with the theory of radiation, the properties
of bodies at very low temperatures, the photo-electric effect,
and the theory of the structure of atoms.

The Quantum Theory.

The bearing of the quantum theory on the emission of
electrons by hot bodies has recently been considered at some
length by the writer.^ It appears that, according to the
quantum theory, equation (18) is not universally true, as it is
according to the classical dynamics, but is only a limit to which
a more general expression approaches when the temperature
becomes sufficiently high. The quantum theory is not yet
completely developed, and there is a certain amount of disagree-
ment as to the subsidiary hypotheses to be made in connexion
with it. The nature of these hypotheses will affect the ex-
pression found for the general form of which (18) is a limit.
The calculations are therefore to be regarded as of a provi-
sional character, subject to possible modification as the quantum
theory is developed. In the paper referred to, a calculation of
the general expression corresponding to (18) has been made
on the following assumptions : —

(1) That the heat energy of a gas can be analysed into the
vibrations in its elastic spectrum and that the entropy of this
system of vibrations can be calculated according to the method
given by Planck in developing the theory of radiation ;

(2) That the elastic spectrum is limited by the number of
molecules according to the principles successfully used by
Debye in calculating the specific heats of solids ;

(3) That Planck's hypothesis of zero point energy has to
be taken into consideration ;

(4) That the interchange of energy between gas and radia-
tion takes place by quanta, the corresponding frequencies
being twice as great in the gas as in the radiation, in accord-
ance with the principle that the pressure exerted by a given

1 " Phil. Mag.," Vol. XXVIII, p. 633 (1914).

36 EMISSION OF ELECTRICITY FROM HOT BODIES

electro-magnetic radiation has twice the frequency of that radia-
tion ; and

(5) That the velocity of propagation of the elastic vibrations
is proportional to the square root of the energy of the cor-
responding vibration.

The first four assumptions have been made by various
writers on the quantum theory, and, so far as the writer is able
to judge, have led to results in different directions which are
in agreement with experience. The fifth hypothesis appears
to be required to make the energy of the molecules take the
equipartition value at high temperatures, and although at first
sight it appears to contradict the known properties of sound
waves, it is not at all certain that the contradiction is a real one.
These hypotheses have been used by W. H. Keesom ^ to calcu-
late the equations of state of gases and the thermoelectric pro-
perties of metals at very low temperatures. The results have
been found to accord with the behaviour of helium at low tem-
peratures and with the general course of thermoelectric
phenomena in the same region of temperature. Moreover, a
form of electron theory of metallic conduction developed by
Wien ^ along similar lines has been successful in removing a
number of difficulties which the theories based on the classical
dynamics were unable to, overcome.

Working from the assumptions just considered, instead of
arriving at (18), which may be written

/ N 9 I Ti y^dy 9 i r'"' y^dy , I - e-"-^ , ^

we are led to

where w^ and w^ are the potential energies of an electron at
the points in the system indicated by the suffixes i and 2 re-
spectively, and x^ and x.^ satisfy the equations : —

f{x^ = Ci^i - g and f{x^ = Q^.^ - g ; . (24)

^ " Comm. Phys. Lab. Leiden.," Supp. No. 30 to No.s. 133-144 (1913).
2 "Columbia University Lectures," p. 29. New York (1913).

EMISSION OF ELECTRONS FkOM HOT BODIES 37
in which

^^""^ 'Ao^ - 1' ^ 5 N/4'' V9n;'

2 M^T UirvM
« " 5 NA2 V 9N / '

(25)

M is the molecular weight of the gas, h is Planck's constant,
N is the number of molecules in one gram molecule of a gas
(Avogadro's number), v-^ and v^ are the volumes which would
be occupied by one gram molecule of the gas under the con-
centration which it has at the points I and 2 respectively.
The respective numbers of molecules per c.c. at these points
therefore are

N/ A N/

«i = / and «5 = / .

It is clear that the right-hand side of (23) when considered
as a function of T, n^ and n^ will in general be quite compli-
cated. It simplifies very considerably, however, when the
quantities x^ and x^ are either both very small or both very
large, or when one of them is very small and the other very
large. It will be seen from (24) and (25) that when C is small
X is large, and vice versa, and that the value of;ris completely
determined by that of C. The quantities N, k, and h entering
into C are universal constants ; so that the value of C is de-
termined by that of the product WZvk It is evidently greater
the greater the molecular weight of the gas, the higher the
temperature and the lower the concentration. We infer from
this that the behaviour of (23) appropriate to small values of
C will at a given temperature occur at much smaller concentra-
tions for an atmosphere of electrons than for an atmosphere of
an ordinary gas, on account of the smallness of the mass of
an electron compared with that of an atom.

When Q and Cj are both large, and hence x^ and x^ are
both small, (23) reduces, after making use of (24) and (25), to

w/j - tt/j = kT log -1 = kT log ^ . . (26)

This agrees with (22), since w^ - w^ is equal to ^ for this case.
Thus (22) is seen to be a limit approached by (23) for high

38 EMISSION OF ELECTRICITY FROM HOT BODIES

temperatures, large molecular weights, and small concentra-
tions. These conditions are those in which, from the point of
view of this form of the quantum theory, the behaviour of
gases conforms to the requirements of the classical dynamics.

When Cj and C2 are both small and x^ and x^ both large
(23) again reduces to a comparatively simple expression, which,
although of importance from the standpoint of the electron
theory of the behaviour of metallic conductors, has no im-
mediate application to the question now under consideration.

According to the electron theory of the optical properties
of metals, the number of free electrons present in the interior
of a metal is comparable with the number of atoms, and is
therefore of the order 10^'. This conclusion is also supported
by a number of other lines of argument. Now the largest
thermionic currents which have been observed in a vacuum
are of the order of a few amperes per square centimetre, which
corresponds to an equilibrium number n of about 10^* at the
temperature of the experiments. As a rule, n would be very
much less than this. In any event, the concentrations of the
external and internal electrons are seen to be of entirely dif-
ferent orders of magnitude. For the internal electrons in fact,
C is small and x large, or at any rate approximates closely
to this condition for the metals which are good conductors ;
whereas for the external electrons C is large and x small.
We see, therefore, that it is the third of the alternatives con-
sidered above which is of interest from the standpoint of the
theory of the emission of electrons from hot conductors.

In this case (23) can be shown to reduce to

«2 = «T3'*^C,.rj>-<"'^-«'^w*T . . (27)
47r/3^MA3'*

where

a =

and

g{C,x^) =^{1 - e-''^ye^''^-^^'^^\ . . (29)

or, using (8),

/ = Ne =

"W -^^^^^^^''''^>~ ' '^' • (30)

2j2_

EMISSION OF ELECTRONS FROM HOT BODIES 39

A numerical computation shows that over the range
1000' K. to 2000° K., ^C, x^ can be replaced without serious
error by the expression «i^>'^, where a^ — '473 and ^j
is about yV as large as the values of the factor iv)^ - Wx^lk
which would be deduced if the equation (30) were applied to
the experimental results given by platinum. In interpreting
the results of this computation it is assumed that, over the
range referred to, »i = N/^i can be considered to be independ-
ent of the temperature. At the higher temperatures this as-
sumption may not be correct, and the value of a^ would thereby
be modified. In any event, a^ does depend on the temperature
(it is sensibly equal to unity at all temperatures below 1000"
K.), and the variation of v^ with T is not likely to affect the
general character of the conclusions to be drawn. Neglecting
the variation of v^ with T it follows that the relation between
the saturation current and the temperature is of the form

/ = A2'P^-*2'T , . . (31)

where

over a range from iO(X)° K. to 2000° K. approximately, and

b^ = (m/2 - tt/i - b^k)\k . . . (33)
It will be noticed that (32) is of the same form as (17) which
was given as a very close approximation by the thermodyna-
mic theory. Since the thermodynamic theory rests on con-
siderations involving a high order of certainty, this agreement
is to be regarded as a point in favour of the quantum theory.
It will also be noticed that according to (32) the constant A,
has the same value for all substances except for the compara-
tively small differences in the quantity a^ which has the
numerical value 0473 in the particular case considered.

Contact Difference of Potential.

There is an intimate connexion between the rate of emis-
sion of electrons from different substances and their contact
differences of potential. This can be shown very simply by
considering the case of an insulating evacuated enclosure con-

40 EMISSION OF ELECTRICITY FROM HOT BODIES

taining two bodies A and B of different niaterials maintained
at the uniform temperature T. The electrons emitted by A
will ultimately either return to A or reach B, and vice versa.
Now suppose that both A and B are uncharged initially, and
that A emits electrons at a faster rate than B. The greater
rate of loss of negative electrons by A will cause A to acquire
a positive potential relative to that of B. This difference
of potential will not increase indefinitely because the electric
field thus set up will tend to stop the transference of electrons
from A to B. A steady condition will finally be established
in which each of the bodies A and B receives in a given time
as many electrons as it emits in that time. This condition is
also characterized by the occurrence of a constant difference of
potential V between any two points close to the surfaces of A
and B respectively. The number of electrons in unit volume
of the space will then vary from point to point, but will not
change with time. A consideration of the nature and number
of the variables entering into the equations governing the
equilibrium of the electrons ^ shows that V is independent of
the size, shape, and relative position of the bodies A and B,
and depends only on their nature and the temperature T.
This result holds true both on the basis of the classical dyna-
mics and on that of the quantum theory. The difference of
potential V is, therefore, the intrinsic contact potential differ-
ence of the bodies A and B at the temperature T.

We have seen in the last section that on account of the
small concentration of the electrons in the vacuous space out-
side of the emitting bodies their equilibrium will always be
governed by equation (i8). Thus if, in the state of equili-
brium, «i is the number of electrons per unit volume just out-
side A and Wj the corresponding number just outside B,

- «V/ftT

, = ^ .... (34)

since eV is the work done in taking an electron from a point
outside B to a point outside A. If Nj and Ng are the numbers
of electrons emitted by unit areas of the surfaces of A and B

1 Cf. O. W. Richardson, " Phil. Mag.," Vol. XXIII, p. 265 (1912).

EMISSION OF ELECTRONS FROM HOT BODIES 41

respectively in unit time, we see from equation (8), which
holds true on all the theories we have considered, that

%r in,'' ■ ■ ■ (35)

v = *J:,ogN./j^_ . . . (36)

Thus the logarithm of the ratio of the saturation currents per
unit area for any two substances should vary directly as their
contact difference of potential and inversely as the absolute
temperature.

The contact difference of potential is also closely related
to the difference in the values of ^, the work necessary for an
electron to escape from each of the substances under considera-
tion. Referring to equation (9), which is based on thermo-
dynamics and therefore is independent of assumptions about
the conditions affecting the electrons inside the substances,
let Ni, Aj, and ^^ refer to the substance A, and N2, Aj, and <^^
to the substance B, in equilibrium at the temperature T.
Then by taking logarithms of the equations corresponding to
(9) for each substance and subtracting we see that

and since Aj and Aj are independent of T,

<f>,-<f>,=.eV-eT^. . . (38)

A similar result may be obtained by a simple application of
the principle of the conservation of energy. Consider the
bodies A and B to be in contact at some portion of their
surface and calculate the work done in taking an element of
electric charge, for example an electron, round a closed circuit
partly inside and partly outside the two bodies, and passing
through the part of the surface where they are in contact. The
work along the part of the path outside the bodies is eV, the
work in crossing the outside surfaces is (f>^ in the case of B
and - ^1 in the case of A. The only work done in the part of
the path inside the bodies occurs in crossing the interface
and is equal to - ePj where P is the electromotive force corre-

42 EMISSION OF ELECTRICITY FROM HOT BODIES

spending to the Peltier effect at the junction. Since the work
in traversing such a closed reversible cycle at constant tem-
perature must be zero it follows that

<^, - </,2 = eV - eP . . . (39)

Thus we see that the second term of the right-hand side of
(38) corresponds to an electromotive force equivalent to the
Peltier effect at the junction between A and B. Unless the
substances are very close together in the Volta series, P is
small compared with V ; so that the differences of </>i and ^2
will be almost equal to the contact difference of potential.

To the extent to which equations (16) and (17) are valid
approximations the differences of <^ at a given temperature
are equal to the differences of 0^ ; so that to the same degree
of approximation kT times the difference of the indices of the
exponential in equation (17), which determines the tempera-
ture variation of the emission, will also be equal to the contact
potential difference. By taking logarithms of (17) and sub-
tracting we also notice that the differences of ^^ are equal to
eV - kT log A2/A1 ; so that to the same degree of approxima-
tion it is necessary that log A2/A1 = o, or that A should have
the same value for all substances. In dealing with the
quantum theory we saw that this result was to be expected
only when dealing with good conductors like the metals.
This is to be expected also in the present connexion because
it is unlikely that with the poorer electronic conductors such
as the oxides that the thermoelectric effects can be regarded
as negligible. In fact S. L. Brown ^ has recorded that a copper-
copper oxide couple whose junctions are at 20° C. and
530° C. respectively exhibits a thermoelectromotive force

which exceeds half a volt. This means that the term T -^tt^

is of the same order as V in such cases.

The reader who wishes further to pursue the relation
between the effects under consideration and thermoelectric
phenomena may be referred to a book by the writer on the
"Electron Theory of Matter," Chapter XVIII (Cambridge

1 •' Phys. Rev.," Vol. Ill, p. 239 (1914).

EMISSION OF ELECTRONS FROM HOT BODIES 43

University Press. 191 4). The development there given is
from the standpoint of thermodynamics and the classical
dynamics, but the modifications required by the quantum
theory can be seen in a general way from the discussion in
this and the preceding sections.

It follows from equation (35) that the relative powers of
electronic emission of different bodies at a given temperature
will be determined by their contact differences of potential ;
so that whether bodies show much or little difference one from
another in the former respect will depend on the magnitude of
the latter quantity. There is still a great difference of opinion
as to the magnitude of the contact difference of potential be-
tween metals whose surfaces are free from gas and in a good
vacuum. The school which attributes these differences of
potential to chemical action between metals and the surround-
ing atmosphere holds that under the conditions referred to the
contact potentials would completely disappear. If this view
is correct we should expect all hot metals to give nearly equal
thermionic currents per unit area at any given temperature, pro-
vided they were in a perfect vacuum and their surfaces were un-
contaminated. The opposite school regards these potential
differences as an intrinsic property of the metals affected and
considers the changes caused by gases and other contaminating
agents to be of a secondary character. From this standpoint
we should expect to find potential differences between metals
in a good vacuum of the same order of magnitude as those
observed in a gaseous atmosphere. The advocates of these
opposing views have waged an intermittent warfare for a
century without coming to a definite settlement.

Until recently most investigators who have attempted to
decide this question experimentally have concluded that their
results favoured the chemical theory. In 191 2 the writer^
pointed out that none of these experiments were conclusive,
all the observed phenomena being explicable on the intrinsic
theory when due account was taken of various secondary
actions which were bound to occur under the conditions of the
experiments. Quite recently a considerable amount of evi-
!•• Phil. Mag.," Vol. XXIII, p. a68 {1912).

44 EMISSION OF ELECTRICITY FROM HOT BODIES

dence favouring the intrinsic theory has accumulated. Thus
Richardson and Compton ^ examined the photoelectric currents
obtained when monochromatic light fell on small discs of vari-
ous metals placed at the centre of a large spherical electrode.
With this arrangement the saturation value of the current
should be reached when there is no difference of potential be-
tween the two electrodes. This was found to be the case if
the contact potentials were included among the potential dif-
ferences operative. Somewhat similar experiments have been
made by Page.^ In all these experiments good vacuum
conditions were attained. In addition, in Richardson and
Compton's experiments with sodium, and in all Page's experi-
ments, the metal surfaces tested were cut mechanically in
vacuo. Still more recently the contact difference of potential
has been measured directly under the best vacuum conditions
with surfaces machined in vacuo by A. E. Hennings,* who
finds that the potential differences are still of the order usually
observed, the metals being more electropositive when freshly
cut. All these experiments support the intrinsic potential
theory, although there is abundant evidence that gases pro-
duce definite and complicated changes in the observed values.
On the other hand, Hughes,* working with surfaces of metals
freshly distilled in vacuo, found the metals to be initially most
electronegative and to become more electropositive under the
action of small quantities of air. Millikan and Souder,^ also,
have found that surfaces of sodium are most electronegative
when freshly cut and become more electropositive on oxida-
tion. It is clear that the experimental evidence as to the
origin of contact potential differences is still conflicting, and we
are still uncertain as to the magnitude of the contact potential
between uncontaminated metal surfaces in a vacuous en-
closure.

1" Phil. Mag.," Vol. XXIV, p. 575 (1912) ; cf. also K. T. Compton, " Phil.
Mag.," Vol. XXIII, p. 579 (1912).

^'♦Amer. Jour. Sci.," Vol. XXXVI, p. 501 (1913).
S" Phys. Rev,," Vol. IV, p. 228 (1914).
* " Phil Mag.," Vol. XXVIII, p. 337 (1914).
6 " Phys. Rev.," Vol. IV, p. 73 (1914).

emission of electrons from hot bodies 4$

The Distribution of the Electrons in Temperature
Equilibrium Outside a Hot Metal Surface.

On p. 27 we supposed that the electrons in an enclosure
in thermal equilibrium containing a piece of hot metal would
be distributed with uniform density except close to the surface
of the metal and the walls of the enclosure. This supposition
will only be valid if the concentration of the emitted electrons
is exceedingly small, a condition which is satisfied in the
cases considered so far. At very high temperatures the
number of electrons emitted becomes very great, and then the
effects which arise from their mutual repulsions can no longer
be neglected The problem which then presents itself is not
merely of theoretical importance but is of considerable interest
in connexion with the electrical behaviour of celestial bodies.
For instance, the aurora borealis has been attributed to
streams of ions from some extra-terrestrial source, probably
the sun, and it is now well established that there are intense
magnetic fields at the surface of the sun which are closely re-
lated to disturbances in the solar atmosphere. It is natural
to look to thermionic causes for the primary origin of the
ionization which gives rise to these effects and the magnitude
of the electrical effects which might thereby arise are seen to
be of interest from the standpoint of cosmical physics.

The general condition for equilibrium in an atmosphere
of electrons at constant temperature is that the force on the
electrons in any element of volume arising from the electric
field should balance the force on the same element of volume
arising from the pressure gradient. Expressed analytically,
if n is the number of electrons per unit volume, e the charge
of an electron, p = we, the volume density of the electrifica-
tion, E the electric intensity, p the pressure of the electrons,
k Boltzmann's constant, and T the temperature, we have the
following equations: —

kl
neK — grad./ = kT grad. n = — grad. p

€

- —grad. div. E = ^(rot rot. E + V'E) . (40)
47r€ 47r€

46 EMISSION OF ELECTRICITY FROM HOT BODIES

Thus E div. E + ^V'E = o . . . (41)

I liH

since rot. E = = o, H being the magnetic force. In

c 'dt

general, then, the distribution of electric intensity will be
governed by the differential equation (41). If this is solved,
the solution being subject to the boundary conditions of the
problem, the distribution of n may be obtained from the ad-
ditional differential equation

grad. log « = ^ E . . . (42)

which is seen to follow from (40).

As an illustration we shall consider only the one dimen-
sional case of the equilibrium of electrons in front of an emit-
ting plane surface infinite in extent. In this case the writer ^
has shown that if v is the volume occupied by unit mass of the
electrons at any point, then

where C = 47rNo'^eVRT, x is the perpendicular distance from
the emitting plane, Nq is the number of electrons in unit mass
(i.e. No = ilmif m is the mass of an electron), and R/No = k.
The integral of (43) subject to

s — = o when v = co

V = CO when .tr = 00 J- . . (44)

N
and z; = t; = _? ^"'/RT when x = o

is v^i* = (It)'"^ '■*" "^ (7^)'"^'"'''^ • • ^'^^^

By comparing with equation (7), p. 29, it is seen that

in the notation there used. Since

— + N^e -T- = O . • • (46)

V dx ^ dx

1 O. W. Richardson, " Phil. Trans., A.," Vol. CCI, p. 503 (1903).

f:-KsJ-^-°- ■ • («)

EMISSION OF ELECTRONS FROM HOT BODIES 47
we have if V «■ V^ when ;r - o

V = Vo - 2

j^ log |l + (^^) e. .| . (47)

The electric intensity at any point x is

^ I + (27r«iNo/RT)"» e^ " "-''^t,^

(48)

The charge on unit area of the emitting plane is given
by o- = - — \-^-\ and the volume density at any point

X isp = -— • It IS clear that pax = o- since — =0

47r ax^ Jo'^ dx

iox X = 00 . Thus the charge on the surface is equal and

opposite to the total charge in the space outside.

It does not seem likely that the effects which arise in this

way can be of sufficient magnitude directly to account for any

important cosmical phenomena. The potential differences

which develop are comparatively small. Thus, taking the

case of platinum at 1500° K., if the experimental values

are substituted in (47), it appears that when x = \o cms.

V - V(, is approximately i 5 volts, and when x = i cm.

V - Vo is I '2 volts, the greatest potential gradient being at
the emitting surface. These potential differences do not vary
very rapidly with temperature in spite of the enormous varia-
tion of the rate of thermionic emission. Thus with platinum
at 6000° C. the potential difference at a distance of i cm. is
about sixteen times as great as at 1 300° C. There is a very
much more rapid change in the density of the charge on the
surface which increases by a factor of about 10* in this interval.
At 6000° C. the surface density may be of the order of 500
e.s.u. per sq. cm., and there will be an equal and opposite
total charge in the overlying space.

It is not supposed that the conditions here contemplated
bear any very close resemblance to those at the surface of the
sun, where there is a very dense atmosphere of highly conduct-
ing hot vapours. But it would seem that the presence of this
conducting atmosphere would tend further to reduce the dif-
ferences of potential which arise directly from thermionic effects

48 EMISSION OF ELECTRICITY FROM HOT BODIES

and to make the actual electrical effects smaller than those
now contemplated. Let us consider the magnitude of the
magnetic fields which might arise from the motion in the sun's
atmosphere of the electrification which arises in this way. The
magnetic intensity H at the centre of a disc charged to surface
density o- and rotating with uniform angular velocity is given

H = 2'ira-Ylc,
where V is the peripheral velocity and c is the velocity of light.
From Hale's observations of the solar atmosphere values of
V as high as lo''^ cm. per sec, appear to be permissible; so
that to account for the observed magnetic intensities in sun-
spots (up to 3000 gauss) values of o- comparable with 10® e.s.u.
are required. One cannot consider values of this magnitude
incompatible with the results of the foregoing calculations,
since the surface density of the source of emission at any
temperature depends very much on the thermionic constants
of the substance. The difficulty is rather to account for the
requisite separation, in such a highly conducting atmosphere,
of the positive and negative charges ; since if such separation
does not occur the electrifications of opposite signs will, for
all practical purposes, revolve together and the resulting mag-
netic fields will be negligible.

In addition to the force due to their mutual repulsion, the
electrons are also acted on by a force which varies inversely
as the square of the distance from the emitting surface and is
due to the electric charge they induce on it. This force is in-
dependent of the concentration of the electrons in the external
atmosphere and is inappreciable except at very minute dis-
tances from the surface.

The Reflexion of Electrons from Solids.

Most of the foregoing calculations of the number of
electrons emitted by hot bodies depend upon a preliminary
determination of the concentration, «, of the electrons in
equilibrium with the hot body in an enclosure at constant
temperature. From the value of n the number N' of electrons
which return from the surrounding atmosphere to each unit of

EMISSION OF ELECTRONS FROM HOT BODIES 49

area of the hot surface is immediately deducible. Since,
for equilibrium, the number N of electrons emitted must be
equal to the number absorbed, we have hitherto assumed N
and N' to be equal. This will only be correct provided all
the electrons which return to the hot body are absorbed by it.
Experiments made by the writer (see p. 1 54, Chap. V) have
shown that a very considerable proportion of the slowly moving
electrons emitted by hot bodies is reflected from the surfaces
of metals, and v. Baeyer ' and Gehrts "^ have shown that the
same thing holds true for the electrons liberated by photo-
electric action. If the proportion of the incident electrons
reflected is denoted by r the correct equilibrium condition is

N = N'(l - r\
since N'(i ~ r) is the number of those which are actually
absorbed. For a number of metals which have been tested
the value of r has been found to be in the neighbourhood of
0-5 ; so that the omission of its consideration, although making
an appreciable change in the calculated value of N, will not
alter the order of magnitude of this quantity.

Liberation of Electrons by Chemical Action.

Since it has been found * that electrons are emitted when
various gases react chemically with the alkali metals and their
amalgams, it is worth while to examine what laws an emis-
sion caused by chemical action would be expected to follow.
From this standpoint the problem is a well-known one of
chemical dynamics. Indications towards the solution can be
obtained by the application of thermodynamics to the products
of the reaction under conditions of equilibrium in an enclosure
at constant temperature. The electrons and positive ions are
to be regarded as products of the reaction which exert a pres-
sure in accordance with the laws of a perfect gas. The results
will be strictly accurate for very small concentrations such as
correspond -to thermionic emission. Let us consider first the
case of gaseous reactions.

1 •' Her. der Deutsch. Physik. Ges.," Jahrgang 10, p. 96 (1908).
» "Ann. der Physik," Vol. XXXVI, p. 995 (igii).
«Cf. p. 128, Chap. IV, and p. 290, Chap. IX.
4

50 emission of electricity from hot bodies

Formation of Ions in Gaseous Chemical Reactions.

Consider the formation of ions in a reaction in which all
the products are gaseous. If the reaction is represented by
the generalized chemical equation

«iAi + WjAa + • • ■ = «'iA'i + w'aA'j + . , ., (49)
the corresponding equilibrium concentrations being denoted
by the letter C with the same suffixes as the A's, it follows
from thermodynamics ^ that

5'«, logC, = k . . . . (50)

and ^ = yRj2 • • • (5 0

where g is the latent heat of the reaction at constant volume
per gram molecule and R is the gas constant per gram mole-
cule. Integrating (51) and combining with (50), after taking
out the logarithm we have

n.(C, )== e" = e -/rt^"^ . . . (52)

when n^ denotes the continued product of Ci^i etc., the indices
for the concentrations corresponding to the left-hand side of
(49) being taken negative. The simplest possible reaction
resulting in the liberation of ions is

A^A++ e . . . . (53)

A being the undissociated molecule, A^ the positive ion and
e the electron. The concentrations being C, Ci, and Cj from
left to right, (52) gives

C,Q = Ce-^^-"' . . . (54)

If a is the coefficient of recombination of the positive ion and
the electron and t is the time, we have from the definition of a

()Ci c)C2

^ = ^ = - aC,C, . . . (55)

Thus a Ci Cj is the number of electrons which disappear in
unit time. But in the steady state this must also be equal to

^ Of. Van't Hoff, " Lectures on Theoretical and Physical Chemistry," Pt. I,
p. 141.

EMISSION OF ELECTRONS FROM HOT BODIES 51

the number of electrons liberated in unit time by the decom-
position of C. Hence when the electrons are removed by an
electric field as fast as they are formed, the saturation current
will be

Nc ■» acQC, - aeCe-^vcf^ . . • (56)

This is proportional to C, as it should be. Since neither a'
nor g vary very rapidly with T, (56) shows that the tempera-
ture variation of the currents under consideration will not be
far from the form AT* e ~ ''''^ which has been found to agree
with the experiments on thermionic currents.

Chemical Action on Solids.

When the ionization results from the chemical action of a
gas on a solid the problem is more complicated than that
furnished by a purely gaseous system. As an illustration we
may consider the reaction

X+ Y^Xy:;tXY+ + ^. . . (57)

where X and XY are solids and Y is a gas. Consider the
equilibrium between the products inside a cavity in the solid
X which contains a certain amount of the gas Y. Let the
equilibrium concentrations of X, Y, XY^. and e be C^, Cj, C„
and C4 respectively. Then from (52)

C^ = ^2^1 ^/:^,''T ^ ^ ^ ^^g^
C3

where q is the heat of the reaction at constant volume per
molecule, when the reaction takes place in the gaseous phase.
Now Ci and C| are the molecular concentrations of the satu-
rated vapours of the corresponding solids and are of the form

where L is the appropriate latent heat of evaporation. Thus
if Q is the heat of reaction calculated in the assumption that
the products present in the solid phase are decomposed and
formed as solids

» Cf. O. W. Richardson, " Camb. Phil. Proc.," Vol. XII, p. 144 (190a) ; " PhU.
Mag.," Vol. X, p. 242 (1905).

52 EMISSION OF ELECTRICITY FROM HOT BODIES

C, = AQ^^RT"'*^ ... . (59)

where A is independent of T. Thus if the concentration
Cj of the reacting gas is kept constant the concentration of the
electrons in equilibrium in the cavity will vary with T, since
Q does not vary much, in much the same way as in the purely
gaseous case already considered, and as in the case of the
purely thermionic emission.

Just as in dealing with the thermionic emission, we are not
able to measure the equilibrium concentration of the electrons
but only the rate at which they are emitted by the solid sur-
face in presence of the gas. If the state of the surface is kept
in the same condition as in the state of equilibrium it will
emit in unit time approximately as many electrons as return to
it under the equilibrium conditions, the approximation arising
from the fact that here we are neglecting electron reflection.
It follows from the kinetic theory of gases that, to this degree
of accuracy, the saturation current will be proportional to
C4T* ; which, combined with (59), shows that under these
conditions a formula of the type i = AT* e " ^'"^ will be close
to the truth.

It is possible, however, in experiments on the emission of
electrons by the action of gases on solids to arrange matters
so that the state of the solid is a long way from that which
corresponds to the condition of equilibrium. Thus in Haber
and Just's^ experiments with metallic liquids the surface of
the metal is renewed as quickly as it is attacked ; so that the
conditions correspond to the commencement of the reaction
rather than to a state of equilibrium. Under these circum-
stances the saturation current will measure the initial velocity
of the reaction defined by the left-hand side of (57). Thermo-
dynamics is inadequate to determine the relation between the
velocity of such a reaction and the temperature ; but it has
been found empirically that, in all cases of chemical reaction
which are sufficiently simple to afford any analogy with the
type now under consideration, the velocity is very closely pro-
portional to ^ ~ '''^' where b is constant.

* See p. 291.

EMISSION OF ELECTRONS FROM HOT BODIES 53

One conclusion at least emerges clearly from this discus-
sion, and that is, that the fact that the thermionic currents
satisfy the formula t = AT* *" */^ affords no evidence either
for or against the view that these currents originate from
chemical action. To settle this question it is necessary to
appeal to evidence of a different character.

We shall now postpone the further development of the
theory of the emission of electrons from hot bodies until some
of the experimental results bearing on the conclusions already
reached have been considered.

CHAPTER III.

TEMPERATURE VARIATION OF ELECTRONIC EMISSION.

The first experiments on this subject were made by the
writer ^ in order to test the theory developed on p. 33 of the
last chapter. The elements investigated were platinum,
carbon, and sodium. Since then measurements of the total
emission at different temperatures have been made by H. A.
Wilson ^ and by the writer ^ on platinum in atmospheres of
hydrogen and other gases, by Wehnelt* on different metallic
oxides, by G. Owen ^ on the Nernst filament, by Deininger ^
on platinum, carbon, tantalum and nickel, in each case with the
element alone and also when covered with a layer of lime, by
Horton ^ on platinum covered with calcium and with lime, by
Martyn ^ on platinum covered with lime in atmospheres of air
and of hydrogen, by Jentztsch ^ on most metallic oxides, by
Fredenhagen ^" on the emission from sodium and potassium,
by Pring and Parker " and by Pring ^^ on carbon, by Lang-
muir ^^ on tungsten, tantalum, molybdenum, platinum and

1 " Camb. Phil. Proc," Vol. XI, p. 286 (1901) ; " Phil. Trans., A.," Vol. CCI,
p. 497 (1903).

""Phil. Trans., A.," Vol. CCII, p. 243 (1903); Vol. CCVIII, p. 247 (1908).

'Ibid., Vol. CCVII, p. I (1906); "Jahrb. d. Rad. u. Elektronik," Vol. I,
p. 300 (1904).

*" Sitzungsber. der physik. med. Soc. Erlangen," p. 150 (1903) : " Ann. der
Phys.," Vol. XIV, p. 425 (1904) ; " Phil. Mag.," Vol. X, p. 88 (1905).

»" Phil. Mag.," Vol. VIII, p. 230 (1904).

•"Ann. der Physik," Vol. XXV, p. 285 (1908).

^"Phil. Trans., A.," Vol. CCVII, p. 149 {1907).

8 "Phil. Mag.," Vol. XIV, p. 306 (1907).

»"Ann. der Phys.," Vol. XXVII, p. 129 (1908).

^""Verh. der Deutsch. Physik. Ges.," Jahrg. 14, p. 386 (1912).

11 " Phil. Mag.," Vol. XXIII, p. 192 (1912).

12 " Roy. Soc. Proc, A.," Vol. LXXXIX, p. 344 (1914).

" " Phys, Rev.," Vol. II, p. 450 (1913).

TEMPERATURE VARIATION 55

carbon, by K. K. Smith ^ on tungsten, and by Schlichter ' on
platinum and nickel. The work of Langmuir and Smith is
characterized by extreme care in the elimination of gaseous
impurities and exemplifies the most recent advances in
technique,' The researches above mentioned are of a quanti-
tative and, for the most part, extended character. In ad-
dition a number of investigations dealing with special points
will be referred to in the sequel. Although the authors of
the researches just enumerated differ considerably in the
final interpretation of their experimental, results, they are in
agreement as to the general character of the variation of the
rate of emission of the electrons by various hot bodies with
temperature. In all cases it has been found that if the
material experimented on is in a condition which does not
change with lapse of time the rate of emission of electrons
increases with enormous rapidity as the temperature is raised.
This is true whether the substance under investigation is in
a good vacuum or is surrounded by various gases. The
extreme rapidity of this variation is well shown in Fig. 8
which represents the results of the writer's early experiments
with sodium. The observations recorded extend over a range
of temperature from 217° C. to 427° C. whilst the corresponding
currents increased from 1*8 x io~' amp. to 1-4 x 10 "^ amp.
Thus with a rise of temperature of a little over 200° C. the'
current increases by a factor of lol In order conveniently
to exhibit all the values on the same diagram the curve is
shown by means of a number of branches, in each of which,
proceeding from left to right, the scale of the ordinates is
successively reduced by a factor of 10. Thus, starting from
the left-hand side, in the first curve the unit of current is lo~"
amp., in the second lO"^, and so on. The various crosses
which lie vertically over one another represent the same ob-
servation on different scales. It will be noticed that the suc-
cessive branches are very similar to one another ; so that the
general character of the temperature variation is much the

i"Phil. Mag.," Vol. XXIX, p. 811 (1915).

« '• Ann. der Phys.," Vol. XLVII, p. 573 (1915)-

3 Cf. also O. W. Richardson, " Phil. Mag.," Vol. XXVI, p. 345 (1913)-

56 EMISSION OF ELECTRICITY FROM HOT BODIES

same at all temperatures. As the temperature is reduced the
current continuously approaches the value zero but never
actually reaches it. The experiments to which Fig, 8 refers
were probably affected to some extent by the presence of a
surrounding gaseous atmosphere, but however carefully gaseous
contamination has been avoided, it has always been found that
the general character of the temperature variation is of the
kind shown in the figure. The difference between different
substances lies in the temperature at which the emission be-

Temp«rabur8 Centigrade.
Fig, 8,

comes appreciable ; and this temperature determines the whole
scale of the diagram. With most substances the currents
cannot be measured on a sensitive galvanometer at tempera-
tures below 1000° C, A correspondingly larger interval of
temperature is then required in order to change the current in
a given proportion.

This will become clearer if we consider the matter from a
more quantitative standpoint. In the last chapter two prin-
cipal formulae were developed for the saturation current i from
unit area of a hot body at temperature T^K, viz. :— '

TEMPERATURE VARIATION

I - AT*^-*/T . ... (I)
and / = CT2^-'"T ... (2)

where A, b, C and d are constants. Obviously these formulae
cannot both be true. As a matter of fact both are approxi-
mations and (2) rests on a more solid theoretical basis than
(i). According to the theory of Chapter II, equation (2)
should be a very close approximation to the truth. In
order to test the relative merits of the equations we may take
logarithms of both sides, obtaining from (i),

logio i - \ logio T = logio A - bh'ioi T . (3)

«o

-S 2

•n

-9

X,« e

Ca 0 0
Ca 0 0
CaO 0

rt Pt

8 V
tO/T

Fig. 9.

and from (2),

logio^ - 2logioT = logioC - dlTioiT. . (4)

According to (i) we should get a straight line by plotting
logjo / - i logio T against T"^ and according to (2) the same
result should follow if we plot log^o i ' 2 log^o T against T'^
In Fig. 9 some very consistent observations by Deininger,^ on
the emission from lime coated platinum wires, are treated in

^ Loc, cit„ p. 296.

58 EMISSION OF ELECTRICITY FROM HOT BODIES

this way, the saturation current per unit area being given in
electrostatic units. The points shown thus : x represent the
values of log^^ C - i log^^ T, and the points thus : 0 the values
of 5 + logjo C - 2 logio T, each plotted against lo^/T. The
points marked -^ and ® may be left out of consideration for
the present. The points shown represent a variation of C
from 75 e.s.u. to approximately 3 x lo® e.s.u., the corres-
ponding range of temperature being from 798° C. to 1198° C.
Both sets of points are seen to fall on straight lines almost as
exactly as they can be drawn; so that if we regard (i) and
(2) as empirical formulae there is nothing to choose between
them. Each is capable of expressing the experimental re-
sults with the exactness required by the accuracy of the
measurements. It is clear that the values of A and ^ or C
and d may be deduced from the intercepts on the axes of
lines like (i) or (2) respectively in Fig. 9. As the experi-
ments are unable to decide between the relative accuracies of
the two formulae, and as the formula (i) was the first in the
field and usually occurs in the literature, we shall make most
frequent use of it in this book, although (2) is more satis-
factory from a theoretical standpoint. After all, the differ-
ence between the two equations may be considered to lie in
the interpretation of the quantities A, b, C, and d, and if A
and b are given for a particular substance and temperature,
C and d may be obtained from the relations : —

C=A^-?T-5 ... (5)
and d= b - iT . . . . (6)

which are valid to the degree of accuracy within which (i) and
(2) can be regarded as consistent.

The experimental evidence shows that the validity of
equation (2) (or (i)) is perfectly general and covers the very
large number of substances investigated over the whole range
of experimentation, provided no permanent change in the
composition of the surface of the substance concerned takes
place as a result of the treatment. The only known excep-
tion appears to be that with certain specimens of commercial
osmium filament the writer and H. L. Cooke ^ observed that
1 " Phil. Mag.," Vol. XXI, p. 408 (igii).

TEMPERATURE VARIATION 59

the curve corresponding to Fig. 9 consisted of two straight
lines meeting at an angle. It is probable that this is due
to some reversible, possibly allotropic, change in the structure
of the material. The range of thermionic current over which
the formula has been found to apply is in many cases very
large indeed. This K. K. Smith ^ has confirmed it in the case
of tungsten over a range of temperature such that the ther-
mionic current varied by a factor of lo^^ His results also
show that even over this extended range there is nothing to
choose between equations (i) and (2), both of which express
the experimental results with exactness.

Conditions Affecting the Attainment of Saturation.

In making measurements of the number of electrons emit-
ted from hot bodies it is essential that the currents should be
saturated, otherwise only part of the electrons emitted by the
hot body will reach the electrode and the measured values
will be too small. It is therefore necessary that the applied
potential difference between the emitting substance and the
receiving electrode should be at least as great as the smallest
potential difference required to cause saturation. Generally
speaking, the applied potential difference may have any value
greater than this, provided the experiments are made in a
good vacuum. If, however, a gaseous atmosphere is present
we have seen in Chapter I that, if the potential gradient ex-
ceeds a certain value depending on the nature and pressure of
the gas, ionization by collision will occur and the measured
currents will be larger than those due to the unassisted elec-
tronic emission. When possible this difficulty should be
avoided by making the experiments under the best attainable
vacuum conditions, as it is difficult to make exact allowance
for the effect of ionization by collisions in experiments of
this character.

The type of curve connecting the current and applied po-
tential difference which is most frequently obtained under fairly
good vacuum conditions is shown in Fig. 10. This represents

»" Phil. Mag.," Vol. XXIX, p. 802 (1915).

6o EMISSION OF ELECTRICITY FROM HOT BODIES

observations made by the writer^ with a U-shaped carbon
filament surrounded by a cylindrical electrode, the pressure be-
ing 0'003 mm. It will be seen that approximate saturation
is attained at about 30 volts, although there is a further rise
of about 10 per cent of the total value on increasing the volt-
age to 1 20. This further increase is almost always, as in Fig.
10, proportional to the increase in the applied potential. It
usually diminishes with continued use of a given tube, and it
appears to be due either to the evolution of gas from the hot
filament or to the presence of a layer of condensed gas on the

eor

lb 20 30 40 50 60 70 80 90 100 110 120

Volte on negative end of filament
Fig. 10.

electrode, or to both these circumstances. The writer has not
observed this effect in a tube which has been well glowed out
and exhausted in the vacuum furnace before testing, although
a case of its appearance under these conditions has been re-
corded by K. K. Smith.^ As an example of the extent to
which complete saturation is attainable in experiments of this
character the following figures given by Deininger ^ may be

cited : —

Potential Difference (volts) —

03 5 10 12 15 ao 35 30

Current (i = 10-8 amp,) —

o'o 237 547 I22"3 167*9 i86"2 202*6 2o6*2 ao8"i
P.D. ->•

40 50 60 70 80 90 100 no 120 130 140 180

c. ->

2og-o 209*0 209*0 211*7 208*1 204*4 204*4 208*1 2o8*i 208*1 208*1 208*1

1" Phil. Trans., A.," Vol. CCI, p. 520 (1903).

2 Loc. cit. » " Ann, der Phys.," Vol. XXV, p. 294 (1908),

TEMPERATURE VARIATION 6 1

In this experiment the temperature must have been about
the same as in the case to which Fig. lo refers. The pressure is
given as less than oooi mm. It will be seen that there is here
no perceptible increase in the current between 25 and 180 volts.

It is only when the thermionic current densities are com-
paratively small that saturation is attainable with potential
differences of 20 volts or under. With the large emissions
which occur at very high temperatures the potential difference
required for saturation may be very much higher owing to the
mutual repulsion of the emitted electrons. This leads to an
interesting effect which was discovered and explained by
Langmuir.^ In examining the thermionic current between
two hairpin-shaped tungsten filaments, under fixed differences
of potential, at various temperatures, the results exhibited in
Fig. 1 1 were obtained. The experimental values lie along the
broken curves, the continuous curve representing the saturation
current at different temperatures. It will be noticed that the
broken curves coincide with the continuous curve up to a cer-
tain temperature which is lower the smaller the applied po-
tential difference. Beyond this point the currents are below
the saturation value, but they still increase with increasing
temperatures of the filament. At still higher temperatures the
broken curves bend round, and the current under a given po-
tential difference becomes entirely independent of the tempera-
ture of the hot filament. Owing to the mutual repulsion of
the electrons a given difference of potential applied over given
boundaries is only capable of forcing a definite number of
electrons across the intervening space in unit time, no matter
how many may be available.

In order more clearly to see how this comes about let us
consider the simplest possible case, that of an emitting plane
opposite a parallel conducting plane which represents the re-
ceiving electrode. Take the axis of x perpendicular to the
planes and let V be the electrostatic potential at any point.
Then the value of V is governed by Poisson's equation which
reduces to

— ^ - ^nrp • . . . (7)

» •• Phys. Rev.," Vol. II, p. 453 (1913).

62 EMISSION OF ELECTRICITY FROM HOT BODIES
p being the volume density of electricity at any point.

...

.*■

♦ -

••-

-■

JPO

rO<j

.(K

.90

t2<

.0(

•

}

■''

• •

' ■"

itl

up*

ffl*

yr?

109

t(.

too

lOO

2e(

Fig. II.

When there are no electrons emitted p is zero at every point ;

so that — - is constant and may be re-
presented by the straight line PQT in
Fig. 12. When the plate is emitting
electrons these will give rise to a nega-
tive value of p in the space as they
cross it, and if the number is small,
the value of p thus arising will be ap-
proximately independent of ^ ; so that
the right-hand side of (7) will be a
positive constant and the graph of V
will be approximately parabolic and similar to PST. As
the current and - p increase this curve will sink below PQT

Fig. 12.

TEMPERATURE VARIATION 63

until the stage PRT is reached, where the tangent at P is
horizontal. Any further increase in the supply of electrons
will now have no effect on the distribution of potential between
the plates because there is nothing to drag them away from
AP, We here assume that the emission velocities of the
electrons are small compared with those which they acquire
under the influence of the field ; so that the results will only
be true for fairly large potential differences (see Chapter V).
Now let us see how the current will depend on the applied

potential when the condition that — - vanishes at the hot plate

is satisfied. Let + e^ denote the numerical value of the nega-
tive charge of an electron and + p^ the numerical value of the
negative density of charge at any point. An electron at a point
when the potential is V (if V = o at the hot plate) will have
acquired an amount of kinetic energy given by the equation

\mv^ = \e^ . . . . (8)

The current per unit area carried by the electrons at that
point will be

i = vp^ . . . . (9)

and equation (7) may be written

^ = 47r/>, . . . . (10)

By elimination o( p and v from (8), (9), and (10)

and integrating, subject to ^ = ^ when V = o,

f^y=.8.W^ . . . (M)

By integrating again, subject to V = o when x ^ o, and
solving for / we find

. J2 17^ V3.'« , ,

64 EMISSION OF ELECTRICITY FROM HOT BODIES

The same general method of treatment with the appropri-
ate modification of Poisson's equation can be applied to the
case of a circular wire surrounded by a coaxial cylinder,
giving

2 n/2 [7^ V3'2 , ,

' - ^ V- 7^.. • • • ('3)
when r is the radius of the cylinder, and

3300\ ^ a)

a being the radius of the wire. In fact Langmuir ^ has shown
from a consideration of the dimensions of the equations that,
whatever may be the geometrical relation between the emitting
and receiving electrode, the current under these circumstances
will be equal to V^'^' multiplied by a factor depending on e^lnt
and the geometry of the system.

It appears then that over the flat part of the broken curves
in Fig. 1 1 the current should be proportional to V^'". This
requirement is found to be borne out by the experimental re-
sults ; so that there can be no doubt of the adequacy of the
foregoing explanation. Langmuir has suggested that experi-
ments with concentric cylinders using equation (13) could be
made so as to determine the value of e-^\m with great pre-
cision.

The effect of the mutual repulsion of the electrons in pre-
venting the attainment of saturation will be important only
when the saturation currents are of considerable magnitude ;
with sufficiently small currents this effect will vanish. We
shall see in Chapter V that the electrons are emitted, not with
zero velocity, but with a distribution of velocities whose mean
square is proportional to the absolute temperature of the hot
body. At 2000° K. this mean velocity is comparable with
that which an electron would acquire by falling through a
potential difference of about 0*25 volt. At relatively low

^ Loc. cit.

TEMPERATURE VARIATION 65

temperatures when the emission is comparatively small, if the
hot body is surrounded by the receiving electrode, we should
expect saturation to be attained without the application of any
potential difference ; since all the electrons are emitted with
some velocity, and any velocity, however small, will be suffi-
cient to carry them across to the electrode ultimately. This
supposition does not accord with the facts as observed in ex-
periments with electrically heated wires surrounded by coaxial
cylindrical electrodes. Under these conditions it is the writer's
experience that potential differences comparable with two or
three volts are required to cause saturation even when dealing
with the smallest currents which are convenient to measure.
There can be very little doubt that in these cases one cause
operating against the attainment of saturation is the effect of
the magnetic field, due to the heating current, on the motion
of the electrons.

To see how this comes about consider the case of a hot
wire, of circular section and radius a, surrounded by a coaxial
cylindrical electrode of radius b. Let V^ be the potential
difference in volts between the wire and the cylinder. The
electric intensity R is everywhere radial and at distance r from
the axis is given in electro-magnetic units by

R = Vi X loV^ log bla = Ajr . . (14)

The magnetic intensity H lies in circles about the axis of the
wire, and, if/ is the current in amperes, its value at distance
r is

H ^2jlior= B/r . . . (15)

On account of its direction the magnetic field will not affect
the angular velocity of the electrons about the axis. Disre-
garding this rotation, the paths of the electrons are periodic
curves, in the plane containing the axis, which keep intersect-
ing the surface of the emitting cylinder. The effect of the
neglected rotation is simply to convert these plane curves into
spirals about the axis. There is a certain maximum distance,
under given conditions, which an electron is able to travel from
the axis, and unless this is equal to or greater than the radius
of the outer cylinder the electrons will return to the surface of

66 EMISSION OF ELECTRICITY FROM HOT BODIES

emission and will contribute nothing to the thermionic cur-
rent.

If r is the perpendicular distance of an electron from the
axis, z its distance from a fixed plane perpendicular to the
axis, and 0 the angle the plane containing the axis and the
electron makes with a fixed plane through the axis, the equa-
tions of motion of the electron are : —

(1 6)
(17)
(i8)

m—- - mrl

<^0\'

Ae Be -dz
r r ^t

Bel^r

2) A at J

= 0

From (1 8)

10 a' A

= 0^ when r =•

From (17)

12
It

Be ,

= 2^ + — log

(19)

(20)
m a

if — = in when r = a.

Substituting these values of — and -^ in (16) and inte-

()/ ct

grating subject to

— = ^0 when r = a,

The maximum value r^ of ;' is given by — = o or from

(21), after substituting the values of A and B in terms of Vi
and y, by

TEMPERATURE VARIATION 67

50W ^ a 5

V. = 10-8 log - K-^ log -"• +-^io

2«

log ^ja

(22)

Thus if r^ is to be just equal to the radius b of the outer
cylinder,

2^ log ^/<a: j

If Vi has a value equal to or greater than this the electrons
will reach the electrode and form part of the current, otherwise
they will not do so. If/ is very small the right-hand side of
(23) is negative, indicating that the current will be able to flow
against an opposing potential owing to the initial emission
velocities. The point of immediate interest, however, is the
first term, on the right-hand side of (23), which is always posi-
tive and is independent of the emission velocities. This shows
that owing to the action of the magnetic field due to the heat-
ing current, a definite potential is necessary in order to drag
the electrons across to the electrode. With thin wires, which
require only a small current to heat them, this potential differ-
ence is unimportant. Thus if bla = 200 and / — i ampere,
Vj is only about 0'2 volt. On the other hand, with thick
wires, which require large heating currents, the necessary values
of Vi may be quite large.

Another important factor which has to be taken into ac-
count, especially with thin wires, is the drop of potential along
the wire due to the flow of the heating current. This is usually
comparable with i volt per cm. In order to ensure that no
part of the wire is at a positive potential compared with the
cylinder, it is necessary that the positive end of the wire should
be at a potential at least as low as that of the cylinder. If
the potentials are applied at the negative end of the wire, it
will appear from this cause alone that an additional negative

68 EMISSION OF ELECTRICITY FROM HOT BODIES

potential equal to the fall along the hot wire has to be applied
in order to ensure complete saturation.

That the mutual repulsion of the electrons, the magnetic
field due to the heating current, and the drop of potential along
the wire, also due to the last-named cause, are the chief general
factors which prevent the attainment of saturation is strikingly
shown by some recent experiments by Schottky.^ Using
concentric cylinders the thermionic currents with small dif-
ferences of potential, both accelerating and retarding, were
measured under conditions such that the heating current was
cut out at thfe instant of measurement. By means of a suit-
able in-and-out switch, operating continuously, matters were
arranged so that no appreciable variation in the temperature
of the wire ensued thereby. Under these conditions the drop
of potential along the filament and the magnetic field due
to the heating current are eliminated, and it was found that
the current saturated at zero potential difference ; except for
an effect, which was smaller the lower the temperature and
smaller the current, arising from the mutual repulsion of the
emitted electrons. In determining the actual difference of
potential between the wire and the electrode, it was found
necessary to add to the apparent applied potential difference
registered by the voltmeter, a difference of potential equal
to the contact potential between the two metals used. Thus
experiments of this kind can be used to measure contact dif-
ferences of potential under good vacuum conditions without
displacing the surfaces subject to test.

Schlichter,^ by using methods of heating the electrode
which do not involve the passage of an electric current
through it, has been able to show that the electron current
with 220 volts driving potential is only about 10-20 per cent
greater than that under zero potential difference, when the
hot metal has been thoroughly glowed out. The special
conditions which affect the attainment of saturation in the
case of freshly heated metals will be referred to again on
page 182, Chap. VI.

i"Ann. der Phys.," Vol. XLIV, p. loii (1914).
^Ibid., Vol. XLVII, p. 573 (1915)-"

TEMPERATURE VARIATION 69

The Values of the Constants.

A considerable number of the researches enumerated at
the beginning of this chapter are of a sufficiently extensive
character to enable the constants of the emission formula to
be deduced from the measurements. The values for the ele-
mentary substances are given in the next table. The numbers
given are the values of Aj, b, C, d^ and ^0, where Aj = A/e,

^0 = — X 300 and A, by C, and d are the constants in equa-
e

tions (i) and (2), when / is expressed in electrostatic units.

Ai in fact is the constant in the equation

N = AiT»^ -^^ . . . (24)

where N is the number of electrons emitted from unit area in
unit time at temperature T. ^^ is the potential difference in
volts which is equivalent to the work an electron would have
to do to escape from the substance, reduced to the absolute
zero of temperature. In some cases the numbers have not
been evaluated by the authors, in others obsolete values of
the ionic charge e have been used. I have reduced all the
data to the common value 6=4-8 x lO"^** e.s.u : —

^^ (equi-
Material. Observer. Aj. b. C. d. valent

volti).

Carbon . i. [Richardson 10'^ 7'8 x 10* 7*55 x 10* 6-48]

2. Deininger 4*68 x 10" 5*49 x 10* 7*46 x lo^" 5*25 x 10* 4'5i

3. Langmuir f4gxio'" 4-87 x ic* 178x10^" 4*57 x 10* 3*92

Platinum . 4. Richardson 7*5 x io»* 4*93 x 10* 475 x 10* 4*1

5. Wilson 6*9 x 10^^ 6*55 x 10* 6-3 x 10* 5*45

6. Wilson i'i7xio" 7*25x10* 7*0 x 10* 6'o

7. Richardson 5 x 10** 678 x 10* 6*55 x 10* 5*65

8. Deininger 3*06 x 10** 6'i x 10* 4*9 x lo^" 5*85 x 10* 5-02

9. Horton i*6 x xo" 6*i x 10* 5*9 x 10* 5*1

10. [Wilson 2x10^' 2'8 X lo* 2*56x10* 2*18]

11. Langmuir 2*02x10** 8*0 x 10* 2*42x10** 7*7 x 10* 6*62
iia. Schlichter 7*2 x 10** 5*11x10* 4*9 x lo* 4*2

Tungsten . 12. Langmuir 1*55x10** 5*25x10* i*86xio" 4*95x10* 4*25
12a. K. K. Smith 3*0 x 10'' 5*47 x 10* 5*20 x 10* 4*46

Tantalum . 13. Deininger 2*7 x lo"* 4*42x10* 4*3 x lo" 4*17x10* 3*58
14. Langmuir 7*45 x lo''* 5*0 x 10* 8*94x10*° 4*7 x 10* 4*04

Molybdenum 15. Langmuir 1*38 x lo" 5*0 x 10* 1*65 x 10" 4*7 x 10* 4*04

Nickel 15a. Schlichter 2*9 x lo** 3*4 x 10* 3*3 x 10* 2*9

Calcium 16. Horton 1*1 x 10" 3*65 x 10* 3*5 x 10* 3*04

Sodium 17. [Richardson lo** 3*16 x 10* 3*1 x 10* 2*65]

70 EMISSION OF ELECTRICITY FROM HOT BODIES

The data from which these numbers have been calculated
are taken from the following list of papers. (The numbers
are the numerals at the beginning of each row in the pre-
ceding table) : —

Nos. I, 4, and 17, "Phil. Trans., A.," Vol. CCI, p. 497
(1903). Nos. 2, 8, and 13, "Ann. der Phys.," Vol. XXV, p.
285 (1908). Nos. 5, 6, and 10, "Phil. Trans., A.," Vol. CCII,
p. 243 (1903); Vol. CCVIII, p. 247 (1908). No. 7, "Phil.
Trans., A.," Vol. CCVII, p. i (1906). Nos. 9 and 16, "Phil.
Trans., A.," Vol. CCVII, p. 149 (1907). Nos. 3, 11, 14, and
15, "Phys. Rev.," Vol. II, p. 450 (1913). No. 12, "Phys.
Zeits.," Jahrg. 15, p. 525 (1914). No. 12a, "Phil. Mag.,"
Vol. XXIX, p. 811 (191 5). Nos. iia and 15a, "Ann. der
Phys.," Vol. XLVII, p. 573 (ipiS)-

Many of the values have only been worked out rather
roughly as the final numbers are incapable at present of being
interpreted with any great accuracy. All the values of C
have not been calculated. They are in a constant proportion
to the values of Aj except for the factor T^, T being the ab-
solute temperature in the different experiments.

All the data in the table, except No. 10, were obtained
under conditions which, at the time when the various experi-
ments were made, led the authors to believe that they were
measuring the emissions characteristic of the elements in
question. It was thus expected that the constants A and b
would have definite values for each material. This statement
is exactly true only so far as concerns b, which depends only
on the relative values of the currents at different temperatures.
In one or two of the experiments there is some latitude in the
value of A, which depends on the absolute value of the cur-
rents, on account of uncertainty as to the exact area of the
emitting surface, occurrence of some impact ionization, and
difficulty of attaining saturation. However, in most of the
experiments these uncertainties were not present, and in any
event they would not be expected to affect the order of
magnitude of A seriously.

A glance at the table shows that the expected result is far
from having been attained. The variation of by for example,

TEMPERATURE VARIATION 71

for a given element is enormously greater than the variations
arising from errors of measurement justify. In fact, the re-
searches referred to at the beginning of this chapter have
proved one thing with great clearness, namely, that the deter-
mination of the emission constants for the elementary sub-
stances is an experimental problem of the most extraordinary
difficulty. There are two chief reasons for this.^ In the first
place the rate of emission is extremely sensitive to the
minutest traces of a large number of gases. In the second
place the general character of the emission from a wire sub-
ject to traces of gaseous contamination is not affected thereby.
That is to say, the hot body adjusts itself to the altered
circumstances, so that the emission still follows a current
temperature law of the form / = AT''* e~^^ but with different
values of the constants. There is therefore nothing in the
behaviour of the phenomenon itself which enables one to tell
when, or if, the desired purification has been attained. More-
over, the effects produced by extremely minute amounts of gas
are so considerable that it is doubtful, at the present stage of
development of this branch of experimentation, whether the
requisite degree of purity can be attained except in the case
of a small number of highly refractory elements. The most
successful experiments from this point of view are those of
Langmuir and K. K. Smith on tungsten, and the numbers
in the table opposite this element deserve more confidence
as representing values characteristic of the substance itself
than any of the other numbers.

The effect of gases on the emission will be considered at
length in the next chapter, but it is necessary to say a few
words about it in order intelligently to discuss the contents of
the preceding table. The early experiments of McClelland,^
with platinum and German silver wires, showed that the emis-
sion was unaffected when the pressure of the surrounding gas
was changed from 0*004 to 004 mm. This rather indicated
that to obtain the characteristic elementary values it was
necessary only to get rid of gas to an extent sufficient to

1 Cf. Chap. IV.

»•• Camb. Phil. Proc.," Vol. XI, p. 296 (1901).

72 EMISSION OF ELECTRICITY FROM HOT BODIES

avoid complications due to secondary actions between the
liberated electrons and the gas, such, for example, as impact
ionization. Thus in the writer's experiments Nos. i and 4 no
precautions to avoid gaseous contamination were taken except
to keep the pressure well under O'Oi mm. by continuous
pumping. Working with platinum wires H. A. Wilson ^
found that the emission had the same value at a given
temperature in air, nitrogen, and water vapour at low pres-
sures. On the other hand, the emission was enormously
increased by hydrogen even when this gas was present in
very small quantity. The vapours of mercury and phos-
phorus pentoxide were also found to increase the emission to
some extent at high temperatures. The writer ^ found later
that the negative emission from platinum in an atmosphere of
oxygen was independent of the pressure at pressures below
I mm. when there was no impact ionization. In experiment
No. 4 the gas present was that given off from the wire and
the surrounding electrode under the influence of heat, and
gases emitted from hot metals usually contain a considerable
proportion of hydrogen. This led Wilson to think that the
observed emission from platinum in general might be largely
or entirely conditioned by the presence of hydrogen. He
therefore sought to remove all traces of hydrogen from the
wires he experimented with by boiling them in pure nitric
acid and also submitting them to the action of nascent
electrolytic oxygen for long periods. We shall see also that
certain oxides, particularly lime, have a much greater power
of emitting electrons than platinum, and if we are to observe
the effects from platinum itself it is necessary to get rid of all
traces of these substances. This would be accomplished by
the nitric acid treatment. After a purification lasting one
hour Wilson observed the values given under No. 5, whilst
those under No. 6 were obtained after treatment lasting
twenty-four hours. It will be seen that the effect of the
treatment is to increase b very considerably. As the value of
A^ is not much affected this corresponds to a large reduction

i"Phil. Trans., A.," Vol. CCII, p. 262 (1903).
^Ibid., Vol. CCVII, p. I (1906).

TEMPERATURE VARIATION 73

of the emission, especially at the lower temperatures. At
1500° C. the values under No. 4 give an emission about
250,000 times as large as the values under No. 6. Notwith-
standing this large reduction in the emission it does not
appear that it can be got rid of entirely by removing all traces
of hydrogen. This is shown very strikingly by an experiment
made by the writer ^ in which a hot exhausted platinum tube
was used. This tube was heated for a long time in air at
atmospheric pressure and was found to give the small emis-
sion, constant at a given temperature, which characterizes a
wire which has been thoroughly soaked in oxygen, as in
Wilson's treatment. Hydrogen was then allowed to diffuse
through the walls of the tube by admitting it to the interior.
Even when relatively large amounts of hydrogen diffused out
of the tube no increase in the observed negative thermionic
emission from the outside of the hot tube could be detected.
It seems impossible to reconcile the results of this experiment
with the view that the emission from platinum is entirely and
fundamentally conditioned by the presence of hydrogen.

The values under No. 7 are for a platinum wire cleaned
with nitric acid and heated in oxygen at a pressure of i 47
mms. The potential difference used in making the measure-
ments was 40 volts, and as there is some impact ionization
under these conditions the value of Aj will be a little too
high thereby. Number 8 is for a clean wire but not specially
oxidized. However, there is no doubt that in Deininger's
experiments as a whole the apparatus was well glowed out,
and they show relatively little evidence of obvious trouble
from gaseous contamination. Number 9 is for a platinum
wire cleaned with nitric acid and heated in an atmosphere of
helium at a low pressure. No. 10 is for a clean platinum
wire in hydrogen at 133 mms. and is included in order to ex-
hibit the enormous reduction in both b and Aj which occurs
when platinum is heated in this gas. The reduction in b
much more than offsets the reduction in A^, so that the com-
bined effect is an increase in the emission. The increase is
more marked at relatively low temperatures. Number 1 1 is a
1" Phil. Trans., A.," Vol. CCVII, p. i (1906).

74 EMISSION OF ELECTRICITY FROM HOT BODIES

preliminary result given by Langmuir, supposedly for very
good conditions as to freedom from gaseous contamination.
As the details have not yet been published it is impossible to
criticize this result, but the values are widely different from
those found by the other experimenters, (See, however,

p. 122.)

In considering the variation of A^ and b it is important to
remember that a given variation of b means a great deal more
than a variation of A^ in the same proportion, b is deduced
directly from the ratio of the currents at two known tempera-
tures, and Aj is then obtained from a knowledge of the ther-
mionic current per unit area at any known temperature. On
account of the exponential relation a small error in b gives
rise to an enormously greater error in Aj. Thus in a parti-
cular case worked out by the writer ^ it was found that an
error of lo per cent in /5 changed A by a factor of lOO, whilst
an error of 33 per cent in b multiplied A by a factor of 3 x lo^
Another possible source of uncertainty, depending on the
form of the temperature law, arises if <^ is a linear function of
T. Thus if b=bQ + ^T we have

Part of the constant A^ as given by the experiments will then
arise from the temperature coefficient of b, the constant be-
coming in fact Aj^e ~ ^. So far as the pure metals are con-
cerned, the theory in the last chapter indicates that the
temperature variation of the quantity corresponding to b is
comparatively small and, to a close approximation, calculable.
The possibility of this complication has, however, to be borne
in mind when we are dealing with a contaminated surface
whose constitution may change with changes of temperature
and other conditions.'^

Let us now consider if it is possible to draw any conclu-
sion as to the probable value for uncontaminated platinum
from the figures given in the table. No. 10 in hydrogen at
133 mm. pressure may be at once left out of account and it is
likely that No. 4 also suffers from hydrogen contamination.

1" Phil. Trans., A.," Vol. CCI, p. 542 (1903).
2Cf. pp. loSfF., Chap. IV.

TEMPERATURE VARIATION 75

It is at least possible that the rather drastic oxygen treatment
to which Nos. 5, 6, and 7 were subjected does more than was
desired by leaving a layer of oxygen at the surface of the
metal, which tends to retard the escape of the electrons.
No. 1 1 may be left out of account pending further details
as it is quite out of line with all the rest. This leaves Nos.
8 and 9 which agree with one another. There is no obvious
objection to them, and it seems likely that the best guess we
can make at present is that the final value of b for platinum
will be somewhere near 6x10* and the other quantities near
the values given under No. 8.^ Schlichter,^ however, has
recently concluded that the lower values of b given by Nos.
4 and 1 1 a are probably nearest to the correct values for un-
contaminated platinum. He has pointed out that the emis-
sion from a pure metal surface is characterized by the occurrence
of saturation without accelerating potential. This criterion was
satisfied by the experiment which led to the values under No.
Iia whereas this test was not investigated in the other experi-
ments. The criterion emphasized by Schlichter is an im-
portant one, but it can scarcely be regarded as an absolute
guarantee that the requisite purity has been attained, since
it is at least possible that a platinum surface saturated with
hydrogen, for example, would satisfy this criterion and still
not give the values of the emission constants characteristic-
of the metal. At least it seems safer to adopt some such
position until the matter has been subjected to a more search-
ing experimental test.

Turning to the values for carbon, No. i can safely be
neglected as being affected by some serious error, probably
arising from impurities in the material used. Nos. 2 and 3
agree moderately well ; on the whole No. 3 should be better
than No. 2.

The values for tungsten, Nos. 12 and 1 2a, are probably
much the most reliable in the whole table. Even here, how-
ever, there is a difference by a factor of almost twenty in the
two values of Aj.

1 Cf., however, O. W. Richardson, " Roy. Soc. Proc., A.," Vol. XCI, p. 504

(1915).

' Loc. cit.

76 EMISSION OF ELECTRICITY FROM HOT BODIES

There is a big difference in the two sets of values for tan-
talum. No. 14 is probably the more reliable. The observa-
tions for molybdenum stand alone and are given by Langmuir
as preliminary, otherwise there is no reason to question their
approximate correctness.

The values under 1 5a are for the saturation currents from
nickel as determined by Schlichter. His values of the current
under zero potential difference were much lower and gave
values of b nearly 50 per cent higher than those in the table.
Thus the criterion referred to above was far from being
satisfied and the behaviour of nickel seems to call for further
examination.

Horton's experiments were made with calcium sublimed
on to purified platinum electrodes in helium at a low pressure.
It was shown that the gas emitted by the calcium during sub-
limation had no measurable effect on the emission. Freden-
hagen ^ has since made experiments with metallic calcium from
which he concludes that the emission from this substance is
caused entirely by oxidation. This appears to be a possible
explanation of the large currents he obtained from calcium
heated in tubes which were not completely gas-tight, but it
would not seem to apply to the results of Horton, who took
very thorough precautions against oxidation, and also obtained
much smaller currents than Fredenhagen. At any rate, the
objection urged cannot be accepted without more substantial
experimental support. At the same time one cannot feel very
certain that the values given by Horton represent the true
emission values for pure elementary calcium, since this sub-
stance is such a powerful absorbent of gases at high tempera-
tures that it is doubtful whether there is any possible method
of freeing it from gaseous contamination.

The writer's experiments with sodium No. 17 were made
under very unsatisfactory conditions, and are not considered
to have any precise quantitative significance. They were
made under conditions such that there was a very considerable
evolution of gas inside the apparatus, and there was no ap-

^ •' Ber. kon. Sachs. Gesell. der Wiss. Math. Physik. Kl.," Leipzig, Vol.
LXV, p. 56 {1913).

TEMPERATURE VARIATION 77

proach to saturation. Moreover, it has been shown by Haber
and Just ' that there is a very considerable emission of electrons
from the alkali metals at ordinary temperatures, when they
react chemically with such gases as Oj, HgO, HCl, etc. Prob-
ably this effect is much augmented when the temperature is
raised ; and Fredenhagen "^ has shown that the large currents
ordinarily obtained from sodium and potassium are enormously
reduced by getting rid of traces of gas by continued distillation
in vacuo. At the same time the smallest currents obtained by
Fredenhagen from sodium and potassium were enormously
greater than those given by the more electronegative elements
like platinum and carbon at equal temperatures, and, moreover,
they were not saturated. On the whole we are only justified
in concluding that little is known definitely about the magni-
tude of the emission from these metals. No doubt the diflS-
culty of removing traces of gas in these cases is similar to that
met with in the case of calcium.

Leaving out of account the data under Nos. i, 10, 15a, and
17, the values of b all lie between the limits 3*65 x 10* and
8 X 10*. An estimate ^ of the order of magnitude of b can be
got by considering the electrostatic attraction of the con-
ductor on the escaping electron. The force on the electron is
attractive, and equal to that arising from an equal charge situ-
ated at its mirror image in the surface. Its amount at distance
z is thus 6 "^l^z^. This force would be infinite at the plane
z = 0, and if the electricity were continuously distributed in
the conductor an infinite amount of work would have to be
done to remove a finite quantity of electricity. Owing to the
discrete distribution of the electricity, however, there is an ef-
fective lower limit to z which may be denoted by d, where d
is a quantity comparable with the average distance between
the electrons in the conductor. The order of magnitude of the
work done by an electron in escaping will thus be given by

\\^ —^dz. If we put ^ = 5 X 10-^ this expression gives

1 " Ann. der Phys.," Vol. XXXVI, p. 308 (191 1)-

'"Verb. d. Deutsch. Physik. Gcs.," Jahrg. 14, p. 384 (1912) ; «*»<'•» Jahrg.
16, p. 201 (1914).

» O. W. Richardson, " Phil. Trans., A.," Vol. CCI, p. 543 (1903)-

78 EMISSION OF ELECTRICITY FROM HOT BODIES

b = 5 X 10* roughly, in agreement with the observed values.
Such a value of d would indicate that the number of electrons
in atoms is of the same order as the atomic weight, in agree-
ment with current estimates.

The values of ^q, the potential difference in volts through
which an electron would have to fall in order to acquire an
amount of energy equal to that necessary to escape from the
substance at the absolute zero of temperature, have been ob-
tained from the relation

d =

€<f>o X lO*

€ being expressed in electro-magnetic units. This deduction
does not require a knowledge of the absolute value of the ionic
charge e. For if we multiply top and bottom by v, the number
of molecules in i c.c. of a perfect gas at o" C. and 760 mm.
pressure, we obtain, after transposing,

, J k —8 . vk —8

^0=^X_xIO = d -K — xio , . (2<\

where vk = K the gas constant for i c.c, and ve = the charge
in electro-magnetic units required to liberate 0'5 c.c. of H2 in
electrolysis (o'5 c.c. since the molecule of hydrogen contains
two atoms). These are both well-known physical quantities
having the values : —

R = 372 X 10^ erg. deg.-^ and ve = '4327 e.m.u.

The values of ^0 are all seen to lie between 3 and 6-6 volts.
So far as the order of magnitude is concerned this supports
the theoretical conclusion reached in Chapter II, p. 41, that
the differences of </>o should be equal to the contact potentials
between the different metals. The values of ^^ are not, how-
ever, reliable enough adequately to test this conclusion in de-
tail. The best support is given by the value ^^ = 3 -04 for
calcium which, when compared with the most probable value
for platinum, would make the former about 2 volts positive to
the latter element. According to the experiments made by
the chemical method by Wilsmore,^ calcium is 3*42 volts

^ " Zeits. fiir physik. Chemie," Vol. XXXV, p. agi (1900) ; Winkelmann's
" Handbuch der Physik," 2nd edition, Vol. IV, Pt. II, p. 855.

TEMPERATURE VARIATION 79

electropositive to platinum, but the chemical method usually
appears to give differences about 50 per cent greater than the
direct contact methods. On the other hand, from the discus-
sion in Chapter II we saw that it is not yet established with
absolute certainty that there is any considerable contact differ-
ence of potential between absolutely pure gas-free metals in
a perfect vacuum. Whether there is or is not, it is difficult
to see how the theoretical relation under discussion can avoid
being satisfied. The question of the existence of contact
electromotive force under ideal conditions of freedom from
gaseous contamination is undoubtedly of the highest and most
immediate importance from the standpoint of the theory of the
emission of electrons. Unfortunately, it is a problem which
furnishes the most extraordinary experimental difficulties.

According to the quantum theory considered in Chapter II,
the value of C (Ag of equation (32), p. 39) should be nearly the
same for all good conductors such as those included in the table
on p. 69. The value of C calculated from equation (32),
Chapter II, is

A, = C = 1-5 X lo^o

It will be observed that the good values of C given in the table
are all somewhat higher than this, but do not exceed it by
more than a factor of 10, approximately. Considering the
difficulty of determining C with any approach to accuracy, this
agreement affords some support for the quantum theory there
developed. On the other hand, the good values of Aj on p.
69 on comparison with the corresponding constants in equa-
tion (19) ofChapter II, which is based on the classical kinetic
theory, give values of «i, the number of free electrons in i c.c.
of the different metals, which range around lo^^ to lo^^ and are
in agreement with the estimates from optical data. On ac-
count of the uncertainty underlying the experimental values
of Aj and C it does not appear profitable to discuss this ques-
tion further at the present time.

Emission of Electrons from Compound Substances.

The property of emitting electrons when heated is not con-
fined to the list of elementary substances which constitute the

8o EMISSION OF ELECTRICITY FROM HOT BODIES

conductors of the ordinary metallic type. In fact there is no
reason to doubt that the property is one which pertains to all
types of matter provided that the condition of stability at the
requisite high temperature is satisfied. This view is strongly
supported by the facts that all known substances conduct elec-
tricity with facility at high temperatures, and all of the very
large number which have been carefully examined in this re-
spect exhibit the power of emitting electrons.

The first demonstration that this property was possessed
by compound substances was given by Wehnelt.^ In making
measurements of the fall of potential at a heated platinum
cathode in a discharge tube he found that the fall was greatly
reduced when the hot cathode was covered with a thin layer
of various oxides, notably those of calcium, strontium, and
barium. The reduced cathode fall was found to be due to the
increased emission of electrons from the cathode caused by the
presence of the oxides. Although the oxides mentioned were
much the most efficient, some reduction was also found to
occur with the oxides of magnesium, zinc, cadmium, yttrium,
lanthanum, thorium, and zirconium. On the other hand, the
oxides of beryllium, aluminium, thallium, titanium, cerium,
iron, nickel, cobalt, chromium, uranium, tin, lead, bismuth,
silver, and copper showed no effect.

The emission from the oxides of the alkaline earth metals
was examined in detail by Wehnelt and was found to show a
close correspondence with that exhibited by the typical met-
allic conductors. The current E.M.F curves were similar,
showing saturation at high and low pressures, and effects due
to ionization by collisions at intermediate pressures of the
order of i mm. Careful experiments ^ have, however, since
shown that the current from these cathodes never fully satu-
rates at very low pressures : there is always a small linear
increase with the voltage similar to that observed with metals
in tubes which have not been thoroughly glowed out. The

1 " Sitzungsber. der physik. med. Soc. Erlangen," p. 150 (1903) ; " Ann. der
Phys.," Vol. XIV, p. 425 (1904); "Phil. Mag.," Vol. X, p. 88 (1905).

^2 Wehnelt and Jentzsch, " Verb. d. Deutsch, Physik. Ges.," Jahrg. 10, p. 605
(1908).

TEMPERATURE VARIATION 8l

explanation of this difference is not quite certain. It may be
simply that these oxide layers continue to give off gas much
longer than the metals, owing to more tenacious retention.
On the other hand, it is possible that the evolution of gas is
due to chemical decomposition and is an important feature of
the action occurring. Wehnelt found the temperature varia-
tion of the approximately saturated current at low pressures
to be governed by the same formula / = AT*^"*/^ as that from
hot metals. This result has been confirmed by experiments
made later by Deininger, Horton, Jentzsch, and others. The
approximate values of the emission constants are given in the
following table : —

Substance. Observer.

Ai.

b. C. i. ^o(volt().

BaO Wehnelt 1

7 X lo"'

4.5 X 10* — — 3*65

CaO Wehnelt »

4-5 X io'«

4-3 X IO« — — 3-48

CaO Deininger *

I*I X lO**

4*3 X 10* 2'65 X ID** 4-05 X 10* 3*48

CaO Horton »

4 X lo^o

4*8 X 10* — — 3*9

CaO Jentzsch *

4-3 X io'«

403 X io< — — 3-36

The values of the constants for CaO agree quite well except
Horton's. In the experiments of Wehnelt, Deininger, and
Jentzsch the layer of oxide was deposited by evaporating a
solution of calcium nitrate and then heating the calcium nitrate
until it turned into the oxide. This is the usual method of
preparing these oxide-coated cathodes. In Horton's experi-
ments, which had a different objective from that of the others,
the lime was prepared by the action of oxygen gas on a hot
surface of metallic calcium. The measurements were made
under a potential difference of 40 volts in an atmosphere of
helium at 3*24 mm. pressure. No doubt these circumstances
would affect the measurements in various ways. Horton found
that at all temperatures between 700° C. and 1400° C. the emis-
sion from lime was much greater than that from calcium. A
comparison with the data in the table on p. 69 shows that the
difference between the effect from calcium and that from lime
prepared from calcium nitrate is not so great as that obtained
when calcium is compared with lime prepared by oxidation.

1" Ann. der Phys.," Vol. XIV, p. 425 (1904).
«/6td., Vol. XXV, p. 285 (1908).
»" Phil. Trans., A.," Vol. CCVII, p. 149 (1907).
* •• Ann. der Phys.," Vol. XXVII, p. 129 (1908).
6

82 EMISSION OF ELECTRICITY FROM HOT BODIES

The experiments of Deininger ^ are particularly instructive
and very consistent. He measured the emission at various
temperatures from filaments of platinum, carbon, tantalum,
and nickel both in the ordinary state and then when coated
with lime from calcium nitrate, and found that the emission
from the lime-covered wires at a given temperature was the
same in all cases.

This shows that in these experiments we are dealing with a
definite property of the oxides which is quite independent of
the underlying metal. The excellence of the agreement may
be judged from Fig. 9, p. 57, where a few of the observations
with lime on platinum, tantalum, and nickel respectively are
plotted. The values have been selected so as to exhibit the
worst as well as the best agreement.

The emission from Nernst filaments has been carefully ex-
amined by Owen ^ and Horton.^ It is smaller than that from
the alkaline earths, otherwise there are no special features.
From the data found by Owen the approximate values of the
constants are A^ = 7 x 10^^ and ^ = 4*6 x 10*.

A systematic examination of a large number of metallic
oxides has been made by Jentzsch,* The oxides were de-
posited on platinum wires by the decomposition of appropriate
solutions. By taking very great care in the purification of the
platinum the emission from the metal was reduced to a low
value and the number of oxides which were found capable of
a greater emission, at relatively low temperatures, was greatly
extended. The emission from practically all of these sub-
stances increases with temperature more slowly than that from
platinum itself; so that even if they have a greater power of
emission at low temperatures, at sufficiently high temperatures
the platinum will catch up to and overtake them. In the case
of zinc and magnesium oxides Jentzsch found that this hap-
pened at about 1600° C. Of the oxides tested the only ones
which were found to give rise to no effect were those of thal-
lium and lead which probably volatilized before sufficiently

1 Loc. cit. 2 " Phil. Mag.," Vol. VIII, p. 330 (1904).

3 " Phil. Trans., A.," Vol. CCXIV, p. 277 (1914).
* " Ann. der Phys,," Vol. XXVII, p. 129 {1908).

TEMPERATURE VARIATION 83

high temperatures could be attained. In the case of lithium
oxide some emission was observed between 700° C. and 800°
C, but this disappeared on raising the temperature further, also
probably on account of volatilization. The values of the con-
stants deduced by Jentzsch from his measurements with dif-
ferent oxides are collected in the following table : —

Values of

Oxide of

Al.

n,.

^ (volts).

2*94 X io'«

2'0 X 10''

4'i6 X 10*

3-58

3'i6 X 10"

2T X 10"

4*49

3-87

2-68 X io»«

1-8 X 10"

4-03

3-48

2*II X lO*'

I "4 X 10"

3-95

3-40

6*45 X 10"

4*3 X 10^'

2-39

2-o6

I-I7 X lo*'

7-8 X 10"

363

313

4*3 X 10'^

2*9 X lO^'

379

3*26

4*o X ioi»

27 X 10"

373

3-21

4' I X io»^

27 X 10"

3-66

3-15

2'i9 X 10'"

1*5 X 10"

3-56

3 -06

1*22 X 10"

8-2 X lO"

371

3*20

1-92 X 10"

1*3 X 10"

351

302

2'23 X 10'"

r"5 X 10^'

469

4-04

174 X 10"

I -2 X 10"

512

4-41

332 X 10''

2*2 X 10"

4 97

4-28

2*33 X 10*8

1-6 X 10"

3 -02

2*6o

2-19 X 10**

1*5 X 10"

2-25

1-94

The values of ^ have been calculated directly from the
t>
relation ^ — b — x lo"® and have not been reduced to the
e

absolute zero. They are therefore a little larger than the cor-
responding values of <^^. The differences are, however, small.
The values are clearly much smaller than those for the re-
fractory metallic conductors, corresponding to the smaller rate
of increase of emission with rising temperature. The values of
n^ as calculated from equation (19), Chap. II, hav^ also been
included. These numbers cannot, however, be regarded as
the number of free electrons present in unit volume of the
oxides. This is evident from the following considerations.
The low electrical conductivity of the incandescent oxides
compared with that of the metals indicates that the classical
kinetic theory will probably apply both to the internal and to
the external free electrons in these cases. Admitting this, let
i/q be the concentration of the external, and v^ of the internal,
free electrons, then by a well-known theorem ^

I/O = v^e-^i^"^ .... (26)

» Cf. O. W. Richardson, •• Phil. Mag.," Vol. XXIII, p. 608 (1912).

84 EMISSION OF ELECTRICITY FROM HOT BODIES

where w is the work done by an internal free electron in es-
caping. Now we know from thermodynamics that v^ is of the
form

/L jY
Rxa

where L is latent heat of evaporation, a quantity whose tem-
perature variation may to a first approximation be disregarded.
Thus v^ is very close to the form const, x e -"n^t./T^ ^^^ since
the variation of iv with T may be disregarded (a linear vari-
ation makes no diflference), and since also v-^ does vary rapidly
with T, as is shown by experiments on the electrical conductivity
of heated oxides, v^ must be of the same form, and given by,
let us say, vx = A' e"^'l^'^ where A' and w' are constants.
Hence from (26)

V, = A'^-<«'+«''>/RT . . . (27)

Thus the process of taking out the exponential temperature
factor, which is what the calculation of Wj really amounts to,
leaves neither v^. nor «i but A' an arbitrary constant. This
argument is only an approximate one and may perhaps appear
involved, but there is no doubt that the conclusion is sound.
The enormous temperature variation of the conductivity of
metallic oxides alone is sufficient to show that n^ is not con-
stant as the numbers in the table would indicate. It is inters
esting to observe that the values of A^ given by the oxides
generally are lower than those given by the metals, the alkaline
earths alone being in the same class with the metals in this
respect

All the oxides for which the constants are tabulated be-
haved quite regularly, but the emission from manganese oxide
was found by Jentzsch to be peculiar. As the temperature
was raised there was found to be a sudden increase in the
emission at a certain stage and this increased value of the
emission was found to persist when the temperature was
subsequently reduced. A second sudden increase to a still
higher value of the emission was detected when the tempera-
ture was raised to a value higher than any previously
employed. These effects are attributed by Jentzsch to the
formation of the various oxides of manganese.

TEMPERATURE VARIATION 85

The emission from Wehnelt cathodes — hot metal cathodes
coated with lime or baryta — has attracted a good deal of at-
tention, partly owing to their practical application as a con-
venient source of powerful electron currents. Fredenhagen ^
has described a number of experiments which led him to the
conclusion that the emission of electrons from these cathodes
is a secondary effect, arising from the recombination of the
earth metal with the oxygen liberated by electrolysis during
the passage of the current through the oxide. This view ac-
quires a certain amount of plausibility owing to the results of
a research of Horton's ' on the electrical conductivity of heated
oxides, in which he concludes that such conductivity, although
mainly electronic (i.e. of the same type as that of metals), is
to some extent accompanied by electrolysis. One result of
Fredenhagen's view is that the electronic emission from lime
at a given temperature should be larger when the lime is
heated electrically than when methods of heating which do not
involve the use of an electric current are employed. This test
is difficult to perform satisfactorily and the earlier experiments
seemed to indicate such a difference. In later experiments
made under better conditions Fredenhagen ' was able to heat
a lime-coated platinum strip by means of (i) an electric cur-
rent through the strip and (2) a beam of heat radiation focussed
on the surface of the lime. This experiment showed no difference
in the emissions at a given temperature, except what might be
due to unavoidable experimental error. The fact that the
mode of heating makes no difference in the emission at a given
temperature has been confirmed by Horton * by experiments
with the Nernst glower. The other grounds on which
Fredenhagen rests his thesis may briefly be summarized as
follows : —

I. The oxide gradually disappears as the cathode is
worked. It probably disappears slowly when it is heated with-
out emission occurring, but the disappearance is undoubtedly

» " Ber. d. Sachs. Ges. d. Wiss. Math. Physik. Kl.," Vol. LXV, p. 42 (1913) ;
" Phys. Zeits.," Jahrg. 15, p. 21 (1914).
"•Phil. Mag.," Vol. XI, p. 505 (1906).

»" Ber. d. Sachs. Ges. d. Wiss. Math. Physik. Kl.,*' Vol. LXV, p. 55 (1913).
«" Phil. Trans., A.," Vol. CCXIV, p. 277 (1914).

86 EMISSION OF ELECTRICITY FROM HOT BODIES

much faster when emission is occurring, i.e. when the oxide is
negatively charged.

2. Gas is given off when the cathode is in action.

3. The underlying platinum shows corrosion, which Fre-
denhagen attributes to the formation of an alloy between the
platinum and the calcium liberated by electrolysis.

4. The emission from calcium in a good vacuum is much
smaller than when it is measured in a tube into which air
slowly leaks.

As regards (i), Wehnelt and Liebreich^ have brought for-
ward very strong evidence that the loss of oxide is due to
a combination of simple evaporation and sputtering due to
bombardment of the oxide by positive ions arising from im-
pact ionization. The second cause is operative only when
the oxide is negatively charged, thus accounting for the in-
ceased rate of loss under these conditions.

The same authors have also considered (2) and from their
experiments conclude that the gas is given off mainly in the
early stages of heating. A spectroscopic examination showed
the presence only of hydrogen, probably arising from the
platinum and from water occluded in the lime. Gehrts ^ has
observed spectroscopic evidence of the presence of calcium
and oxygen in the glow from lime cathodes, but only under
conditions such as would lead to extensive evaporation or
sputtering of the lime owing to intense cathodic bombard-
ment by positive ions.

Tests made by Wehnelt and Liebreich show that the
platinum corrodes to the same extent whether it is covered
with lime or not.

The cogency of (4) appears to be disposed of by the
results of the experiments of Horton, who showed that the
emission from lime was much greater at a given temperature
than that from metallic calcium. Horton^ has also shown
by direct experiment that there is no measurable electronic
emission when calcium is oxidized at 500° C. to 600° C,

1 " Phys. Zeits.," Jahrg. 15, p. 557 {1914).

2" Verb, der Deutsch. Physik. Ges.," Jahrg. 15, p. 1047 (1913).

3 " Phil. Trans., A.," Vol. CCXIV, p. 292 (1914).

TEMPERATURE VARIATION 87

although there is a very marked emission when the oxide
formed is heated to 700° C. to 800° C. subsequently. This
experiment would seem to prove that the act of oxidation
is not an important factor as compared with the effect of
change of temperature.

Taking all the evidence together it seems to the writer
that the view which attributes the emission from metallic
oxides to the escape, owing to increased kinetic energy, of
those elections which give rise to the electrical conductivity
of such materials has much more to be said for it than any
other so far put forward. This position is strengthened by
the recent experiments of Germershausen,' who has shown
that the removal of the last traces of gas from a Wehnelt
cathode and its surroundings increases the emission from it
Under these conditions the discharge from the lime becomes
very steady and shows temperature and voltage characteristics
similar to those exhibited by tungsten filaments under the
best vacuum conditions. (See pp. 61 and 117.)

Horton "^ and Martyn ^ found that the emission from the
Wehnelt cathode, like that from a hot platinum wire, was
greatly increased in an atmosphere of hydrogen.* Martyn,
whose experiments were made in air and hydrogen at atmo-
spheric pressure, found that when the currents were approxi-
mately saturated the results could be expressed in a very
simple manner. If at a given temperature x is the thermionic
current from a clean platinum wire in air, ax that from a lime
coated platinum wire in air, and bx that from a clean platinum
wire in hydrogen, then the thermionic current from a lime
coated platinum wire in hydrogen at the same temperature is
abx. a and b were both found to be very nearly equal to 10*
at 1600° C, and varied to some extent with the temperature.

» " Phys. Zeits.," Jahrg. 16, p. 104 (1915).

«•• Phil. Trans., A.," Vol. CCVII, p. 149 (1907).

» " Phil. Mag.," Vol. XIV, p. 306 (1907).

* Horton (" Roy. Soc. Proc., A.," Vol. XCI, p. 322 (1915)) has recently
concluded that this increase occurs to any appreciable extent only when the
pressure of the hydrogen is considerable and that it is perhaps to be attributed
to an interaction between the hydrogen and the platinum. At pressures com-
parable with o'oi mm. he found little difference in the emissions from lime or the
Nernst glower in hydrogen, air, oxygen, or nitrogen.

88 EMISSION OF ELECTRICITY FROM HOT BODIES

This result, which has only been established approximately,
appears to require, to a corresponding degree of approxima-
tion, that the contact potential difference between lime in an
atmosphere of hydrogen and lime in air should be equal to
that between platinum in hydrogen and platinum in air, when
the temperatures are the same in both cases. This follows
from a consideration of the equilibrium of the electrons in an
enclosure containing bodies of lime and platinum in suitable
electrical connexion. The enclosure is imagined to be divided
into two separate parts by a diaphragm permeable to electrons
but not to gases, one part containing hydrogen at a definite
pressure and the other containing air or exhausted. The
partial pressure of the electrons is the same on both sides of
the diaphragm whose presence cannot affect the conditions
which determine their equilibrium. Let n^ and Vi respectively
denote the equilibrium concentration and the potential of the
electrons just outside the platinum in air, n^ and V2 the cor-
responding quantities for lime in air, n^ and Vi' for the
platinum in hydrogen, and n^ and Vj' for the lime in hydro-
gen. Then, as in Chapter II, p. 40, the condition of equili-
brium of the electrons in the enclosure requires that

«j/«2 = g-e(Vl-Va)/ftT _ ^ ^ (28)

«27«2 = ^"'^^''"^'^'*'^ • • • (29)

But if we neglect electron reflection, since the saturation
currents t are proportional to the corresponding values of « at
constant temperature,

«l/«2 = «*iA2 = «. • • • (30

and

«27«2 = h'Jh ^b . . . (32)

If Martyn's result is to hold

Klh^ n{ln^ = ab\ . . . (33)

so that, from (28), (29), and (30),

V;-V, = V/-V,. . . . (34)

which is the condition referred to. Since from (34)

v; - v; = Vi - V2, . . . (35)

TEAfPERATURE VARIATION 89

this condition is also embodied in the statement that, to the
degree of accuracy in question, the contact potential difference
between platinum and lime should be the same in air as in
hydrogen. The contact differences mentioned are those which
would obtain at the temperatures of the experiments, not at
ordinary temperatures.

As to the nature of the process by which the hydrogen
affects the emission, and, according to the foregoing theory,
the contact differences of potential also, this may be tentatively
attributed to an effect of positive hydrogen ions dissolved in
the solids. The writer ^ has pointed out there is considerable
evidence in favour of the view that some of the hydrogen which
dissolves in platinum is not merely dissociated into atoms but
exists in solution in the form of positive ions. If this is ad-
mitted it follows from the laws of chemical equilibrium that
there will also be a certain concentration of hydrogen ions in
the external hydrogen, and the same may be expected also of
the hydrogen which is entangled or absorbed in the layer of
lime. If /i, /2» ^^C'j ^^^ ^he partial pressures of the hydrogen
ions in equilibrium in the various phases of the system, then,
as Sir J. J. Thomson "^ has pointed out, the difference of con-
centration in any two phases will give rise to a difference of

kY
potential across the interface equal to — log /xZ/a. etc., just

as a similar term in the electromotive force arises in the theory
of concentration cells. Until further information is available
it seems most satisfactory to attribute the changes in contact
potential difference and electron emission brought about by
gases to an effect of this character. The matter will be dis-
cussed again in the next chapter, pp. 108 ff.

The discharge from hot lime cathodes is affected by other
gases as well as by hydrogen. This is shown, for example,
by data recently published by Fredenhagen.^ The phenomena,
except at very low pressures, are complicated by effects arising

» " Phil. Trans., A.," Vol. CCVII, p. i (1906).

'"Conduction of Electricity through Gases," 2nd ed., p. 204, Cambridge
(1906).

• " Phys. Zeits.," Jahrg. 15, p. 19 (1914). Cf., however, Horton, " Roy.
Soc Proc.," loc. cit.

go EMISSION OF ELECTRICITY FROM HOT BODIES

from a number of different causes, and it is impossible to dis-
entangle the details in the data at present available. Some
very interesting features of the discharge from a Wehnelt
cathode in gases at low pressures have been studied by Sir
J, J. Thomson.^ In air at about 0'2 mm. pressure, for ex-
ample, there is a very rapid increase in the current with in-
creasing potential at relatively low potentials. At a certain
stage (at 37 volts potential difference in one of the tubes used)
a faint glow appears at the anode. This glow gradually be-
comes more extensive and brighter as the potential difference
and current are increased. With a constant potential differ-
ence at this stage the currents increase with increasing distance
between the electrodes, showing that part of the current arises
from impact ionization, or at least from some secondary phe-
nomenon, in the gas. At a slightly higher potential (at 53 volts
in a particular instance) the luminosity, hitherto confined to
the neighbourhood of the anode, suddenly extends throughout
the tube. This discharge, which appears very sharply at a
quite definite potential, is accompanied by an enormous in-
crease in the current. At this stage the discharge is an ordinary
luminous discharge, and the small potential difference required
to maintain it corresponds to the reduction in the cathode fall
originally discovered by Wehnelt.

These large currents with relatively small potential differ-
ences are attributed by Thomson to ionization by repeated
impact. He supposes that if a molecule is struck several
times in succession by an ion the energy is stored up in
the molecule : so that ionization by collision will occur with
smaller potential differences than when single impacts alone
are operative. In other words, with a given potential differ-
ence on the tube impact ionization will be much more frequent
with large than with small currents.

Experiments on this subject have been made more recently
by Child,^ who considers Thomson's explanation inadequate
on the grounds that the phenomena occur under conditions
such that the frequency of occurrence of repeated impacts is

^ " Conduction of Electricity through Gases," 2nd ed., p. 478.
2«'Phys. Rev.," Vol. XXXII, p. 492 (191 1).

TEMPERATURE VARIATION 91

prohibitively small, and also because he concludes from his ex-
periments that the effects are determined rather by the nature
and temperature of the cathode than by the magnitude of the
primary thermionic current. Thus with hot platinum cathodes
much larger primary currents are required to produce the effects
than with hot lime cathodes. He attributes the large currents
to the emission of electrons from the cathode under the in-
fluence of the bombardment by positive ions liberated by single
impact ionization in the gas.

This subject is an important one from the standpoint of
the mechanism of the ordinary luminous discharge and of the
arc, and in view of the disagreement referred to there seems to
be room for further experiment.

One of the great advantages of the hot lime cathode is
that it may be used to furnish an intense source of electrons
of very small linear dimensions. Thus if a minute speck of
lime is deposited on a piece of platinum wire or foil which is
heated, the emission per unit area from the lime is so enor-
mously greater than that from the metal that, even when the
disparity in area of the surfaces is taken into account, the total
emission from the metal may be neglected in comparison. Very
narrow streams of electrons moving with a definite velocity may
be produced in this way. The application of this possibility
to the measurement of elm for the electrons, as developed by
Wehnelt and perfected by Bestelmeyer, has already been re-
ferred to (p. 11). Another advantage of the cathode is that
it is chemically stable in presence of most of the commoner
gases. For work in high vacua the writer has found that fila-
ments of tungsten or osmium are preferable to hot lime as a
source of intense streams of electrons, owing to their greater
permanency and freedom from emission of gas. They can,
however, only be used under very good vacuum conditions or
with inert gases, as a trace of oxygen is sufficient to eat them
up almost instantaneously.

J. Lilienfeld ^ has investigated the potential gradient re-
quired to drive electron currents of considerable magnitude
through long tubes under good vacuum conditions. He finds

1 " Ann, der Physik," Vol. XXXII, p. 675 (1910) ; Vol. XLIII, p. 24 (1914).

92 EMISSION OF ELECTRICITY FROM HOT BODIES

that over a considerable range the potential gradient is nearly-
proportional to the square root of the current and is constant
along the length of the tube. If the last-named result were
strictly true it would follow from Poisson's equation that the
volume density of the electrification must be zero during the
passage of the current. To explain his results Lilienfeld
adopts the rather heroic hypothesis that the negative ions
are compensated for by the presence of positive ions formed
by the dissociation of the vacuum. It appears, however, that
under the conditions of these experiments, even if there are
no positive ions, the volume density of the negative electri-
fication would not be large, and it is doubtful if the measure-
ments of the potential gradient are accurate enough to detect
the expected variation along the length of the discharge.
The difficulty of determining the local potential by means of
sounding wires in a unipolar discharge is well known. Minute
traces of gas would also greatly reduce the negative volume
density, and it may not have been possible completely to re-
move them even with the very elaborate precautions in this
respect which were taken by the author. At any rate it is
clear that there are a number of possible explanations of a
rather ordinary character which have still to be disproved.

The Emission of Electrons from Various Compounds.

The power of emitting electrons when heated is not con-
fined to the oxides and elementary substances. It is prob-
ably a common property of all forms of matter which are
stable enough to continue in existence at sufficiently high
temperatures. The writer^ found that the following salts
emitted electrons at comparatively low temperatures, viz. :
the iodides of calcium, strontium, barium, and cadmium, cal-
cium fluoride, calcium bromide, manganous chloride and ferric
chloride. The emission from these salts possesses important
features which are not exhibited by the substances hitherto
considered.

The iodides of the alkaline earth metals are remarkable

1" Phil. Mag.," Vol. XXVI, p. 458 (1913).

TEMPERATURE VARIATION 93

for the large magnitude of the emission at relatively low tem-
peratures. A specimen of barium iodide, heated on a plati-
num strip of which it covered a few square millimetres, was
found to give a current of two milliamperes at a temperature
so low that the strip was invisible in an ordinarily lighted
room. With all the salts mentioned the emission consists in
general of a mixture of electrons and negative ions of atomic
magnitude, the proportion between the two varying with the
temperature and other conditions.

The behaviour of calcium iodide appears to be typical of
that of the iodides of the other alkaline earth metals. At low
temperatures, when first heated, the emission consists entirely
of heavy ions. With freshly heated specimens of the salt no
electrons could be detected at temperatures between 325° C.
and 523° C. The value of e/w for these heavy ions was
measured. The mean of 4 determinations gave elm = 807.
This corresponds to an electric atomic weight of 1 20. As the
chemical equivalent weight of iodine is 127, the heavy ions are
evidently atoms of iodine in combination with a negative
electron. If the fresh salt is heated continuously at a con-
stant low temperature the emission increases rapidly to a
maximum in about fifteen minutes and then slowly decreases.
This increase to a maximum and subsequent decrease is found
to occur also at the higher temperatures at which electrons are
present. A similar phenomenon has been found to charac-
terize the emission of positive ions from salts heated on strips
of metal (see Chap. VIII, p. 243).

At 534° C. there was no certain evidence of the presence
of electrons on first heating, but they began to be detect-
able immediately after passing the maximum. After two
hours the current had decayed very considerably and the
electrons carried about 30 per cent of the total current.
At 654° C. the electrons were detectable at the outset and
reached their maximum before the heavy ions. After fifteen
minutes the electrons carried about 85 per cent of the current
and after two hours about 60 per cent. In general, however,
the proportion of the current carried by electrons increases both
with duration of heating and with rising temperature. As in

94 EMISSION OF ELECTRICITY FROM HOT BODIES

other cases of thermionic emission the emission of both ions
and electrons tends to increase rapidly with rising temperature,
other things being equal. It was noticed that the currents
were smaller after the cold salt had been left in a vacuum and
greater after similar exposure to air at atmospheric pressure.
Measurements with strontium and barium iodides indicated
that the heavy negative ions from these bodies also were iodine
atoms combined with an electron.

Experiments with calcium bromide showed that the whole
current from this substance at low temperatures was carried by
heavy ions initially. The value of e/w indicated that these
ions were atoms of bromine combined with an electron.

In the case of ferric chloride the negative emission did not
last long enough for measurements to be made with it. The
emission from cadmium iodide also was of a temporary
character. It was possible to show that both heavy ions and
electrons were present in the emission but not to measure the
value of e.lm for the former. In the case of calcium fluoride
the bulk of the current was carried by electrons. When there
are too many electrons present the method used for measur-
ing elm for the heavy ions gives unsatisfactory results, and in
the case of calcium fluoride all we can say is that the heavy
ions were of molecular or atomic dimensions. Manganous
chloride gave off both electrons and heavy ions. The electric
atomic weight found for the latter had values ranging from 59
to 88. These irregular results were probably affected by the
presence of too many electrons. They show, however, that the
heavy ions are of molecular or atomic magnitude.

An interesting question arises as to whether the negative
' atomions ' are emitted from the salts as such or are formed
by the combination of electrons with dissociated atoms of the
haloids subsequent to emission. This question cannot be
answered with certainty ; but the fact that over a considerable
range of temperature no electrons can be detected when the
salts are first heated, although considerable currents may be
carried by negative atomions, rather favours the view that the
latter are emitted as such. On the other hand one would ex-
pect negative ions sometimes to be formed by the union of

TEMPERATURE VARIATION 95

electrons with uncharged atoms and molecules. Sir J. J.
Thomson ^ has brought forward evidence of such processes in
vacuum tube discharges at low pressures, and some of the
effects of gases on the negative thermionic currents from car-
bon which have been observed by Pring'^ may be accounted
for' in this way. The negative discharge from hot platinum
and tungsten in a good vacuum is purely electronic or, at any
rate, the percentage of heavy ions present is too small to be
detected (cf. p. 9).

The Complete Photoelectric Emission.

It is well known that when light of sufficiently short
wave-length is allowed to fall on metals an emission of
electrons takes place under its influence. Since all substances
emit light when they are raised to a high temperature an
emission of electrons from hot bodies owing to the action of
light will occur, even when they are not illuminated from an
external source. The emission of electrons which arises in
this way may be termed either the autophotoelectric emission,
to indicate that it is caused by the light radiation supplied by
the hot body itself, or the complete photoelectric emission, to
indicate that it is excited by the complete (black body) radia-
tion with which the material is in equilibrium at the tem-
perature under consideration. By applying thermodynamical
principles to the equilibrium of the electrons liberated in this
way by a body maintained in a vacuous enclosure at constant
temperature, the writer* has shown that the number n of
liberated electrons present in unit volume in the state of
equilibrium depends upon the temperature T according to the
equation

n^Aefm'^,. . . . (36)

where A is a constant independent of T but characteristic
of the substance, ^ is the change of energy accompanying the

» •' Roy. Soc. Proc., A.," Vol. LXXXIX, p. i.(i9i3)-

«/6»d., p. 344(1913).

»Cf. O. W. Richardson, "Roy. Soc. Proc., A.," Vol. XC, p. 177 (i9M)-

« " Phil. Mag.," Vol. XXIII, p. 618 (1912).

96 EMISSION OF ELECTRICITY FROM HOT BODIES

liberation of one electron, and k is Boltzmann's constant.
This equation is identical with equation (7) of Chap. II,
but the constant A and the energy ^ may not have the
same values in the two cases even for the same substance.
The fact that photoelectric emission under a given illumination
is practically independent of the temperature of the illuminated
substance shows that the photoelectric <^ varies very little with
T. It follows from this, together with (36), by an argument
quite similar to that used in the thermionic case, that the
autophotoelectric saturation current is governed by the formula

i=Kl^e-'^, .... (37)

where A and b are constants and the index \ does not differ
much from unity. Thus, so far as the variation with tempera-
ture is concerned, there is no clear difference between the
thermionic and autophotoelectric currents, and it is possible
that the observed thermionic currents may all be attributable
to photoelectric activity. This point has also been brought
out by W. Wilson ^ who has calculated the emission on the
assumption that all the radiant energy absorbed by hot bodies
is converted, by quanta, into the kinetic energy of electrons
ejected from the atoms. In this way an expression for the
thermionic current is obtained which is practically the same
as {17) and agrees satisfactorily with the experimental results,
so far as the variation of thermionic current with temperature
is concerned.

It is of the utmost importance to settle whether thermionic
emission of electrons is due to photoelectric action or not.
As the autophotoelectric current and the thermionic current
both vary in the same way with the only controllable variable,
the temperature, the only method available for deciding this
question is to find whether the values of the autophotoelectric
current at a given temperature, as calculated from photoelectric
data, agree with the observed thermionic current at that tem-
perature. Such indications as are available point to the con-
clusion that the autophotoelectric currents are smaller than
the observed thermionic currents, although it is impossible to

1 "Ann. der Physik," Vol. XLII, p. 1154 (1913)-

TEMPERATURE VARIATION 97

give a completely decisive answer at present. The question
is beset with extraordinary difficulties, arising from various
causes. The most important of these are the difficulty of
determining the correct values of either the photoelectric or
the thermionic currents under given conditions, ignorance of
the precise mechanism of photoelectric emission and resulting
doubtfulness as to the validity of any hypotheses which may
be taken as the basis of calculation, very serious mathematical
difficulties attending the rigorous treatment of the theoretical
problems involved, and the difficulty of obtaining some of the
necessary data in an exact form.

Subject, more or less, to these reservations an idea of the
magnitude of the autophoto-electric emission from, let us say,
platinum may be obtained as follows : —

Data are now available ^ which give the number of
electrons emitted from platinum when unit light energy of
the different effective frequencies falls on it at normal incidence.
The magnitude of the auto-photoelectric emission will not,
however, be obtained if we simply multiply this number by
the corresponding intensity in the "black-body" spectrum
and integrate the product over the whole range of frequency,
on account of the different optical conditions in the two cases.
In the photo-electric experiments, in which a beam of light is
incident normally, the intensity of the exciting illumination
is greatest at the surface and falls off exponentially as the
depth of penetration increases. In the natural emission, on
the other hand, the electromagnetic radiation is isotropic and
its intensity is the same at all depths. This difference be-
tween the two cases can be allowed for if we have a know-
ledge of the coefficients of absorption of the electromagnetic
radiations of various wave-lengths and of the electrons which
they cause to be emitted.

In this connexion it is desirable to emphasize the fact that
the assumption, of an exponential law of absorption, for the •
very slowly moving electrons with which we are now con-
cerned, can only be regarded as the very roughest kind of ap-
proximation. The problem involved here is in reality a very
I Richardson and Rogers, •• Phil. Mag.," Vol. XXIX, p. 618 (1915)-

98 EMISSION OF ELECTRICITY FROM HOT BODIES

complex one ; the stream of electrons which travel in a given
direction suffer loss of their number both through true absorp-
tion and through scattering, and also lose energy as well.
Little is know definitely either as to the relative importance or
as to the precise effect of these different actions. In addition,
the electrons which escape lose most of their energy in passing
through the surface ; although this fact need not prevent their
rate of loss being approximately exponential when they are
travelling in the interior. In any event, the exponential law
of absorption is the only assumption with which it is possible
to arrive at any result in the present state of the subject.

Considering the case of a beam of light of definite frequency
incident normally, let I be the energy crossing unit area just
within the surface of the metal in unit time. Let a be the
coefficient of absorption of the liberated electrons when in the
metal, /3 the coefficient of absorption of the light, and N the
number of electrons ejected from the atoms of the metal when
unit energy is absorbed by them from the light. Only part of
the N electrons actually escape from the surface of the metal.
A simple calculation, allowing for the absorption of both light
and electrons, shows that the number N^ which escape from
unit area in unit time is

N,.-^N . . . (38)

The definition of the absorption coefficient a as used in
these calculations is not that usually given. The meaning of
a may be deduced from the statement, that of all the electrons
ejected from atoms in a plane slab of infinitesimal thickness
perpendicular to the radiation, the proportion e ~ "'' reach a
parallel plane distant x from the slab.

using Planck's notation, the corresponding number Nj^j/
emitted by the isotropic radiation inside the material, t^dv of
frequency between v and v + dv, is, by a similar calculation to
that which leads to (38)

TEMPERATURE VARIATION 99

N,</i/ = ^ — ^rl-, . , . (40)

■ 2^

whence we find for the total autophotoelectric emission, after
eliminating N by means of (38),

N, = J^N,^.= _[ --R^ d. . (41)

For any particular temperature T, the integral on the right-
hand side of (41) can be evaluated graphically if we know NJI
and /9/a for all frequencies. Values of N^/I for all frequencies
for which the factor

hv^\\e *T - I )
is appreciable have been given by Richardson and Rogers,* but
much less is known about the values of a and ^} The only
datum bearing on the value of these coefficients is an observa-
tion by Rubens and Ladenburg ^ who found that when ultra-
violet light passed through a thin gold leaf the emission of
electrons from the front side was 100 times as great as on the side
of emergence, whereas the intensity of the incident light was
1000 times that of the emergent light. From these num-
bers Partzsch and Hallwachs * have calculated that for gold
a= 1*03 X 10' cm. -iandyS= 0-59 x lo'cm. "'. Since gold
and platinum do not differ much from one another in atomic
weight and density, the value of the electron absorption co-
efficient a will probably be much the same for both metals.
According to some data deduced by Drude * from katoptric
measurements with sodium light /9 for platinum is greater
than for gold in the ratio 4 '26/2 "82. If this ratio holds also
for the rays which are photoelectrically active the value of /9
for platinum would become 089 x 10® cm."' instead of
0'59 X 10® cm. "'. Thus, with the data available the best esti-
mate that we can make is that

(a+/3)/a =1-86 . . . (42)

i"Phil. Mag.,"loc. cit.

»Cf., however, O. W. Richardson, •' Phil. Mag.," Vol. XXXI, p. 149 (1916).

> " Verh. der Deutsch. Physik. Ges.," Jahrg. 9, p. 749 (1907).

* " Ann. der Physik," Vol. XLI, p. 269 (1913),

* " Lehrbuch dpr Optik," ist ed.,'p. 338,

loo EMISSION OF ELECTRICITY FROM HOT BODIES

This is to be taken as a rough average value over the
wave-lengths which are active photoelectrically. As the values
for particular wave-lengths are not known the fraction (42) has
been taken outside the integral in computing (41). From the
known values of h and k and from the values of N^/I given
by Richardson and Rogers it appears, on evaluating (41),
that the autophotoelectric saturation current from platinum at
T = 2000° K. is

Nje = 5 X 10"" amp./cm.*^ . . (43)

In this calculation allowance has been made for the loss of
light by reflection from the platinum surface in the photo-
electric measurements. On the other hand, the intensity of
the electromagnetic radiation in the hot metal has been taken
to be the same as that of the corresponding black body radia-
tion in free space. This assumption is erroneous, but not
likely to alter the order of magnitude of the final result.

The value (43) of the autophotoelectric current is much
smaller than the values of the thermionic currents ordinarily
observed. Thus at 2000° K. Langmuir^ gives the following
values for the thermionic current densities for a number of
elements which include platinum : —

Element -» W.

Ta.

Mo.

Thermionic Current -*• 3 x 10-3

7 X 10-3

13x10-3

6x10-4

10-3

(amps, per sq. cm.)

The smallest thermionic currents ever recorded from plat-
inum in the neighbourhood of 2000° K. are those observed by
H. A. Wilson '^ with well-oxidized wires. He found 4 x 10 ~^
amp./cm.' at 1686° C. which corresponds to nearly 10 "'
amp. /cm. 2 at 2000° K.

We are thus led to the conclusion that the autophotoelectric
emission gives rise to an insignificant portion only of the ob-
served thermionic currents. This conclusion is only to be re-
garded as one to which the evidence at present available points
with considerable probability. It cannot be held to be estab-
lished beyond the possibility of a doubt, on account of the un-

1 " Phys. Rev.," Vol. II, p. 484 (1913).

'" Phil. Trans., A.," Vol. CCII, p. 243 (1903).

TEMPERATURE VARIATION idl

certainty involved in some of the assumptions underlying the
calculations. In view of the importance of the subject it is
very desirable that this question should be settled quite defi-
nitely ; but it is questionable whether any considerable advance
on the present calculations can be effected without a material
extension of our knowledge of the conditions underlying photo-
electric action.

CHAPTER IV.

THE EFFECT OF GASES ON THE EMISSION OF ELECTRONS.

I. The Emission from Platinum in an Atmosphere
OF Hydrogen.

We have seen that the emission from a well-purified and oxi-
dized platinum wire is affected very little by the presence of
an atmosphere of a number of the commoner gases at various
low pressures. Hydrogen, on the other hand, as H. A. Wilson
found, has a very marked effect in stimulating the emission
from this metal. The emission from platinum in an atmo-
sphere of hydrogen has been the subject of a large number of
experiments both by H. A. Wilson ^ and also by the writer.^
The observations are in some minor respects not entirely
harmonious, a result which probably arises from the complexity
of the phenomena in detail and from the difficulty of dis-
tinguishing the relative importance of different influencing
factors. The following discussion is confined to the more
important points, about which the agreement is substantial.

In the first place, even in hydrogen, the emission at con-
stant pressure is found to follow the formula t = AT*^"'''"''^.
The constants A and b have, however, different values from
those which characterize the emission in other gases and in a
vacuum. As regards the constancy of A and b they are inde-
pendent of the temperature, but may be functions of the pres-
sure p of the hydrogen.

Working with wires which had not been heated in hydrogen
for long periods Wilson arrived at the following conclusions :

i"Phil. Trans., A.," Vol. CCII, p. 263 {1903); ibid.,Vo\. CCVIII, p. 247
(1908); "Roy. Soc. Proc, A.," Vol. LXXXII, p. 71 (1909); "Electrical Proper-
ties of Flames," etc., p. 16, London (1912).

^Ibid., Vol. CCVII, p. I (1906).

102

THE EFFECT OF GASES 103

When a wire, whose temperature was maintained constant, was
allowed to remain for some time in hydrogen at different
pressures the emission assumed steady values which were found
to be governed by the formula

i == B/'. . . . . (I)

when B and z are independent of the pressure but depend on
the temperature. Throughout the range of temperature used
z was always between 0-5 and ro and increased as the tem-
perature diminished When a change from one pressure to
another was made, the emission did not immediately assume
its final value but changed gradually from the value character-
istic of the original pressure to that proper to the final pres-
sure. A similar time lag in the value of the emission was ob-
served when the temperature was changed at constant pressure.
These effects are at once accounted for if it is admitted that
the emission is determined not directly by the pressure of the
external hydrogen but by the amount of hydrogen which is
dissolved in the wire ; since it is an established fact that
hydrogen requires an appreciable time to diffuse through
platinum. Since the emission at constant temperature di-
minishes with time, after passing from a lower temperature,
and increases with time, after passing from a higher tempera-
ture, it is necessary to suppose that the equilibrium amount of
dissolved hydrogen diminishes as the temperature rises. At
least this must be the case under the particular conditions
which Wilson^ gives as an illustration, viz: p =» 0'II2 mm.
and T varying between 1284° C. and 1520° C. The following
numbers given by Wilson * indicate the way in which the cur-
rent under 40 volts potential difference varies with the pressure
at 1 340° C. : —

Current -:• Preasure.

3"g X lo-'

3*3 X 10-'

i*4i X IO-*

4'3 X lo-'
36*0 X I0-*

39*o X lo-'

» " Phil. Trans., A.," Vol. CCII. p. 267 (1903).
«/6id., Vol. CCVIII p. 255 (1908).

Pressure (mms.).

Current (amps.).

760

3 X 10- »

450

I'5 X 10-'

156

2'2 X 10- *

6 X \0-*

O'll

4 X 10-*

00013

5 X lo-'

104 AMISSION OF ELECTklCJTV FROM HOT BODIES

The effect of hydrogen on the constants A and b is shown
in the following table taken from the same paper : — ^

G«a.

Pressure
(mms.).

Ai.

b
(Observed).

b
(Calculated).

Air (1)

small

7-14 X Io26

7-25 X 10*

7'I X 10*

Air (2)

small

4-38 X 10^6

6-55 X 10*

6-9 X 10*

Hydrogen

0*0013

6-25 X 10^^

5-5 X 10*

Hydrogen

0*II2

3 '13 X lo^'*

4'5 X 10*

4*52 X 10*

Hydrogen ,

133"0

1*25 X lo^i

2*8 X 10*

2*7 X 10*

The first value for air was given by a wire which had been
subjected to the nitric-acid treatment previously described
(p. 72) for twenty-four hours, the second only for one hour.
The calculated values of b will be considered later.

The phenomena described above are quite different from
those observed by the writer^ under what appeared to be
similar conditions. For example, the emission from a platinum
wire in hydrogen was found to be practically constant whilst
the pressure of the gas was reduced from i mm. to o-ooi mm.
It was also found that a wire which had been saturated with
hydrogen at a relatively high pressure and temperature could,
after the pressure had been reduced, give off very considerable
quantities of gas, presumably hydrogen, without the emission
being much affected thereby. Similar results have since been
observed by Wilson.' In one of his experiments there was
very little variation in the emission when the pressure of the
hydrogen was reduced from 200 mms. to o*ooi mm. He also
confirmed the result that a wire which has been saturated with
hydrogen may be heated in a good vacuum until it ceases to
evolve gas, and retain the high power of emission previously
conferred by the immersion in hydrogen, but he found that a
wire under these circumstances still contains a large quantity of
hydrogen which it is capable of retaining with great obstinacy.
The presence of hydrogen in the wire under these conditions
was established both by heating it in oxygen and measuring
the diminution in pressure when the water formed was ab-
sorbed, and also hy measuring the resistance of the platinum,
which is affected by the presence of absorbed hydrogen.

1" Phil. Trans., A.," Vol. CCVHI, p. 251 (1908).
^Ibid., Vol. CCVII, p. 51 (1906).
^Ibid., Vol. CCVHI, p. 255 (1908).

THE EFFECT OF GASES toj

It is clear from the facts which have been described that
the emission from platinum in an atmosphere of hydrogen
shows two quite distinct types of behaviour, under conditions
which at first sight appear to be identical. The cause of this
difference was investigated by Wilson who found that the con-
dition in which the emission was sensitive to changes in the
pressure of the hydrogen occurred only with "fresh" wires,
that is to say, with wires which had not been hea'ted in hydro-
gen for any considerable length of time. The condition of
in sensitiveness to change of pressure, on the other hand, was
found to be characteristic of wires which had been subjected
to continued heating in hydrogen. Such wires may, for brevity,
be described by the term " old ". Wilson has pointed out that
the observed facts are consistent with the view that in a fresh
wire the hydrogen exists in a state of solution, whereas in an
old wire most of it is present in the form of a compound which
is formed with extreme slowness. The essential difference
between solution and chemical combination lies in the fact
that the amount of gas dissolved is a continuous function of
the external pressure, whereas the amount chemically combined,
once the reaction has been completed, is constant, if the ex-
ternal pressure exceeds the dissociation pressure, or zero if the
pressure is below that value. Since the amount of hydrogen
present in the wire is held to determine the value of the emis-
sion at a given temperature, on this view the emission will only
be a continuous function of the pressure of the external hydro-
gen with fresh wires, in which the gas is present in the dis-
solved state. The dissociation pressure of the hydrogen
compound must be very small (under O'ooi mm.) at the tem-
perature of the experiments referred to (up to 1400° C), since
the large emission from an old wire could not be removed by
pumping. However, dissociation pressures vary rapidly with
temperature, and Wilson has found that the large emission
from an old wire can be " pumped out " if the temperature is
raised to about I7CX)° C. This view is also substantiated by
the fact that the large emission from an old wire can be "burnt
out " almost instantaneously in an atmosphere of oxygen at
much lower temperatures ; since the pressure of hydrogen in

lo6 EMISSION OF ELECTRICITY FROM MOT BODIES

equilibrium with water vapour and its dissociation products
under the conditions of such an experiment is very low.

The writer ^ noticed a peculiar susceptibility to changes in
the electric field in examining the emission from platinum
wires in an atmosphere of hydrogen at pressures comparable
with I mm. The currents showed approximate saturation
with potential differences of about lo volts, and the increase
due to impact ionization began to be observable definitely at
about 20 volts. Over a considerably higher range of potential
than this the current was found to be a definite function of the
applied voltage ; but when the voltage exceeded 2(X), the cur-
rent rapidly fell away from its initial value with lapse of time.
Thus at 177 mm. pressure, and 1084° C, a steady current of
147 X io~^ amp. was obtained with a potential difference of
19 volts; on raising the voltage to 286 the current readings
had the following values at the times stated : —

Time (minutes) 2 3 5 7 10 13

Current (i = io-*amp.) 63 44 37 33 28-5 a6

If the high potential is maintained, the current goes on drop-
ping, but at a diminishing rate, for several hours. If the high
potential difference is removed after most of the drop in the
current has taken place and is replaced by a low voltage, the
observed phenomena are quite different and rather surprising.
The current with the low voltage is small at first and remains
practically constant and very steady for a considerable interval.
It then begins to increase, slowly at first, then more rapidly,
then slowly again and finally attains a constant value which is
much higher than the steady value finally attained under the
high voltage applied previously. Thus, after the numbers in
the table above had been obtained, when the wire was giving
a current of 26 x io~^ amp. after exposure to 286 volts for
thirteen minutes, the potential was suddenly changed to 80
volts. The current at once dropped to 7 x lo"^ amp. and
remained at this value for several minutes. It then began to
rise, the rate of increase being most rapid after the lapse of
100 minutes. Fifty minutes later the current had attained the

1 " Phil. Trans., A.," Vol. CCVII, p. 46 (1906).

THE EFFECT OF GASES to;

practically constant value of 220 x lO"* amp. This is more
than ten times the value of the steady current which would
have been attained if the potential difference of 286 volts had
been left on indefinitely.

These effects did not occur either at very low pressures
(Z- 01 mm.) or at high pressures (200 mm.) or when the wire
was charged positively. The conditions under which they were
found to occur are those under which the platinum would be
subjected to an energetic bombardment by positive ions aris-
ing from impact ionization. It seems natural to interpret the
falling off of the current under the application of high voltages
to the destruction by this bombardment of a structure at the
surface of the platinum which facilitates the escape of the
electrons. This structure will begin to form again as soon as
low voltage conditions are restored, and the bombardment be-
comes ineffective. It is doubtless responsible, at least in part,
for the increased emission in a hydrogen atmosphere.

An effect which is probably related to this, has been ob-
served by Wilson.i After the large emission from a wire
saturated with hydrogen has been removed by heating in
oxygen the wire appears to recover its lost power very slowly
when subsequently heated in a hydrogen atmosphere ; but the
rate of recovery is very greatly increased, if the wire forms one
of the electrodes in the passage of a luminous discharge in
hydrogen at a low pressure.

Platinum is not the only metal from which the emission of
electrons is increased by immersion in an atmosphere of
hydrogen. Similar effects have been noted by Wilson "^ with
palladium and by J. J. Thomson ^ with sodium. All three
elements are notable for their power of dissolving and combin-
ing with hydrogen. On the other hand, Langmuir* found
that hydrogen caused an enormous reduction in the emission
from tungsten, an effect which he attributes, however, to the
action of water vapour formed by secondary actions, rather
than to the direct action of the hydrogen itself.

» " Phil. Trans., A.," Vol. CCVIII, p. 265 (1908).

«/ii<f., Vol. ecu, p. 271 (1903).

^ " Conduction of Electricity through Gases," 2nd ed., p. 203.

* •• Phys. Rev.," Vol. II, p. 463 (1913).

io8 EMISSION OF ELECTRICITY FROM HOT BODIES

Theory of the Emission from Fresh Platinum
Wires in Hydrogen.

The essential features of the emission from fresh platinum
wires in an atmosphere of hydrogen may be summarized in
the two following statements : — ^

(i) The emission at any constant temperature is very
closely proportional to />', where the index ^^ is a proper
fraction whose value diminishes with rising temperature ; and
(2) under constant pressure the emission at different tempera-
tures is governed by a formula of the type / = AT* e~^^'
where, however, the constants A and b are functions of the
pressure of the hydrogen, and their values are, in general,
quite different from those of the corresponding quantities ap-
propriate to the emission from platinum wires in a vacuum.

These laws, including the actual changes in the values of
the constants A and b, must be intimately connected with the
contact potential differences between pure platinum and plati-
num immersed in an atmosphere of hydrogen. This follows
from considerations similar to those pointed out already in
Chapter III, page 78. The presence of hydrogen will alter
the change of energy which accompanies the escape of an
electron, as well as change the contact potential. These two
effects are closely connected together but they are not identi-
cal, and the change in the contact potential is more directly
related to the change in the emission constants than is the
interfacial change in energy. The distinction is an important
one and one which is particularly liable to confusion ; so that
it is worth while to devote a little consideration to the purpose
of making it clearer.^ To do so it is necessary to refer to
certain matters of theory which were touched on at the be-
ginning of Chapter II, where, by making use of the laws of
thermodynamics, certain relations were deduced between
the equilibrium concentrations of the external electrons, on
the one hand, and the energy change ^ and the specific heat
of electricity in the hot body, on the other. When gases are

iCf. H. A. Wilson, " Phil. Trans., A.," Vol. CCVIII, p. 248 (1908).
■■' For a fuller discussion cf. O. W. Richardson, " Roy. Soc. Proc, A.," Vol.
XCI, p. 524 (1915)-

THE EFFECT OF GASES 109

present the proofs of these relations which have been given
require modification, A metal in the presence of a gas is a
much more complex affair than a pure metal ; but, to a first
approximation, it can be represented as a piece of pure metal
covered with a layer of contamination of definite composition
and of finite thickness. \i the proofs are modified, so as to
suit such a structure and to allow for the presence of the gas,
it still appears that

n - a/ "' ... (70

where A is independent of T and 0 is now the energy change
when an electron passes through the outer surface of the con-
taminated layer. Obviously </> is not a quantity which is
directly accessible to measurement. In carrying out the cycle
on page 30 involving the transference of electrons between two
metals at different temperatures we have now to include the
work 7; which corresponds to the Peltier effect at the inter-
face between the pure and uncontaminated surfaces and by so
doing we obtain, instead of equation (i 3) (Chapter II) and after
taking out the logarithms and replacing p by nkT,

« = CT'-.-^" *^ T t . . (,3-)

where C is a universal constant. By making use of a known
result in thermoelectricity this may be replaced by

„ = CT^,-{rT + r/^?-^} . . (13")

if o"! is the specific heat of electricity in the contaminated
material. Thus (l 3) of Chapter II is still valid, as it should be,
if we keep to a single definite substance. If <^', -;;'(= o),
and «' are the values for the pure metal.

fi = CT e
and

f»'-f-n'-(» + n)\

«Vi

ne-kT (340

no EMISSION OF ELECTRICITY FROM HOT BODIES

where ^ Vi is the contact difference of potential between the
pure and the contaminated materials. This equation is the
same as equation (34) of Chapter II, and may be obtained in a
similar way to that followed on page 40. Since, if we neglect
electron reflection, the saturation currents i, i' at a given tem-
perature are in the same ratio as the corresponding equili-
brium electron concentrations «, «', we may replace (34') by

i' = ie - 'V,/ftT ^ ^ ^ (^34")

We know from experiment that for the pure metals

/' = A'T*^ - "'/^T ... (2)
where A', a (^-=^ kb') and \ are independent of T, X being
comparable with unity. Now eV^ will depend on the tem-
perature and on the pressure p of the hydrogen. To indicate
this, let us denote its value by kTf {p, T) where / is a
function whose nature we shall seek to determine. Then the
expression for the current when hydrogen is present will be-
come, from (2) and (34"),

/= AT^^ - ST+-^(^''^> . . (3)

Since (3) has to become identical with (2) when p = o,/(p, T)
must approach zero as P approaches zero. Again, the experi-
mental results show that (3) as a function of T has the same
form as (2), but that the new constants corresponding to A'
and ft)' are now functions of / but not of T. This require-
ment is satisfied if / (j>, T) is of the form Fi (/) + ^ Fj (/)),

where F^ and F^ are functions of/ only ; for we can then write
(3) in the form

/ = AV^i<^>T^^-['' -*Pa(^"/*''^, . . (4)

the new values of the constants at pressure p being

A" = A'e^i(P^ and «" = «' - kF^ip) . . (5)
Again the law of variation of emission with pressure at con-
stant temperature requires that (3) should approach very
closely to

i=Bp . . . . (I)

where B and z are functions of T only, z diminishing as T

^ '• Electron Theory of Matter," p. 456 (Cambridge, 1914).

THE EFFECT OF GASES 1 1 1

increases and lying between ^ and i over the range of tem-
peratures covered in the experiments. It is clear, however,
that (i) cannot be the complete function, otherwise / would
vanish when/ = o, whereas we know that /then reduces to
the value characteristic of a vacuum. But if we replace (i)
by

/ = B(i + ap'y . . . . (6)

where a and c are constants and dt/* is large compared with
unity at all pressures which are measurable, both requirements
are satisfied. By comparing with equation (4) we then get,
omitting all the terms which do not involve /,

(I +a/>^y = /.(^)H^«<^>

flog (I + ap^)^FM + l,V,(/>) . . (7)

Since z is independent of/, and since Fj and F, are inde-
pendent of T and are not constant, the only values of these
functions which are compatible with (7) are

Fi(/) = } log (I + a/0 ... (8)

FaC/) = I log (I + a/0 ... (9)

z = a/T + a . . . (10)

Wilson^ has shown that, if a =• 1-27 x 10*, <: = 073, a
=» 2'4 X 10', and a' = - c, the experimental results are ac-
counted for with very considerable approximation over the
whole of the wide ranges of temperature and pressure which
have been covered in the quite considerable number of investi-
gations available. Substituting the new expression for the
contact potential in equation (2) we have for the current at
pressure / and temperature T°K

i = A T^e- [ - *T log (I + »pc)(^ - I )]/*T
= A'(i + a/>')i^ - OtV - -'/*T . . .(II)
1 •' Electrical Properties of Flames," etc., p. 20.

112 EMISSION OF ELECTRICITY FROM HOT BODIES

«' - * ~ log (I + a/>e) /-«\

= A'(i + af) - 'T^^- ^AT • ^ ^

From (ii) we see that when the temperature is constant and
the pressure varies

/x(i + a/^)C4-0 • • • • (13)

oc/*, very nearly, \i z = — - c,

since unity is very small compared with apf^ for the pressures
in question. The extent to which this result is satisfied may
be illustrated by means of the following numbers given by

Wilson : — ^

'ressure (mms.
of mercury).

» (arbitrary units).

i -^ right-hand
side of (13).

o*ooo6

2*65

0-0015

2-70

0-0033

3-01

0-0053

2-65

0-0080

2-92

0-0140

2-85

From (12) we see that z still satisfies an equation of the
type

/= A'T'V - -"/*T, . . . (14)

but that the constants A" and o" have new values, being given
by

A" = A'(i + «/0-' . • (15)

a
and fi>" = a)' - k -log(i + ap'^) . . (16)

= 0,' - k'Lxog^'l^,, . . (17)

We have seen that it is very difficult to determine the correct
values of A' or A", but that (15) is very near to being satis-
fied is shown by the fact that when/ is changed from 0*0013
mm. to I33"0 mm.. A" diminishes regularly till it becomes only
about 1/5000 of its initial value, whereas A' = A" x (i +
ap'^') only changes in an irregular manner and shows an ex-
treme variation of a factor of 3. Again from (17) we see that
the values of «' can be calculated from the value eo for a
vacuum if we know the values of A' for a vacuum and of A"

^"Electrical Properties of Flames," etc., p. 16.

THE EFFECT OF GASES 1 13

at different pressures. The values of (^ » (a"lk calculated in
this way are given in the table on p. 104 and show an ex-
cellent agreement with the observed values.

In the last chapter, p. 89, in discussing Martyn's experi-
ments on the emission from platinum and lime in air and in
hydrogen, it was pointed out that the effect of the gas on the
platinum could be accounted for by supposing that the con-
tact difference of potential between pure platinum and plati-
num in an atmosphere of hydrogen was equal to kT log P-JP%,
where /j and/j are the pressures o{ th& positive hydrogen ions
inside and outside the metal respectively. This view becomes
identical with the one now under consideration if we suppose
that

A/A = (I + ap')^^~') . . . (18)

where p is the pressure of the external hydrogen gas. So
far as the writer is able to judge there is not enough known
about the phenomena attending the solution of hydrogen in
platinum to enable one to determine whether a formula such
as (18) is likely to approximate to the truth or not. It is
clear, however, that the right-hand side of (18) varies with
temperature qualitatively in the way to be expected. At low
temperatures the dissociation (and ionization) of the external
hydrogen is small, both absolutely and also, most probably,
in comparison with that of the internal hydrogen. Since there
is evidence that positive hydrogen ions are formed with less
expenditure of energy inside the metal than outside, it follows
that the external ionization will increase more rapidly with
rising temperature than the internal ionization. Since /j and
^3 are proportional to the respective numbers of positive hydro-
gen ions per cubic centimetre, it follows that the right-hand
side of (18) should have a large value at low temperatures
which should diminish very much as the temperature rises.
This is found to be the case. Thus when / = i mm. the right-
hand side of (18) is equal to 3 x 10^ at 800° C. and falls to
2*4 X lo^ at 1800° C.

Another point to be borne in mind is that the right-hand
side of (18) has been obtained in a manner which is largely

1 14 EMISSION OF ELECTRICITY FROM HOT BODIES

empirical and, like all functions which are derived in this way,
is subject to the liability that it is not the true function but
merely one which simulates the mathematical behaviour of the
true function. If this is the case, however, it is necessary that
the correspondence should be very close indeed. For the
formulae give results very near to the truth, not only over such
limited ranges of pressure as those illustrated in the table on
page 112, but over all the very extended range of temperature
and pressure which has been examined by various experi-
menters. Thus if? = /q when/ = o, (13) may be written

z'A; = a(i -v ap')\^~i . . . (19)

At 900° C. at 26 mms. pressure the writer 1 found t'/iQ = 4 x
I0^ The calculated value given by the right-hand side of
(19) is 2 X lo^ U c is put equal to 078 instead of 073 the
right-hand side of (19) becomes 3 x 10^ instead of 2 x 10®.
Thus the apparent disagreement may be attributed to the un-
certainty in the precise value of the constants. Again at
1570° C. and 760 mms. Martyn^ found i'/zq = 4*4 x 10*, the
calculated value from (19) being 6*5 x lo^ At 1340° C. and
0*0013 ^^- Wilson^ found i'/zq = 170, the calculated value
being 122. Thus the values given by (19) are very close to
the actual values over the range of pressure from o to 760
mms. and of temperature from 900° to 1575° C.
By comparing (18) and (19) we see that

I = /•//, = (I + ap^)(^:') = A/A; . . (20)

so that on the hypothesis under immediate consideration the
ratio I, of the saturation current at pressure/) to that at pres-
sure zero, is equal to the ratio of the pressure (or concentration)
of the internal to the pressure (or cencentration) of the external
positive hydrogen ions, in the presence of platinum subject to
a total external hydrogen pressure/. The whole subject is
well worth further investigation to see if this result is substanti-
ated by more complete experimental knowledge.

i"Phil. Trans., A.," Vol. CCVII, p. 45 {1906).

» " Phil. Mag.," Vol. XIV, p. 306 (1907).

' " Electrical Properties of Flames," etc., p. 21.

THE EFFECT OF GASES 115

It is evident from the argument on pages 40, 74 and no
that the change in A' caused by hydrogen may be attributed to
the occurrence in the expression for the contact potential differ-
ence, between the metal in an atmosphere of hydrogen and the
pure metal, of a term which is proportional to the temperature.
In other words, the change in A' may be considered to arise
from the temperature variation of the changed value of to.
We also notice that any change in the observed value of to
will arise only from that part of the expression for the contact
potential which is independent of T. Thus if for any given
value Wi of the work which corresponds to the contact po-
tential difference we are able to calculate its variation with
temperature we ought to be in a position to calculate the
changed value of A' corresponding to <w^.

The problem has been attacked from this point of view by
H. A. Wilson,^ who calculates the whole work done in passing
from a point in the interior of the pure metal to the outside.
This amount of work includes both that which corresponds to
the Peltier effect at the interface and the change of energy at
the outer surface in the treatment given above, and is there-
fore equivalent to the contact potential difference. Wilson
supposes that the work necessary for the escape of an electron
arises from the presence of an electrical double layer of thick-
ness t, and negatively charged on the outside, at the surface of
the metal. Whether such a layer really exists or not, its im-
aginary presence will give rise to effects in many respects
identical with, and in others similar to, those arising from the
actual mechanism which causes the origin of the contact po-
tential difference. It is to be remembered, however, that the
conception is an artificial one whose chief attraction lies in its
amenability to calculation. If the double layer consists simply
of charges, of surface density + o-, at distance / apart, the
work done in taking a change e across it is 47r<r/6. Wilson
supposes that a and t are independent of temperature, so that
their values in any particular case determine the zero-tempera-
ture value of the work in question. The results indicate that

» •• Phil. Trans., A.," Vol. CCVIII, p. 268 (1908) ; " Roy. Soc. Proc.. A.,"
Vol. LXXXII, p. 71 (1909); " Electrical Properties of Flames," etc., p. 22.

Ii6 EMISSION OF ELECTRICITY FROM HOT BODIES

t is also unchanged when hydrogen is present and that the
effect of hydrogen may be interpreted as causing a reduction
in the value of or. The variation of the work with temperature
is supposed to arise from the diffusion of the electrons into the
surface layer owing to their heat motion. This diffusion
will increase with rising temperature and will increase the
effective strength of the double layer ; so that the work neces-
sary for an electron to escape will increase as the temperature
increases. The diffusion will also be greater at a given tem-
perature the smaller the value of o- ; so that the temperature
coefficient when hydrogen is present will be greater than the
temperature coefficient in its absence. The actual calculations
involve a consideration of the equilibrium of the electrons in
the double layer and are somewhat complicated. For them
the reader may be referred to Professor Wilson's book, " The
Electrical Properties of Flames and of Incandescent Solids,"
page 23. As a result, if tuj is the value of the work under
consideration, the calculations give the following values of
2g)i/^ at temperature T°K.

Gas.

Pressure.

2W]/ft.

Air

o'ooi3

0'II2

133*0

145,000 + 2*35 T

110,000 + 1 1 "83 T

90,000 + i7'82 T

56,000 + 28-86 T

These numbers lead to values of A' and al in hydrogen
at different pressures in close agreement with the experi-
mental values already considered. It is also found that if the
equations are solved for / the different values of A' and aS
always lead to values between / = 5*6 x lo""® cm. and 107
X io~® cm. These can be considered to be constant within
the limits of error. The values are also in agreement with
the value of the thickness of the double layer calculated from
the polarization capacity of platinum polarized with hydrogen
by the electrolysis of dilute sulphuric acid.

It is interesting to observe that the value of the tempera-
ture coefficient of wi/^ in air or a vacuum given by these
calculations is very close to that of ^ given by the theory in
Chapter II. If the temperature variation of m^lk were made
equal to that of ^ we see, by comparison with equation (16),

THE EFFECT OF GASES 117

Chapter II, page 33, that the value of icajk would.be changed
only from 145,000 + 2-35 T to 145,000 + 3T.

The Effect of Gases on the Emission from
Tungsten.

Tungsten possesses a number of notable advantages for
the purpose of experiments on the emission of electrons from
hot bodies. It is the most refractory material known, melt-
ing at 3270° C, and its volatility is low even at the highest
temperatures. Thus it can be heated, without any consider-
able loss by evaporation, for comparatively long periods at
temperatures so high that all known impurities are driven out
of it. At these high temperatures enormous electron currents
may be obtained, the only limits being set by the heating
current required to fuse the wire which is the source of supply,
and by the potential difference required to overcome the
mutual repulsion of the emitted electrons. For example, the
writer has observed a thermionic leakage of 0-4 amp. from a
fine filament which required 0'8 amp. heating current. In
this case the thermionic current density amounted to 4 amp.
per sq. cm. The large currents from tungsten are absolutely
steady when attention is paid to the proper preparation of
the tubes (see p. 13) and are very suitable for exact work.
Moreover, owing to the importance of tungsten as a material
for lamp filaments, its electrical and radiating properties at
high temperatures have been very thoroughly studied. Finally
it acts as a self-purifying agent by attacking all except the
inert gases, forming compounds which are then volatilized on
to the walls of the tube.

The effect of different gases on the emission from tungsten
at about 2000° C. has been investigated by Langmuir.* In
these experiments the thermionic currents were larger than
those usually dealt with, being for the most part in the
neighbourhood of 1-20 milliamperes. The difficulty in at-
taining saturation owing to the mutual repulsion of the
electrons was therefore generally an important factor (see

' " Phys. Rev.," Vol. II, p. 450 (1913) ; " Phys. Zeits.,*' Jahrg. 15, p. 516
(1914).

1 1 8 EMISSION OF ELECTRICITY FROM HOT BODIES

p. 6i). The gases experimented with include hydrogen,
water vapour, oxygen, nitrogen, and argon. When satura-
tion was attained the currents were always found to be
capable of representation by the formula i = AT* e~''l'^.
The constants A and 6 have, however, in general different
values in different gases. The values also are probably
different for the same gas at different pressures. Very
small amounts of gas were found to cause very large
changes in the values of the constants. The values of the
constants under good vacuum conditions varied very little in
different experiments either with the same or with different
tubes. The following numbers are cited as the results of
separate determinations for this case : —

A = 6-6 X lo^" e.s.u. per cm.' b = 5-58 x 10* degrees C.
A = io'2 X 10" b = 5-55 X 10*

A = 708 X 10I8 b = 5-25 X 10*

It was found that the values of the constants were not
appreciably altered by the presence of argon. The saturation
currents in this gas have, so far as can be ascertained, the
same value as in a vacuum. The only effect of the argon
when present in small quantity is to facilitate the attainment
of saturation through the action of the positive ions, formed
by impact ionization, in reducing the effect of the mutual re-
pulsion of the electrons. This result is of great importance.
No doubt when the pressure of the argon is appreciable the
current will be magnified owing to ionization by collisions,
but the effect would not be of importance in the experiments
now under consideration owing to the low pressures (up to
o*oo2 mm.) ol the argon used.

All the other gases tested were found to increase the
values of l?otk the constants, as is shown by the following
numbers : —

Gas.

Pressure (mm.).

Vacuum

0*00007

IO*2 X 10^*

5*55 X io«

0-0I2

1*62 X lO^l

8*25 X 10*

0*0005

1*29 X 10^2

8*5 X 10*

0*007

2*28 X 10^8

11*5 X 10*

0*0017

2*31 X 10^^

10*5 X 10*

—

2*04 X lO^-*

9*43 X 10*

0*002

6*5 X 10^9

7*32 X 10*

—

5 X lo^*

6*82 X 10*

THE EFFECT OF GASES 119

It is clear from the values for hydrogen that there is no
relation between the magnitudes of A and b for this gas
and the corresponding pressure. For this and other reasons
Langmuir is inclined to attribute most of the change in the
constants apparently caused by hydrogen to the effect of
traces of water vapour either formed by it or introduced with
it. In all cases the changes in the emission caused by the
gases persisted for some time after the gas had been removed,
showing that the effect was not directly due to an action
between the filament and the external gas but to a semi-
permanent change produced by the gas in the character of the
tungsten surface. No doubt the precise determination of the
constants in a given gas at a definite pressure is a difficult
matter as all the gases except argon are " cleaned up " during
the course of the experiment ; so that the pressure is con-
tinually diminishing in any given case. Of the three gases
oxygen, nitrogen, and hydrogen, oxygen is absorbed most
rapidly at about 2000°. The absorption of nitrogen appears
to be an electro-chemical phenomenon which exhibits interest-
ing effects. These will be considered later.

The magnitudes of the changes in A and b caused by dif-
ferent gases suggest that all these changes are due to a
common cause, or, at any rate, that the mechanism of the
action of the different gases is of such a nature as to possess
important common features in the different cases. Thus in the
table on p. 118 the values of A and b always increase and
diminish together. This is seen more clearly from Fig. 13
in which the values of log^o A are plotted against those of
b X lO"*. Fig. 13 contains all the data of the table and
some others in addition. It will be observed that the values
of logio A, no matter what gas has given rise to them, are
very near to satisfying a linear relation with the corresponding
values of b. It is very doubtful, owing to the time varia-
tions which must be occurring in many of these experiments,
whether the linear relation is not satisfied within the limits of
experimental uncertainty.

As with the similar effects observed with hydrogen and
platinum these effects may be considered in relation to the

I20 EMISSION OF ELECTRICITY FROM HOT BODIES

contact potential difference between pure tungsten and tung-
sten which is contaminated with the gases under considera-
tion. In the absence of gas, i.e. in a thoroughly "cleaned
up " vacuum, let the saturation current be

Suppose that the contact potential difference due to the

k
gas is - {b^ + /ST) where k is Boltzmann's constant, e is the

"5 6

bi-IO*

7 T 9 10 It tZ

A/2:x, 0^:0, A^2*^* Vacuum: (Q.

Fig. 13.

ionic charge, )9 is a constant, and b^ may, in general, be a
function of T which contains no linear term in T, this term
being represented by /9T. The current when the gas has pro-
duced its effect will be represented by

= Ao^-^Ti^-(*o + V)/T . . . (21)

THE EFFECT OF GASES 121

If the range of temperature is not too large this may still
be represented by

/•' = AT»<r-*/T .... (22)

with A and b constants, if b^ does not vary too rapidly with
T. The values of A and b are

A - Ao^ - <» . . . . (23)

b ^b,+ b^. . . . (24)

Since A is always greater than A^, /3 is negative, and from (23)

7 = - ^ - log^^ . . . (25)

If the linear relation indicated by Fig. 13 is really ful-
filled, we have

b == b^ + b^' " ^'log-x- + c, . . (26)

■"•0

where c and c are constants. Since bo « o when A — A©,
c •» bf^. Thus

^0' = <^' log -KT ^ y^' • • • (^7)

The contact potential difference due to the gas is thus
equal to

>^t(^-7) = 7>&t(^ - i) . . (28)

In this equation >fe is a universal constant, c is independent
of T and has the same value for all the gases tested, 7 is in-
dependent of T but is determined by the modification in the
state of the surface caused by the gas. Since for a given gas
the only factor except T capable of controlling the state of
the surface would appear to be the pressure of the gas, it
would seem that ultimately 7 must be a function only of the
pressure of that gas which causes the change in question — 7
may, however, be a different function of the pressure for each
gas which gives rise to these effects.

The effect of these gases on the emission from tungsten
shows a very close correspondence with the effect of hydrogen
on the emission from platinum. Turning to the table on p.
104, remembering that A is proportional to A,, we see that

122 EMISSION OF ELECTRICITY FROM HOT BODIES

the effect on platinum of gradually increasing the pressure of
the surrounding hydrogen, is to cause a corresponding series
of changes in A and b. In these changes A and b always in-
crease or diminish together. The chief difference between the
effect of hydrogen on platinum and the effect of the various
gases under consideration on tungsten is that, in the case of
platinum the change from the normal is towards lower values
of A and b, whereas, in the case of tungsten, the change is to-
wards higher values. Moreover, it follows from the considera-
tions brought forward on p. i\o et seq., that the contact potential
difference caused by the gases, considered as a function of
pressure and temperature, is of the same form in both cases,
the main difference being that the equivalent work is negative,
corresponding to a more electropositive condition, in the case
of hydrogen and platinum, whereas it is positive, correspond-
ing to a more electronegative condition, when tungsten is
contaminated by various gases. Thus from equation (ii),
p. 1 1 1, we see that the equivalent work in the case of hydrogen
and platinum may be written

««/ = - (^ - l) /^T log (I + af\ . . (29)

whereas from (28) the corresponding quantity for tungsten is

W = + (^ - ^)^T7 . . . (30)

We have seen already that the quantity 7 in (30) plays a simi-
lar part to the function log (i + ap^') in (29) ; so that the terms

{— - \\ in (30) and f— - i j in (29) are precisely com-
parable with one another. Moreover, the constants c and
a\c in these expressions have almost equal values. The data
on p. Ill give

a\c = 3-29 X 10^
whereas from Fig. 13

c = 2-56 X 10^
A still closer agreement is obtained if all the known pairs of
values of A and b for platinum are considered.^

1 Cf. O. W. Richardson, " Roy. Soc. Proc, A.," Vol. LXXXIX, p. 524
(1915). In this article it is also shown that there are indications of a similar rela-
tion affecting the emission of positive ions from hot platinum. Cf. also p. 226,

THE EFFECT OF GASES

It appears to be a legitimate inference from these results
that the two effects under consideration are due to similar
causes acting in opposite senses in the two cases. If in the
case of platinum the cause lies in the difference of concentra-
tion of positive hydrogen ions inside and outside the metal, it
would be natural to attribute the effects with tungsten to a
difference in the concentration of negative ions, probably ions
of the electronegative elements oxygen and nitrogen, inside
and outside the surface layer. On the other hand, if the plati-
num effects arise from the action of positive hydrogen ions on
a double layer at the surface, it would seem reasonable to as-
cribe the tungsten effects to the similar action of negative ions
furnished by oxygen or nitrogen. It is to be remembered
that the two hypotheses contrasted are not necessarily contra-
dictory.

In an atmosphere of nitrogen at low pressures, Langmuir
observed peculiar effects which were not exhibited by any of
the other gases. At the lower temperatures tested, it was
found that the electron currents in this gas were larger with
small than with large potential differences. For example, the
following currents in milliamperes per square centimetre were
obtained under the conditions indicated in the table : —

Temperature "K.

220 Volts.

100 Volts.

aao Volts.

2045

0-34

0-29

2090

070

0-63

2140

I -50

1*29

2igo

4*i-.o

2-9

2250

6-3

4 '9

7-0

2325

i6-2

5-0

19*3

2390

21*0

5"o

20*0

Pressure of Nj ->

0*0013 mm.

o'ooi2 mm.

The reason for this peculiar behaviour becomes clearer
when the variation of current with applied potential differ-
ence at constant temperature is studied in nitrogen under
different small pressures. The results of experiments of this
character at 2icx>° K. in nitrogen at 0'OOOi6 mm., O'OOio mm.
and 00025 mm. pressure are shown in Fig. 14. The read-
ings for a pressure of o*oooi6 mm. approximate to those for
good vacuum conditions. At low potentials they follow the
full curve IV which represents the variation, with applied

124 EMISSION OF ELECTRICITY FROM HOT BODIES

potential, of the current when limited by the mutual repul-
sion of the electrons (space-charge effect) as considered in
Chapter III, p, 63. At higher potentials they leave this curve
and ultimately fall on the horizontal dotted line III', which
represents the saturation current under vacuum conditions
at the temperature of the experiment. The dotted curve III,
in fact, which passes through all the values at 0*0001 6 mm.

—

X-

CL-

rrr'

/■

en
1.

..^

yy-

...

}

?•

T7T

Sr-

1 1

a.
*—

/ ,'

•tL

^ j

1 \

*«

? ,

»rr

: i

1 —

i
.1 i

M 1

ifn

rtT

nfi

^it,

kn<

>t«

nt;

«/•

Fig. 14.

is similar in a general way to the curves obtained in all the
gases under consideration other than nitrogen. In nitrogen
at higher pressures, however, the curves are quite different, as
is shown by I and II. Considering curve I, for example, we
see that it is coalescent with III and IV at potentials below
20 volts. At potentials between 20 and 75 volts the currents
given by I are larger than those given by III and IV. This

THE EFFECT OF GASES \%$

efifect, which is similar to effects given by other gases, is at-
tributed to the action of the positive ions produced by impact
in reducing the mutual repulsion of the electrons, and so per-
mitting a nearer approach towards saturation. At 75 volts
the rise in the current with increasing potential suddenly
ceases, and is replaced by a fall which is most rapid at first
and then diminishes until a steady value of the current is
finally reached. This ultimate saturation current is much
smaller than the saturation value in a vacuum. The be-
haviour above 75 volts has so far been observed in nitrogen
only. It is attributed by Langmuir to the occurrence of a
chemical reaction between the tungsten and the positive
nitrogen ions formed by impact ionization. This reaction is
known not to occur with uncharged nitrogen molecules at
these temperatures, thus accounting for the absence of any
diminution of the currents at low potentials. The nitride
formed is supposed to hinder the escape of the electrons, and
as the rate of its formation will go on increasing with the
applied potential (up to a certain limit), the general course of
the factor cutting down the current will resemble a curve such
as r. Thus the general character of the current- voltage
curves is accounted for. The amount of the compound ulti-
mately formed will be greater the greater the pressure of the
nitrogen ; so that the final saturation current will be reduced
as the nitrogen pressure is increased. This is seen to be the
case with the data given. Finally, as the temperature is
raised, the compound formed will evaporate more quickly
and so less of it will be retained on the filament Thus this
effect should diminish at higher temperatures, as in fact is
found to be the case.

Returning to the general case of the effect of gases on
tungsten we have seen that both the constants A and b in the
emission formula are increased thereby. At any given tem-
perature the effect of an increase of A alone is to increase the
emission, to which indeed it is proportional, whilst an increase
in b diminishes the emission. It appears, however, that the
changes in the two constants are of such a magnitude as to
cause in combination a reduction of the current. A lai^e

126 EMISSION OF ELECTRICITY FROM HOT BODIES

number of experiments, under the most varied conditions, have
been made by Langmuir, who has found no exception to the
rule that the saturation current from tungsten in presence of
small amounts of any gas is never greater than the saturation
current under the best vacuum conditions at the same tempera-
ture. This result is of the greatest importance. The only
gas which has been found not to affect the value of the satu-
ration current is the inert gas argon, although the other inert
gases would probably be found to act in the same way if
tested. All the other gases tried were found to reduce the
value of the saturation current. The effect of all these gases
on tungsten is thus the exact opposite of that of hydrogen on
platinum. Under some conditions the chemically active gases
may appear to increase the emission from tungsten, but this is
a spurious effect due to the fact that true saturation has not
been attained. Under such conditions the positive ions liber-
ated by impact ionization in the gas may admit of a nearer
approach, under a given potential difference, to the saturation
value.

Thermionic Currents from Various Materials in
Gases at High Temperatures.

Interesting experiments dealing with a number of substances
have been made by Harker and Kaye.^ They examined the
conductivity between two cylindrical electrodes inside a carbon
tube at temperatures between 1400° C. and 3000° C. At the
higher temperatures the conductivity is very great, the currents
being proportional to the voltage up to 10 volts potential dif-
ference, and increasing rapidly with temperature. When one
of the electrodes is kept cold, and there is no applied potential
difference between them, there is, in general, a considerable
discharge of negative electricity in the direction from the hot
to the cold electrode. With fresh electrodes at the lower
temperatures the direction of this discharge is reversed and
corresponds to a positive emission from the hot electrode.
The negative effect at higher temperatures is greater on first

1 " Roy Soc. Proc, A.," Vol. LXXXVI, p. 379 (1912) ; Vol. LXXXVIII,
p. 344 (1913).

THE EFFECT OF GASES 127

heating, presumably owing to the presence of volatile im-
purities which are more efficient in this respect. The smaller
steady currents finally obtained were about 0"I5 ampere at the
highest temperatures. These experiments were made at at-
mospheric pressure, and the currents were found to be much
the same in an atmosphere of nitrogen, hydrogen, or furnace
gases. The electromotive force between the hot and the cold
electrode was found to be i "8 volts.

In the second paper the authors investigate the emission
from strips of platinum, iridium, iron, tantalum, nickel, copper,
brass, and carbon at temperatures up to the melting-points of
the metals in an atmosphere of nitrogen at pressures from
I mm. to atmospheric. The strips were heated by an alter-
nating current, and no external potential difference, other than
that arising from the alternating circuit, was applied to drive
the thermionic currents to the surrounding cylindrical elec-
trode. The current from platinum under these conditions
diminished with rising pressure. As a rule small positive
emissions were observed at low temperatures. These became
negative at high temperatures, and varied with the temperature
in the same way as such currents have been found to do in
general. With nickel, copper, and brass positive emissions
only were detected.

Kaye and Higgins^ have examined the currents, in an at-
mosphere of nitrogen at atmospheric pressure, which flow from
a carbon crucible containing various substances to the walls
of a surrounding carbon-tube furnace. Simultaneously they
measured the conductivity of the furnace vapours present by
means of an auxiliary electrode. The substances tested in-
clude : baryta, lime, soda-lime, strontia, magnesia, silica, alu-
mina, ferric oxide, tin, aluminium, iron, copper, and brass. The
temperatures varied from 2000° C. to 2500° C. Brass gave a
large positive emission. All the other substances increased the
negative emission above the value proper to the carbon cru-
cible. The observed currents varied from O'l to 10 ampere.

The conditions in most of the experiments just described
are so complicated that it is difficult to disentangle the various
»" Roy. Soc. Proc., A.," Vol. XC, p. 430 (1914).

128 EMISSION OF ELECTRICITY FROM HOT BODIES

causes which might give rise to the observed effects. No
doubt these are partly caused by electrons and ions emitted by
the hot surfaces on account of the high temperature, but they
may also be due partly to ions emitted by chemical action.
The actions are also greatly complicated by the presence of
the hot vapours which must have properties similar to those
of flames.

The Relative Importance of Various Factors in
Causing the Emission of Electrons from Hot
Bodies.

We have already considered three possible causes of elec-
tronic emission, namely : the escape of the electrons owing to
the purely thermal increase of their kinetic energy (p. 27), the
liberation of electrons as one of the products of chemical action
(p. 49), and the complete photoelectric emission (p, 95). We
have seen (p. 100) that the available photoelectric data indi-
cate that the last of these is too small to account for the
emissions which have been observed from hot bodies ; so that
unless and until fresh observations are made which tend to
conflict with this conclusion, it does not appear necessary to
consider this particular question further.

It remains to deal with the relative claims of the purely
thermal effect and of chemical action. In the last few years a
number of writers have advocated the view that all the observed
effects are attributable to chemical action. The case for this
position is, briefly, as follows : —

We have seen in Chapter II that any electronic emission
arising from chemical action would be likely to follow a law of
temperature variation practically identical with that required
by the purely thermal effect ; so that the fact that the theo-
retical law is satisfied by the experimental results offers no
criterion for distinguishing between the two views. In certain
cases there is some evidence that electrons are liberated as a
direct result of chemical action between solids and gases. The
experiments of Haber and Just '^ have shown that when the
alkali metals, their alloys, or amalgams, are attacked by oxygen,

1 " Ann. der Physik," Vol. XXXVI, p. 308 (19").

THE EFFECT OF GASES 129

hydrochloric acid gas, phosgene gas, water vapour, and certain
other chemically active gases or vapours, electrons are liberated
in considerable quantity. It may be urged (cf. Chapter IX,
p. 290) that in reality this also is a thermal emission, caused by
a local increase of temperature in the surface layer arising from
the heating caused by the chemical action. Most of Haber and
Just's experiments were made with drops of various amalgams
and with the liquid alloy of sodium and potassium. From a
determination of the amount of chemical action occurring they
calculate that in a particular experiment the heat generated by
the chemical action was not sufficient to raise the temperature
of the whole of a drop more than 2° C. But it is clear that
the temperature of the surface layers must have been raised to
a very much greater extent, and as it is only the temperature
of the surface layer which is of any account if the effect is a
purely thermal one, it cannot be said that the experiments so
far made by these authors prove that the emission is a direct
consequence of chemical action. Similar conclusions to those
of Haber and Just have been reached by Fredenhagen,^ who
has shown that the emission ordinarily observed when the al-
kali metals are heated can be reduced to very much smaller
values by the careful elimination of gases. The smallest
currents recorded by Fredenhagen are, however, not smaller
than those calculated '^ by an application of the considerations
on p. 40 to the known emission from platinum or tungsten,
in spite of the strong electropositive character of the alkali
metals. The large values are restored, at least partially, when
small quantities of gases, and especially of oxygen, are allowed
to come in contact with the metal. But when one remembers
the extraordinary sensitiveness of the emission to changes of
temperature and that, in any event, the effect is a purely su-
perficial one, it is questionable whether the observed enhance-
ment of the emission may not be due to the local increase of
temperature caused indirectly by the chemical action. It is,
of course, abundantly proved that an emission is caused by
chemical action in these cases, but it is extremely difficult to

1" Verh. der Deutsch. Physik. Ges.," Jahrg. 14, p. 386 (1912).
»Cf. O. W. Richardson, '• Phil. Mag.," Vol. XXIV, p. 742 (1912).

130 EMISSION OF ELECTRICITY FROM HOT BODIES

be sure that the effect is the direct result of the chemical action
and is not caused indirectly by the heat generated at the
surface. (See, however, p. 296.)

The remaining cases which have been cited as examples
of the emission of electrons by chemical action are the oxida-
tion of calcium and the emission from incandescent carbon.
Fredenhagen ^ has put forward the view that the activity of
the lime-covered cathode is caused by the recombination of
the calcium and oxygen which are separated by electrolysis
during the passage of the current. The arguments in favour
of this view have already been dealt with on p. 85 where
they were not found to resist a critical examination successfully.
We have already seen (p. 86) that Horton, who made a direct
test of the question, was unable to detect any emission from
calcium arising directly from oxidation. Wehnelt,^ who has
devoted much attention to the lime-covered cathode, has re-
cently expressed the opinion that in the case of this material
there is no evidence which would favour a chemical rather
than a purely thermal cause for the origin of the emission.
Finally, Germershausen ^ has shown that the emission from
lime is increased by the removal of every trace of gas from
its surroundings. Under these conditions the discharge be-
comes very similar to that from tungsten as observed by the
writer and by Langmuir.

The emission from carbon has been attributed to chemical
action between the carbon and traces of gaseous contamination
by Pring and Parker,* and by Pring.^ Using comparatively
large rods of carefully purified carbon they found that the
negative discharge to a small electrode in the neighbourhood
of the rod diminished progressively as the gases were removed
from the rod by continuous heating. The currents finally
obtained at the highest temperatures were very much smaller
than those recorded by other observers with carbon (see

^"Leipziger Ber.," Vol. LXV, p. 42 (1913).

'" Physik. Zeits.," Jahrg. 15, p. 558 (1914).

' Ihid., Jahrg. 16, p. 104 (1915).

*" Phil. Mag.," Vol. XXIII, p. 192 (1912).

«"' Roy. Soc. Proc., A.," Vol. LXXXIX, p. 344 (1913).

THE EFFECT OF GASES

»3»

pp. 69 and 75). An application^ of the considerations de-
veloped on p. 65, however, shows that the magnitude of the
heating currents and the geometrical arrangement of the ap-
paratus used by these authors were such that no electrons at all
would be able to reach the electrode at the higher temperatures.
Thus there is no difficulty in accounting for the smallness of
the observed currents on the purely thermal theory of the
emission. The only difficulty, which is present on any theory
of the origin of the electrons, is to explain why the observed
currents were not actually zero. The small currents can be
accounted for ^ if it is supposed either that traces of gas pre-
sent interfere with the motion of the electrons or that some of
the electrons combine with uncharged molecules or atoms of
the gas to form negative ions whose motion is almost un-
affected by the magnetic field. Either of these assumptions
would explain the fact that the observed currents are increased
by the admission of traces of various gases. The relatively
large effects produced by very small amounts of gas are in
favour of the second hypothesis, which also explains the re-
lative efficiency in this respect of the various gases tested.
Another factor which would tend to make the currents ob-
served in these experiments too small is the effect of the
mutual repulsion of the electrons considered by Langmuir
(see p. 61). Moreover, the results of the experiments are in
complete disagreement with the results of experiments made
with well-glo wed-out carbon filaments by Deininger ' in 1 908,
and of the more recent experiments of the writer and of
Langmuir. In the last two cases the precautions described
on p. 14 were taken in preparing the bulbs, and although it
is not claimed that every trace of gas was got out of this very
difficult substance, the conditions were much better in this
respect than in the experiments of Pring and of Pring and
Parker. The same claim can almost certainly be made for
Deininger's work. In fact, it is quite impossible to attain
good vacuum conditions with the large quantities of hot

» O. W. Richardson, " Roy. Soc. Proc, A.," Vol. XC, p. 174 (1914^.

' Loc. cit.

'•'Ann, dcr Physik," Vol. XXV, p. 285 (1908).

9 •

132 EMISSION OF ELECTRICITY FROM HOT BODIES

material used by Pring. Taking all the facts into considera-
tion they appear to the writer to afford no support to the con-
tention that the emission from carbon has anything whatever
to do with chemical action. It may be that such a chemical
effect exists, but its existence is not demonstrable, or even
rendered probable, by the evidence which has been submitted.

Thus there is no case in which it has been established
with certainty that chemical action is the direct and immediate
cause of an emission of electrons. The majority of chemical
actions between solids and gases certainly do not give rise to
electrical effects of this kind to any appreciable extent (see
Chap. IX). The only case in which the evidence renders the
occurrence of electron emission as a chemical effect probable
is that of the alkali metals. The experiments of Haber and
Just and of Fredenhagen do, on the whole, indicate a balance
of probability in favour of a direct chemical effect in this case,
although, in the judgment of the writer, they cannot be held
to establish it with certainty.

The advocates of the chemical point of view have held
that the emissions usually observed are due to actions between
the hot metal and minute traces of residual gas and not to
chemical actions on any considerable scale. In support of
this it may be urged that, as the effect is a purely superficial
one, a small quantity of gas will exert as large an effect as a
greater amount, down to a certain limit. On the other hand,
it cannot be said that a comparison of the specific effects of
different gases lends any support to the chemical theories. In
the case of platinum, the only gas which causes any consider-
able increase in the emission is hydrogen, and although there
is probably some chemical combination in this case it certainly
is not of a violent character. In the case of tungsten all gases
which act chemically on the metal have been found to reduce
the emission and not to increase it.

The difficulty, discussed on pp. 71 et seq., of determining
the precise values of the constants A and b, and the depen-
dence generally of the emission on factors which are difficult
to control and to specify, has been held to favour the view that
these effects are caused by the interaction between the hot

THE EFFECT OF GASES 133

bodies and traces of gaseous contamination of uncertain com-
position. It would, however, seem more reasonable to at-
tribute these features of the phenomenon to the fact that it is
of an entirely superficial character and is very sensitive to
changes in the nature or composition of the surfaces. For
example, the admission of oxygen will coat the hot metal with
a layer of oxide. If, as appears to be the case with calcium,
the oxide is more active thermionically than the metal, the
emission in presence of oxygen will exceed the normal value.
If the oxide is inactive its presence will tend to prevent the
electrons escaping from the metal and will thus reduce the
emission. The effect of oxygen on tungsten is probably of
this nature. Minute traces of gas would be sufficient to pro-
duce effects of this kind, and if the composition of the gas
were uncertain and variable the effects would be correspond-
ingly so. A similar difficulty arises in other superficial
phenomena, such as the photoelectric effect, surface tension,
and optical reflexion, although, as a rule, it is not so marked.
This is on account of the extreme sensitiveness of the thermi-
onic emission to small changes in the work required for an
electron to escape. There is, in fact, no comprehensive body
of evidence supporting the view that interaction with gases
is an invariable and direct cause of thermionic emission ; the
evidence that gases act indirectly by modifying the quantity
of the emission quite generally is of a much stronger character.
In this connexion the close relationship between electron
emission and contact potential difference, which is required
on theoretical grounds, and the sensitiveness of both these
phenomena to superficial contamination, should also be kept
in mind.

Experiments made by the writer^ have shown that the
emission from tungsten in a good vacuum is a property of the
element itself, and cannot be attributed to chemical or other
secondary actions between the tungsten and traces of other
contaminating material. The advantages of tungsten in in-
vestigations of this character have been alluded to already
(p. 117), The tests were made with experimental tungsten

» •• Phil. Mag.," Vol. XXVI, p. 345 (iQ^S).

134 EMISSION OP- ELECTRICITY FROM MOT BODIES

lamps carrying a vertical filament of ductile tungsten which
passed axially down a concentric cylindrical electrode of copper
gauze or foil. The tungsten filaments were welded electrically
in a hydrogen atmosphere to stout metal leads. These in turn
were silver-soldered to platinum wires sealed into the glass
container. The lead to the copper electrodes was sealed into
the glass in the same way. The lamps were exhausted with a
Gaede pump for several hours. During this time they were
maintained at 5 50° to 570° C. by means of the vacuum furnace
described in Chapter I. The duration of this exhaustion
varied from 8 to 24 hours with different bulbs. It was con-
tinued until the apparent evolution of gas was very small and
practically constant. This small final development of gas,
which appeared to persist indefinitely, is believed to be due to
the dissociation of the glass walls of the tube and to the diffu-
sion through them of gases from the vacuum furnace which
could only be exhausted to about i cm. pressure. The ex-
haustion was completed by means of liquid air and charcoal,
the tungsten filament meanwhile being glowed out by means
of an electric current at over 2200" C. Most of the tests were
made after the furnace had been opened up and the lamps
allowed to cool off. This treatment has been found completely
to stop the emission, under the relatively slight heating caused
by the radiation from the hot filament, of gases from the walls
of the tubes and from the cold electrodes which had previously
formed such a persistent source of difficulty in experiments with
hot wires.

Although the filaments used were quite thin (about O'OO/
cm. diameter), these lamps were found capable of being run so
as to give thermionic currents of about 0"i ampere for hours.
Tests were made covering the following alternative possible
causes of the emission : —

(i) That the emission is caused by the evolution of gas
from the filaments.

In one experiment the tube was shut off by a mercury trap
and the gases allowed to accumulate. The filament gave an
electronic current of 0*50 ampere continuously for 30 minutes.
The pressure of the gas which had accumulated was less than

THE EFFECT OF GASES 135

lO"^ mm. and was too small to measure. Taking into account
the volume of the bulb, these figures show that for every
molecule of gas evolved 26 x 10* electrons were emitted.
No conceivable process could cause so many electrons to arise
from each gas molecule.

(2) That the emission is caused by chemical action or some
other cause depending on impacts between the gas molecules
and the filaments.

If for purposes of computation we consider the gas to be
hydrogen, which is the most unfavourable assumption, since
this gas makes most collisions, the data of the last experiment
show that 1 5,000 electrons would have to arise every time a
molecule impinged on the filament. This number is of course
quite prohibitive. Moreover, in certain other experiments quite
appreciable changes in the gas pressure caused no change in
the emission.

(3) That the emission is a result of some process involving
consumption of the tungsten.

In these experiments there is a loss of tungsten from the
filament which is believed to be due to evaporation. The loss
was determined by measuring the change in the resistance
of the filament At the same time the thermionic current
was measured, giving the number of electrons emitted. In
one experiment it was found that for each atom of tungsten
lost 984,000 electrons were emitted. In this case the mass of
the electrons emitted was three times the mass of tungsten
lost. This experiment and others similar to it show conclu-
sively that the emitted electrons must have flowed into the
tungsten from outside points of the circuit.

(4) That the emission is caused by interaction with some
condensible vapour which does not affect the McLeod gauge.

This explanation is cut out by the fact that the currents are
not affected when the tube is cut off from the liquid air and
charcoal and the hypothetical vapours allowed to accumulate.

These experiments have not been accepted as conclusive
by Fredenhagen ^ and by Horton * on the ground that they

* ••Phys. Zeits.," Jahrg. 15, p. 19 (1914).

•" Phil. Trans., A.," Vol. CCXIV, p. 278 (19x4).

136 EMISSION OF ELECTRICITY FROM HOT BODIES

still leave open the possibility that the emission is due to inter-
action with the tungsten of some substance present in the
filaments. In regard to this suggestion it is to be remembered
that the assumption of the presence of foreign substances in
the filament is a pure hypothesis. It is very unlikely that any
gaseous substance, and most substances are gaseous under these
conditions, could remain in a thin filament kept at over 2200°
C. in a vacuum of lO"*' mm, pressure for a long time. The
behaviour of the filaments during the experiments is distinctly
opposed to this suggestion. When they are first glowed out
there is a considerable evolution of gas lasting for a few
seconds, and after that nothing. When the filaments are
sealed in a small closed tube and allowed to disintegrate
through overrunning no gas is evolved. There is good evidence
that the small quantities of gas which occasionally appear in
experiments of this kind come from the walls of the tube and
the relatively heavy parts of the metal electrodes owing to in-
adequate preliminary treatment. The only impurities which
would seem to have any chance of remaining in the filaments
during these experiments are the highly refractory elements such
as molybdenum, tantalum, carbon, thorium, etc. Even these
would be expected gradually to disappear, and there is no evi-
dence of any progressive change in the emission at constant tem-
perature with properly prepared tubes. In any event it is
questionable whether their presence would help the chemical
theory, which would then be reduced to the position of ad-
mitting the existence of an emission from alloys but not from
the pure metals. That the emission cannot be attributed to
the commoner gases is also shown conclusively by the experi-
ments (see p. 125) of Langmuir, who found that they all
reduced the emission, except the inert gases which left it
unaltered.

These experiments with tungsten definitely exclude chemical
action as the cause of the emission from this substance. Such,
at least, is the considered judgment of the writer. Although
equally searching tests have not been made with other
materials, a general survey of the phenomena does not in-
dicate any definite connexion with chemical action, certainly

THE EFFECT OF GASES 137

in the case of the refractory elements. This is supported by
the results of Langmuir,^ who finds that with tantalum,
molybdenum, carbon, and platinum as well as tungsten, the
emission is increased with progressive elimination of gaseous
contamination and corresponding freedom from liability to
chemical action. There is, of course, no compelling reason
to expect a purely thermal origin for the effects in all cases.
It may be that in the case of the alkali metals such effects as
have been observed are due entirely or chiefly to chemical
action ; but this has not yet been proved, certainly not with
anything like the thoroughness of proof of the contrary pro-
position in the case of tungsten. If the emission is ever
caused by chemical action we should expect this type of
effect to be exhibited by the alkali metals, where the reactions
are much more vigorous than with the refractory elements, as
is shown by the very much greater heat liberation per gram
equivalent.

There is another argument, to which great weight should
be attached, which is definitely against a chemical origin of
the effects exhibited by the refractory elements. We have
seen that the variation of the emission with temperature en-
ables us to form an estimate of the energy change associated
with the liberation of one electron. We shall see in the next
chapter that more direct methods are available for determin-
ing this quantity, both from the absorption of heat when elec-
trons are emitted, and from the liberation of heat when electrons
are absorbed. All three methods give consistent results, and
show that the quantity in question is very considerable.

If we compare this heat change per gram equivalent of
electrons, with the heat liberated per gram equivalent in vari-
ous chemical reactions, we find, in the case of tungsten or
platinum, that it is about equal to the corresponding quantity
for the most vigorous chemical actions known, such as the
combination of the alkali metals with the haloids, and is far
greater than the heat of any known reaction of the elements
under consideration. Thus the rate of variation of the emis-
sion with temperature is right for the physical theory of the
>" Phys. Rev.," Vol. II, p. 484 (1913).

138 EMISSION OF ELECTRICITY FROM HOT BODIES

phenomena, but is wrong, so far as we can judge, for the
chemical theory. It is desirable at present to restrict this ar-
gument to the more refractory elements which are less active
chemically, as the thermionic data for the more electropositive
elements cannot be considered to be known with sufficient
definiteness.

CHAPTER V.

ENERGETICS OF ELECTRON EMISSION.

I. The Kinetic Energy of the Emitted Electrons.

We saw in Chapter II that the law of temperature variation of
the emission of electrons could be deduced in various ways
from a consideration of the properties of the atmosphere of
electrons in equilibrium with hot bodies present in a vacuous
endosure. The essential and important results of these
theories have been very fully confirmed by the experimental
results already described. The further consideration of such
atmospheres of electrons suggests certain other important pro-
perties of the streams of emitted electrons which have not yet
been discussed. We have seen that the electron atmospheres
are in all respects analogous to a gas, the only important dif-
ferences arising from the much smaller value of the molecular
weight, and, owing to the fact that the electrons carry an
electric charge, the much greater value of the intermolecular
forces. Just as in the case of gases the modification of the
pressure due to the intermolecular forces becomes negligible at
very low pressures, we see that the pressures due to very at-
tenuated electron atmospheres will be the same as those which
would be exerted if the electrons were uncharged. In point
of fact, the electron concentrations to be dealt with are exces-
sively small ; so that the pressures will be given by the law
of a perfect gas

P =. nkl, .... (I)

as we have already assumed. In (i) « is the number of elec-
trons per C.C. in the atmosphere in equilibrium, and k is Boltz-
mann's constant.

We know also, from the principles of the dynamical theory
of gases, that in such an atmosphere the average kinetic energy

139

140 EMISSION OF ELECTRICITY FROM HOT BODIES

of each molecule is proportional to the absolute temperature
and equal to f^T, and that the velocities of the different mole-
cules are distributed amongst them in accordance with Max-
well's Law. The same conclusions will apply to the streams
of electrons as they are emitted from a metal surface, even
when they are allowed constantly to flow away, and there is
no possibility of the attainment of steady equilibrium condi-
tions. This follows, since any such change as that contem-
plated will not affect the conditions which determine the
emission of the electrons. The emitted stream will thus have
the same properties whether the external conditions are those
of equilibrium or not. When the conditions are those of equi-
librium it follows, from the principles of the dynamical theory
of gases, that the emitted stream must have the properties
specified above ; whence it follows that this statement as to
the properties of the emitted stream must be true in general.

This conclusion is valid even if the principles of the dyna-
mical theory of gases are not universally applicable, for in-
stance, if the emission of the electrons is governed by the
principles of the quantum theory in some such manner as they
are developed on p. 35 ; for the equilibrium concentration of
the external electrons in these cases is so small that the prin-
ciples of the classical dynamics will still apply to them even
if the phenomena as a whole are governed by the quantum
theory. On the other hand, if the distribution of velocity
amongst the emitted electrons is governed by Maxwell's Law,
it does not follow that the same thing is true of the distribu-
tion of velocity amongst the free electrons inside the hot body,
for the concentration of these must be of an entirely different,
and in all probability much higher, order of magnitude.

The result of this argument may be summarized as
follows : We expect, as a consequence of the theories de-
veloped in Chapter II, that the distribution of kinetic energy
amongst the electrons in the emitted stream will be identical
with that amongst those molecules of a gas, at the same
temperature as the hot body, which leave either side of any
surface in the gas in any definite interval of time. In ac-
cordance with Maxwell's Law the average energy of the

ENERGETICS OF ELECTRON EMISSION 141

electrons emitted is 2>^T, and, if the emitting surface is taken
perpendicular to the axis of x and «, v, w are the velocity
components of an electron parallel to x, y and z respectively,
then the number emitted in unit time with velocity com-
ponents between u and u + du is

N^« = N . 2Aw«^-''""'V«, . . (2)

the number with velocity components between v and v + dv,

N,dv = N . J^ e-'""'^dv, . . (3)

and the number with velocity components between w and
TV + dw,

^^w^ N^^^-^^-Vzt/,

(4)

where N is the total number emitted in unit time, m is the
mass of an electron, and h = (2^T)-^ It will be noticed that
the average kinetic energy of the emitted electrons is 2kT
and not %kT, the average kinetic energy of the electrons (or
molecules) in unit volume in equilibrium. The larger value
arises from the fact that the more rapidly moving particles
occur more frequently in an emitted stream than in the
number present in a volume selected at random under equi-
librium conditions.^

These conclusions have been tested in a large number of
experiments made by the writer, partly in collaboration with
F. C. Brown. The first investigation, made by Richardson
and Brown,^ is concerned only with the component of velocity
u normal to the emitting surface. The apparatus used is
shown in section in Fig. 15.

The emitting surface was that of a small piece of thin
platinum foil H heated electrically. The foil nearly filled a
small hole at the centre of the metal plate L, the upper sur-
faces of L and H being flush with one another. The heating
current was let in through / , /j, which were connected by a
high resistance shunt not shown in the figure. The shunt

iCf. O. W. Richardson, "Phil. Trans., A.," Vol. CCI, p. 50a (1903);
" Phil. Mag.," Vol. XVIII, p. 695 (1309).
»•• Phil. Mag.," Vol. XVI, p. 353 (1908).

142 EMISSION OF ELECTRICITY FROM HOT BODIES

was provided with a sliding contact which could be connected
through the metal base B to L. In this way the middle of
the strip H could be kept at the same potential as the sur-
rounding plate L. This device, for controlling the potential
of inaccessible parts of an enclosed apparatus, carrying an
electric current, is often useful in experiments of this char-

— e,

PUMP. &(fe.

— B,

to CenTI MITERS

Fig. 15.

acter. Opposite L is a parallel plate U covered with plati-
num, to avoid effects arising from contact difference of
potential, and provided with a guard ring G and electrostatic
shield S. U is connected to the insulated quadrants of a
sensitive electrometer, whose time rate of deflection measured
the number of electrons passing from H to U. The tempera-
ture of H was controlled, and estimated, by measuring its
resistance in the manner described in Chapter I, p. 15. The

ENERGETICS OF ELECTRON EMISSION 143

electron currents from H to U were measured when different
potentials were applied so as to oppose their passage.

Now let us consider the theory of this experiment suppos-
ing, first of all, that the planes U and L are infinite in extent.
The plates are maintained at fixed potentials ; so that the
electric intensity is everywhere normal to them, i.e. parallel to
the X axis, and constant. If V is the potential at any point
Xf y, z between the two plates the equations of motion of an
electron at that point are —

li^x J)« 2)V

w r-^ ^^ in— =0 and m—-r = ni — = 0 . (6)

From (6), the v and w velocity components are constant

•\^
during the motion, and using the factor « «= to integrate (5),

if u^ is the emission value of u at the lower plate, where
V = o. If the upper plate is charged negatively, so that
the potential difference tends to oppose the passage of the
electrons, both e and V are negative ; so that the product eV
is positive, u will be reduced to zero on reaching a point at
which V = mu^j2€ ; after passing this point the electron will
return to the lower plate. If V^ is the difference of potential
between the plates, we see from (7) that an electron will get as
far as the upper plate, provided

V^^^V, (8)

Otherwise it will return to the lower plate. Thus with an op-
posing difference of potential equal to Vj, only those electrons
will contribute to the current from the upper plate which
satisfy (8). It follows that if F(«oy«o ^s the proportion of
electrons emitted for which the u component of velocity lies
between «o and «o + ^«0) y(^o)^^o and f{w^W(i denoting the
corresponding functions for the v and w components, the
current from the upper plate will be given by

144 EMISSION OF ELECTRICITY FROM HOT BODIES

01' -'V 2-Vi J - 00 J -00

where C is the capacity of the electrometer and its connex-
ions and N is the number of electrons emitted, with any
velocity, in unit time. If the upper plate has a finite radius r
we have to take account of the fact that the radial velocity
may be sufficient to take some of the electrons a horizontal
distance greater than r before the vertical distance x^ between
the plates has been covered. Under these circumstances
equation (9) is altered to

,00 ,--(«o+\/«o'*-a-v)

/ = Ne F(«,y«o F(WyW, (10)

where F (W) <^W denotes the probability of the radial velocity
W = ^v^ + w^ lying between W and W + </W. However,
the difference between (9) and (10) was negligible in the
experiments referred to ; so that we need consider only the
simpler expression (9).

If Maxwell's Law holds, the values of NF(«)q du^, etc.,
will be given by the right-hand sides of the corresponding
equations (2) to (4) and by substituting these values in (9)

t = Nee = he . . (n)

if z'q is the value of / when Vi = o. Remembering that A
= (2/&T)-\ and taking logarithms, we obtain

log^/^o = - ^ = - RT^i . . (12)

where v is the number of molecules in i c.c. of a perfect
gas at 0° C. and 760 mms. pressure, and R is the constant
in the equation pv = RT calculated for this quantity of gas.
We have seen that both ve and R are well-known physical
constants, being equal to 0-4327 e.m. unit and 371 1 x 10^
erg./deg. C. respectively.

The results of one of the experiments are plotted in Fig.
16. The points shown thus: © give the current /as ordinates
and the points shown thus: x the values of log t. The

ENERGET/CS OF ELECTRON EMISSION

'45

abscissae are the values of the corresponding opposing po-
tentials in each case. From (12) we see that log / should be
a linear function of Vj at constant temperature. This re-
quirement is satisfied very accurately by the points: x on

3 -4

^OTerfTIAj. . VOLTS.

FiQ. 16.

the diagram. From the slope of the straight line, knowing T
and assuming that ve = 4327, we can calculate the value of
the constant R. The values of R obtained in this way under
a variety of conditions are collected in the following table.
The numbers in the last column are a little higher than those

146 EMISSION OF ELECTRICITY FROM HOT BODIES

given in the original paper, where an inaccurate value of ve
was used.

Treatment of Platinum before

Pressure

Absolute
Tempera-
ture (°K.).

Maximum Current

Heating.

tnms.

(amperes).

ergs./oC.

i6 hours' heating

0*015

1556

4*7 X 10 -1^

4*36 X 10'

o*oo8 1
0*009 i

1473

1*2 X 10 -"

4*46 X 10"

Just after lime was placed)
on the platinum . . )

o*oo6
o*o5

1503

3 X 10 -"

3*72 X io3

Just after hydrogen was let

into the vacuum

0*04

1553

4 X lo-ii

3*83 X 10'

About 35 hours' heating

0*015

1660

1*4 X 10 -1^

3*08 X lO^

About 30 hours' heating

o*oi

1560

3 X 10-12

3*29 X \Q^

Highly charged with nega-

tive electricity and strongly

heated subsequently .

0*02

1840

4 X I0-"

3*40 X 10"

Highly charged with positive

electricity and strongly

heated subsequently

1813

I X 10 -11

3*6i X lo^

The mean of the numbers in the last column gives R =
3719 X I o^ as compared with the theoretical value 3 7 1 1 x 10''.
No doubt this excellent agreement is partly accidental, but it
shows quite conclusively that the average kinetic energy of the
emitted electrons is very close to that of the molecules of a gas
at the same temperature as the hot body. The fact that the
linear relation between log i and V^ is satisfied shows not only
that the average energy is the same, but also that the energy
is actually distributed among the electrons in exactly the same
way as it would be distributed among the molecules of a mon-
atomic gas at the same temperature. The experiments con-
sidered above have only proved these statements to be true so
far as the part of the kinetic energy is concerned which de-
pends on the component of velocity perpendicular to the
emitting surface.

Richardson and Brown also made a few observations on
certain other substances with the object of ascertaining the law
of distribution of velocity among the electrons emitted by
them, using the same or a similar method. The substances
tested were : platinum saturated with hydrogen so as to give
a large emission, platinum coated with lime, and the liquid
alloy of sodium and potassium. These experiments were not
at all satisfactory, but, so far as they went, they indicated that
the distribution of energy amongst the electrons emitted by
these bodies was not in accordance with Maxwell's Law.

ENERGETICS OF ELECTRON EMISSION

There are a number of ways in which such a result might arise
exceptionally without vitiating any general principle ; but it is
not worth while to discuss the matter further in the absence
of more satisfactory experimental evidence. The importance
of the subject makes it very desirable that more experimental
work should be done with these substances.

The distribution of velocity for the components parallel
to the emitting surface was ex-
amined by the writer^ using a
different type of apparatus. A
vertical section of one form of
this is shown in Fig. 17. The
parallel metal plates A, B are
provided with narrow central
parallel slits perpendicular to q— ■
the plane of the figure. A nar-
row platinum strip, provided
with an arrangement for keep-
ing it flat, worked from outside
the apparatus, almost fills the
slit D. The platinum is heated
electrically and its front surface
is flush with that of the plates.
The electrons emitted by the
strip are carried by the electric field to the opposite plate OO,
but some of them pass through the slit into the box-shaped
electrode T, which is insulated from the plates. All the
parts OTQO are rigidly bolted together and can be moved
up and down through known distances by means of the
accurate screw S. By means of suitable electrometer con-
nexions (see p. 196) the number of electrons passing through
the slit and the number reaching the plates can be measured
simultaneously. These quantities were measured for different
vertical displacements of the slit in OO relative to the level
of D. This information enables the distribution of the vertical
component of velocity of the emitted electrons to be ascer-
tained.

Fig. 17.

> •• Phil. Mag.," Vol. XVI, p. 890 (1908) ; Vol. XVIII, p. 58i (1909).

10 *

148 EMISSION OF ELECTRICITY FROM HOT BODIES

In these experiments an accelerating difference of potential
Vj is applied between the plates A and B so as to pull the
electrons from D towards OO. Since it can be shown that
the effect of the mutual repulsion of the electrons is negligible
with the small currents used, it follows that if the electrons
were emitted with no velocity component parallel to the sur-
face of emission they would travel in straight lines normal to
the plates. Under these conditions the graph of jj/, the ratio
of the current through the slit to the total current received by

J-8
1-6
1-4

10
•8

^7 8 9 10 U 12

Sc/iLS Of x(/-= '06ZS cm)

FiQ, i8.

both the slit and the plates, against x, the vertical displace-
ment of the slit, would consist of three inclined straight lines
as is shown on the right-hand side of Fig. i8. The observed
graph is that drawn through the points marked thus : ®
and shows very clearly the spreading out of the electrons
owing to the vertical component of velocity.

Now consider the case when the electrons are emitted with
initial velocity components Uq Vq Wq. Let us take the planes
to be perpendicular to the axis of z and w, and the axis of
X and u to be parallel to the vertical line in Fig. 17. If Z is
the electric intensity arising from the difference of potential V^

^-r

: \ I LaA

ENERGETICS OF ELECTRON EMISSION 149

between the plates, the equations of motion of an electron are

and

If / = o when the electron starts from the strip, the initial
conditions (at / = o) are

dx dv dz .

For the present problem we are concerned only with the x
and z displacements, i.e. with the motion projected into the
plane of Fig. 17. Integrating equation (14) and the first of
equations (13) subject to the initial conditions above, and
eliminating /, we get

„,.i./^[r+(,+^-^y]. . (,5)

where z^ is the perpendicular distance between the planes,
and jTj is the vertical level at which an electron emitted at the
level x^ with velocity components u^ w^ strikes the opposite
plane. Considering electrons setting out with different values
of «o, those for which u^ exceeds the right-hand side of (15)
will strike the plane at a level higher than jr^, and those with
smaller values of u^ at a lower level than Xy It follows from
this that if ^' is the width of the hot strip and ^ that of the
slit, both supposed to be of indefinite length, the current pass-
ing through the slit at the level x^ is

i^^\ dxA Y{w,)dwA ' /(«oy«o (16)

where Nj is the total number of electrons emitted by the strip,
and ¥{w^'Wq and / (u^u^ are the proportions of them for
which Wq lies between «/(, and w^ + dw^, and u^ between «<,
and u^ + du^ respectively. If ^ and ^ are both small, as in
the experiments, there are two important cases for which (16)
reduces to a quite simple expression.

I50 EMISSION OF ELECTRICITY FROM HOT BODIES

First suppose that Wiel^mw^ is a large quantity. It is
worth while remarking that if, as we have seen is the case,
Maxwell's Law holds for w^, this condition cannot be satisfied
by all the electrons ; since all values of w^ up to infinity are
included in the theoretical formula. On the other hand if Vj
is of the order of lOO volts the fraction of the whole number
of electrons which does not satisfy this condition is exceed-
ingly small and may safely be neglected. When 2V-^(£\m'w^
is large, (i6) reduces to

after substituting the values of F(Wo) and f{u^ which are re-
quired if Maxwell's Law is to be satisfied. In (17) and (18) ^,
V and R have the meanings given to them on p. 144. When
the centre of the slit is opposite the centre of the strip x^ - -r^,
which in what follows may be denoted by the single letter x
without confusion, is equal to zero ; so that, if i^ is the current
through the slit when in this position,

^0 = ^^^ ^(4RTt^) • • • (^9)
Thus, dividing (18) by (19) we obtain

/ft = .-^''" . . . (20)
or

I'cV x^

Equations (i7)-(2i) have been shown to follow if the
distribution of the vertical component of velocity at emission
is distributed in accordance with Maxwell's Law. We may,
however, proceed quite differently by deducing the law of
distribution of velocity directly from the experimental curves.
When 2V^€/mw^^ is very large it follows from (15) that the
electrons which reach the opposite plane at the level x,
measured from the level .«: = o of the narrow emitting strip,
are emitted with the vertical velocity component

corre-

ENERGETICS OF ELECTRON EMISSION 151

««=2WJ • • • (")

The part of their kinetic energy which arises from this velocity
component is thus

i;«V-''''''W • (23)

It follows from (22) that the electrons for which u^ lies be-
tween Uq and «Q + (Iuq have a value of ;ir which lies between

( Tf' )*^o ^^^ ( — —}K^o + ^^o)- Given x, to find the

sponding value of «(,, all we have to do is to multiply by a factor
involving the known quantities ejm, Vi, and Zi. Thus in Fig. 1 8
the abscissae represent the values of «o as well asof :r, and since
the currents are proportional to the numbers of electrons, the
ordinates represent the numbers corresponding to given values of
Uq. Thus curves like that in Fig. 18 form a complete graphical
representation of the mode of distribution of the component
«o of velocity amongst the emitted electrons. For example, to
find the average kinetic energy arising from u^ from Fig. 18
we can proceed as follows : l^ y is the ordinate at any point
and vq the number of electrons corresponding to unit area
of the diagram the number which corresponds to a strip of
height y and breadth dx is v^ydx. The kinetic energy of

these electrons is v^dx x \mu^ = Vq ^yx^dx. The total

4^1

eV f"
amount of this energy is thus v^ — - 1 yardx, and the total

4'S^i'^J - *

number of electrons to which it belongs is vA ydx. The

J _ 00

average amount of this part of the kinetic energy pertaining

to each electron is therefore

—y-^ \f_^y,. • ' • ^24;

The two integrals may be evaluated graphically in the usual
manner.

The relations (17) to (24) have been tested in various ways.
The curve on the left in Fig. 18 is the curve

/• = I •38^-"-^^' . . . (25)

152 EMISSION OF ELECTRICITY FROM HOT BODIES

and is seen to pass through all the experimental points. This
shows that the mode of distribution of the u^ velocity com-
ponent accords with the requirements of Maxwell's Law.

Comparing (25) with (20) we see that ^ = 55*1. Substi-

tuting the known value of ve and the experimental values of
Vi, T, and Zi, this gives R = 4*8 x lo^ which, considering
all the possible sources of error, is in satisfactory agreement
with the theoretical value 371 x lo^ Another test, which is
not independent of the last, can be applied by plotting log i
against x^y when a straight line should be obtained in accord-
ance with (21). This is found to be the case except for large
values of ;r, when the currents are so small that various sources
of error have a serious effect. The value of R obtained from
the slope of the line thus got was found to be 47 x lo^ The
third method is independent of the foregoing. Since the total
current from the slit and the plates is N^e, \ij\ denotes the
fraction of this which passes through the slit when in the
symmetrical position, then

/o = y^ie, .... (26)

and from (19)

R 'zfY.!;. . . . (.7)

where ^ is the width of the slit and/^ is the maximum value
of the ordinate in the left-hand curve of Fig. 18. On sub-
stituting the experimental values (27) gave R = 27 x 10^.
In applying the graphical method it was found that the points
were not quite symmetrical on the two sides of the central
position {x ~ o). On one side they were very close to the
curve y = iT4i;»r2(e _o.o495^^ ^^^ q^ ^j^g other to the curve
y B I'oyCfX^e'^'^*^^^" . These curves are of the form demanded
by Maxwell's Law. If n is Avogadro's number the Uq part of
the kinetic energy was found, for this number of electrons, to
be 3 '2 X 10* ergs per c.c, as against the calculated value
2*8 X 10" ergs per c.c. The value of R calculated from the
exponent 0'0495;r^, assuming Maxwell's Law vo hold, was
5-4 X I0^

ENERGETICS OF ELECTRON EMISSION 153

These methods are not as accurate as the one used in test-
ing the normal component of velocity ; so that the mean of
the four values obtained from R, namely 4*4 x 10' instead of
371 1 X 10', is to be regarded as satisfactory under the cir-
cumstances.

The other case in which (16) simplifies, arises when Vj = o,
when it reduces to

If, as before, we denote the current through the slit when
;r = o by ^^^, then from (28)

^0 " Nief/2^ri ; . . . (29)

so that

/,— (1 + -.) . . . (30)

Thus the ratio, of the current which flows through the slit at
different distances x from the central position, to its value
when .r = o, is determined solely by the distance z between
the plates and is independent of the temperature of the source
and the charge of the electrons. The extent to which this
formula is confirmed by the observations is shown in Fig. 19,
where the full line represents the curve calculated simply from
the distance between the plates, and the points shown repre-
sent observations under different conditions as to the tempera-
ture of the platinum, the magnitude of the emission, and the
direction of the heating current. A similar agreement was
obtained when the distance between the plates was altered.

Taken in conjunction with the experiments on the distri-
bution of the normal component of velocity described on
p. 144, these experiments with zero electric field afford a
valuable confirmation of the conclusion that Maxwell's Law
of distribution holds good for the tangential components of
velocity. For it is easily shown ^ that if Maxwell's Law holds
for the normal component and not for the tangential, or vice

> O. W. Richardson, " Phil. Mag.," Vol. XVI, p. 909 (1908).

154 EMISSION OF ELECTRICITY FROM HOT BODIES

versa, the results of the experiments with zero electric field
would be different from those obtained.

It will be noticed from the figure that the observed currents
are consistently larger than the theoretical values at consider-
able distances from the central position. A similar deviation
from theory, but usually more marked, is observed in the ex-
periments in which an accelerating potential is applied between
the plates. This difference which, although rather erratic in
its behaviour, usually increases with continued heating of the

&-7

—

— ^

]

■<•

14 16 18 10 a 24 J6 28 30 32 34 36 36 40
DlSPLAUMENT or <Slit (I' -OSZS cm)

Fig. ig.

strips, seemed to point to a deviation from Maxwell's Law of
velocity distribution. A large number of experiments on the
subject, however, led the writer to conclude that there was no
foundation for such a view ; but that the effects in question
were due to subsidiary causes, such as the roughness of the
metal surface caused by recrystallization, and the deflection of
the moving electrons by gas molecules.

In all the experiments with a movable slit it was noticed
that the current received by the slit was always greater than
that received by an equal area of the plates when in the same
position. This effect was attributed by the writer ' to the re-

1 " Phil. Mag.," Vol. XVI, p. 898 (1908) ; Vol. XVIII, p. 694 (1909) ; " Phys.
Rev.," Vol . X, p. 168 (1909).

2 r rV''^*^! r* i

/= /;-7=]e-»'"Vi ^-^^-'air 4- ^-^»^[ (31)

V TT V. J ft J /-fc.iv. •'

EMERGE TICS OF ELECTRON EMISSION 1 5 5

flexion of the electrons impinging on the plates. It was esti-
mated that about 30 per cent of the slow moving electrons
present in the absence of an electric field were reflected in this
way from a brass surface. About the same time, similar ef-
fects were observed by von Baeyer ^ in experiments with the
electrons emitted from metals under the influence of ultra-
violet light, and were ascribed by him to the same cause.

The kinetic energy of the electrons emitted by carbon and
tungsten has recently been investigated by Schottky^ who
measured the electron current / which flowed from hot wires
of circular section made of these materials, to a concentric
cylindrical electrode, against a difference of potential V^. If
the initial distribution of velocity among the emitted electrons
is in accordance with Maxwell's Law, and if r and R are the
radii of the wire and cylinder respectively, then

V TT I J 0 J JihtKWi

where Iq is the value of / when V^ = o, ^ = /'/Rj, and X =
(i - 6'^Y^. Under the conditions which held during the

experiments (^ = r/R < 1/30 and n = 2heV^ = ^^' ^<ioj
equation (31) is identical, within \ per cent, with the equation

The experimental results were compared with the values cal-
culated from (32), a value of n being assumed so as to give as
close a fit as possible. In every case an excellent agreement
with the formula was obtained, provided the currents which
reached the electrodes were small ; but with larger currents,
obtained either with higher temperatures of the hot wire, or
with small applied potential differences, there were consistent
deviations from the formula. This deviation is accounted for
satisfactorily by the effects arising from the mutual repulsion
of the electrons discussed in Chapter III. P'rom the experi-

»"Verh. d. Dcutsch. Physik. Ges.," 10 Jahrg., pp. 96, 953 (1908);
" Phys. Zeits.," 10 Jahrg., p. 168 (1909).

a "Ann. der Physik," Vol. XLIV, p. ion (1914)'

156 EMISSION OF ELECTRICITY FROM HOT BODIES

mental values of T and V^ knowing i^e, the value of R can be
calculated from these experiments. The values found are all
somewhat under the theoretical value, the error for carbon
ranging from 5 per cent to 26 per cent, and for tungsten from
2 per cent to 23 per cent, but it is probably difficult to obtain
the temperatures accurately under the conditions of the
measurements.

An important change in the method of experimenting was
introduced by Schottky, which removes two possible sources
of error present in the earlier experiments. Both in the heat-
ing circuit and in the line for measuring the thermionic current,
he inserted a make and break switch. These switches were
both operated 250 times per second by the same mechanism,
so that when one was in the other was out. Thus, when the
electron currents were being measured, there was no magnetic
field and no fall of potential down the wire due to the heating
current, and any error which might arise from their presence
was, therefore, avoided. Owing to the short time of interrup-
tion of the current, the fall of temperature of the wire thereby
arising would be inconsiderable.

It follows from the various experiments which have been
described that the velocities of the electrons emitted by hot
metals are identical with those which would be possessed by
the molecules of a gas, of equal molecular weight with the
electrons, which cross any area drawn in an enclosure contain-
ing the gas in equilibrium at the same temperature as the hot
metal. Since the proof of this identity rests on experiment it
can only be held to be established within the limitation of
accuracy set by the experimental methods employed ; but the
deviations from the strict theoretical requirements have always
been found to be such as could readily be accounted for as
arising from various secondary causes which it has not been
possible completely to eliminate. From this result the ap-
plication of Maxwell's Law of velocity distribution to the
atmospheres of electrons in equilibrium outside metals follows
immediately, but, as has been pointed out on p. 140, it does
not necessarily apply to^the electrons inside the metals.

It is obviously impossible to make experiments, similar to

ENERGETICS OF ELECTRON EMISSION 157

those described, with gases whose molecules are uncharged,
on account of the smallness of the controllable forces which it
is possible to bring to bear on individual molecules. For this
reason the experiments of the writer and F. C. Brown formed
the first experimental investigation of the distribution of
velocity among the particles of any system to which Maxwell's
Law could apply, although the law itself was predicted by
Maxwell ^ on theoretical grounds in 1 860.

2. Steady Thermionic Currents between Conductors
Maintained at Definite Temperatures and Po-
tentials.

The case considered on p. 143 of the electron current from
a hot strip to a neighbouring slit forms an example of a class
of problems which the writer * has shown can be solved in a
much more general manner. Suppose that in a region of
space otherwise vacuous there is a hot surface A emitting ions
and one or more conducting surfaces B. There may be an
electric field in the region under consideration ; so that any
or all of the surfaces may be charged. The ions emitted by
the surface A will move under the combined influence of their
initial velocity and of the electric field and will ultimately either
return to A, reach B, or go off to an infinite distance. If the
distribution of temperature on the surface A is maintained
constant the number, and mode of distribution of velocity, of
the ions it emits will remain constant, and if in addition the
potentials of the various surfaces are maintained constant, it is
clear that, whatever may happen at first, a steady state will
ultimately be established in which the number and mode of
distribution of velocity among the ions received by any of the
surfaces in a given time will be invariable. The problem is to
find the number of ions which reach any of the surfaces B in
a given time, together with their velocity components, when
the steady state has been established. In the discussion it
will be assumed that the motion of the ions is determined
solely by their positional and velocity co-ordinates at emission

» " Phil. Mag.," Vol. XIX, p. 12. (i860).
«/6i«f., Vol. XVII, p. 813 (1909).

158 EMISSION OF ELECTRICITY FROM NOT BODIES

and by the electric field. The forces exerted by the ions on
each other ^ and by molecules of gas into whose spheres of
action they may chance to penetrate are left out of account.
These conditions are realized if thermionic currents of moderate
size are experimented with in high vacua. In order to avoid
complications arising out of recombination we shall also sup-
pose the temperature conditions to be such that ions of one
sign only occur. We shall now consider the general problem,
using rectangular co-ordinates.

Let the co-ordinates of a point of the surface A be x^y^z^
and let an ion be projected from x^y^z^ with the velocity com-
ponents u^VqWq. Let us seek the condition that this shall
strike the surface B, whose equation is

ir(xyz) = O, . . . . (33)

within an infinitesimal distance of the point x^^Zy If V is
the potential at any point of the field, the equations of motion
of the ion will be

'b'^x >()V 2)2^ ^Y ^^z W , ,

t)/2 ^x t)/2 ^y Ti^ iz

On integration these equations give three equations between
Xy y, 2, and / involving six arbitrary constants which are deter-
mined by the values of ^ro^o^o^o^o^o- After elimination of the
time there result two equations which may be written

4>lxyzx^'^z^^v^w^) = o . . . (35)
<\)lxyzxoyoz^u^v^w^) = O . . . (36)

The curve in which the surfaces ^^ and ^2 intersect is the
trajectory of the particle projected under the given initial con-
ditions. The intersection of this curve with the surface
yjr{xyz) = o gives the point where the particle strikes the
surface. The co-ordinates x^^Zi of such points will there-
fore be given by solving (33), (35), and (36) for x, y, and z, and
the density of these points on the surface yfr will determine
the thermionic current density into this surface in the steady
state.

1 Particular problems of the same general character in the treatment of
which the influence of the interionic forces have been taken into account have
been considered on p. 45 and p. 63.

EJVERGET/CS OF ELECTRON EMISSION 159

In general the equations for Xyy-^z^ will not be of the first
degree ; so that there will be a number of roots corresponding
to the successive real and imaginary intersections of the sur-
faces ^j, <^2» ^"d >/r. In any case the path of the particle will
end as soon as it has reached the conducting surface B, and
if this surface includes the whole of the analytical surface
i/r {x\y^z) = o the root to be chosen is that real root which
corresponds to the shortest time of transit from ^oy^^o- ^^^
proper root can usually be picked out in simple cases. If the
surface B is only a part of the analytical surface yjr =0 bounded
by a curve or curves, it may in general be necessary to include
roots corresponding to any number, less than that of the degree
of the equations, of previous intersections of the trajectory and
the surface yfr = o. The problem then becomes much more
complicated.

The equations (35) and (36) may be solved for «„ and Vq
giving

«o = <f>si^}'^(J'o^o'^o\ ' • • (37)

^0 = H^y^^^J'o^o'^o) ■ ' • (38)

The equation ^3 = constant, together with "^^xyz) = o, will
determine a curve lying in the surface i/r which contains the
points of intersection with >/r of all trajectories for which «o
and Wq are constant. Similarly ^^ = constant determines a
curve corresponding to constant values of Vo and Wq. If ^ and
17 denote lengths laid out along the normals to the level sur-
faces of «o and v^, respectively, at any point, then

(39)

Let the number of particles which are emitted in unit time
with velocity components between «o and Uq + du^ be denoted
by/i(«oyi«o. the corresponding number with respect to Vo and
z^o + dv^ being y^(z;(,)d?z/(,. For a constant value o^w^ the number
which simultaneously have velocity components within the
ranges above will be proportional to /^{u^^lz^^u^v^ and these
will fall on an area </S of the surface -^ = o, given by

i6o EMISSION OF ELECTRICITY FROM HOT BODIES

dS cos (u.vmS) = :, "^ X ,

^ ^^0 sin u^Vq

~^ ^'

where «o^o«S is the angle between the normal to the surface
i/r = o and the tangent to the curve in which the surfaces
«o = 03' ^0 = <^4 intersect ; and u^Vo is the angle between the
normals to the surfaces Uq = ^3 and v^ = ^4. Hence,

du^dv^

WnxJ \byj \dzi/ J (40)

= xC«^>ri'8'i^aro^oWo)^S . . . (40

If the probability that the Wq component of velocity lies be-
tween zUq and w^ + dw^ is denoted by/s(wo)dwQ, the number of
electrons reaching the surface yfr = o with values of Wq within
this range is proportional to

dtvo j j A{wQ)fi{uQYi{vQ)xdS,

and, if N is the total number of ions emitted in unit time by
unit area of the surface A, the total number Nb received by
the surface i^ will be the real part of

ffNdS,Jdw,fJA{w,)A{<f,,)A{4>,)xdS, . (42)

where dSo denotes an element of the surface A and the in-
tegral with respect to dw^ is taken over all the values o( w^
which occur.

If we multiply (42) by the charge e of an ion we][obtain
the current to the surface -yfr. We can obtain the three com-
ponents of the resultant pressure on this surface due to the
impact of the ions if we multiply the integrand with respect

to ^ by w — , fn J!l, and m -p- respectively. The values of '
^/ Tit 0/

the velocities are obtained from equations (34) and should be ex-
pressed as functions of ;r^j^i;jrQ>'(y8ro and Wq by means of the equa-
tion previously given. In a similar way we obtain the kinetic
energy received by the surface if we multiply the integrand by

ENERGETICS OF ELECTRON EMISSION i6i

^-K^O'-lW *("■)']•

This must be identical with (42) x <(Vq - Vi) + the value of
the integral when \m{u^ + v^ + w^^ is substituted for

HC^)' - m - C^')'}

Vo being the potential of the surface A and Vi that of i/r.

It is often easier to effect a direct integration with respect
to «Q and Vq than to carry out the transformation outlined
above. Since x^'^ = du^dv^ (42) may be replaced by

f}NdS,Jdw,jf/^(w,)/,(u,)/,(v,)du,dv,, . (43)

the limits of integration being suitably changed. If the
surface B forms the whole of the analytical surface "ijfixyz) — o
the limits of integration for u^ and v^ will be determined,
for any value of w^, by the values of ?<5 and v^ which corre-
spond to the curve which is the locus of the points at which
the trajectories having the given value of w^ are tangential to
the surface yjrixyz) = o. They will thus be certain functions
of w^ which are determined by the equation to the surface.
If the surface B consists of the portion of ^|r = o which is cut
off by some closed curve, the limits for «„ and Vq will be de-
termined partly by the bounding curve and partly by the locus
of the tangents. It will often be possible so to choose the
direction of w^ that/^iw^) does not depend on u^ and v^^

The Initial Velocities.

The experiments described at the beginning of this chapter
showed that the initial velocities of the electrons were dis-
tributed in accordance with Maxwell's Law. We shall see
later that the same statement has been found to be true for
the positive ions emitted from hot bodies in a large number
of cases (cf p. 1 89). We can therefore write down the func-
tions yi(«5),/2(z/o), and^(zt;„) which express the initial frequency
of a velocity component within a given range. They will
depend both on the kind of axes chosen and on their orienta-
tion relative to the emitting surface. The following list

(45)

1 62 EMISSION OF ELECTRICITY FROM HOT BODIES

embraces all the more important cases. In each case N is the
total number of ions emitted per unit area in the interval of
time under consideration, m is the mass of an ion and 3/4^ the
mean kinetic energy.

1. Rectangular Co-ordinates. — The formulae for this case
are repeated here for the sake of completeness although they
have already been given. The axis of z is normal to the
emitting surface.

Number between i and 2 + dz = NzF(i)d2 = 2Nkmz e'^^^'^dh (44)
„ X „ X ^ d^ =^ ^f{x)di: = N(^— j e-^'^'^dx

„ y „ y ■¥ dy= N/( jyj = N( — J e-^'^^'dy

2. Spherical Co-ordinates. — Let i^r be the resultant velocity,
6 the angle it makes with the normal to the surface, and ^ the
angle the plane containing -^ and the normal makes with a
fixed plane containing the normal. Then the number emitted
per unit area per second which have t/t between i/r and -^ +
d'^, 0 between 6 and 6 + dO, and ^ between j) and <f) + d<j> is

Ni/r cos^F(T/r cos ^)/('\/rsin 0 cos 4>)f{'^ sin 0 sin ^) •y^'^d-^^ sin 0d0d<p
= N^jr^Fi-yir cos 0)F^{-^ sin 0) sin 0 cos 0dfd0d(f>

= ^^^^^h-^*^'^^sm0 cos 0d^d0d(\, .... (46)

3. Cylindrical Co-ordinates. — (a) The axis of z is along the
normal to the surface, p is the radius perpendicular to the
axis of z, and 0 is the angle p makes with a fixed plane pass-
ing through the z axis.

The number between i and z + dz = NzF(z)dz =

2Nkmze-^'^''' dz . . . (47)
whilst the number for which p is between p and p + dp and 0
simultaneously between 0 and 0 + d0 is

N/{p sin 0)/{p cos 0)dp pd0 = N — pe' *'^''' dpd0 . (48)

(/3) The axis of z lies in the tangent plane to the surface.
(j) is the total component of velocity perpendicular to z, i.e.
the projection of the resultant velocity on a plane perpendicu-
lar to the z axis. 0 is the angle (f) makes with the plane con-

ENERGETICS OF ELECTRON EMISSION 163

taining the axis of z and the normal to the surface. The
number whose velocity components lie between z and ^ + ^^ is

— ) tf-*'"*t/i . . (49)

The number which have components between <j> and
^ + d^y and for which at the same time 6 lies between 6 and
e + d0, is

N^ cos ^F(<^ cos e)f{j> sin e)^d<\)de

= 2N[^-^) <^2^-w« cos ed^de . (50)

The number for which <f> lies between (j) and (f> + d<f) and
for which ^ has any value will therefore be

N(f>^d^[ ¥(<!> cos e)/{<f> sin 6) cos ^^(9

- -wit

= 4N('— Y''<^V-'""*V<^ . . (51)

In the paper by the writer referred to on p. 157 from
which the matter in this section is practically an excerpt, the
general solution is applied to a number of particular cases.
Although the results are of considerable importance, it would
take up too much space to do much more than enumerate the
problems considered. The reader who is especially interested
in this part of the subject may be referred for details to the
original paper, where the following particular cases are con-
sidered : (i) No electric field between A and B. (2) A and
B are portions of parallel planes, and the electric intensity is
uniform and normal to the planes. When A and B are
narrow parallel strips of indefinite length this case becomes
the same as that considered on p. 143, and the solution by the
general method is found to be identical with that given on p.
144. The equations (37) and (38) for Uq and v^ respectively
are quadratic. By taking the positive sign we obtain the first
intersection of the trajectory with the plane B and by taking
the negative sign the second intersection. Taking the second
intersection, and making the plane B coincide with the plane
A, we obtain an expression for the current emitted by one
part of a plane and returned to it at another part in a retard-

1 64 EMISSION OF ELECTRICITY FROM HOT BODIES

ing field. (3) A and B are inclined planes, and the electric
intensity is uniform and normal to A. In this case again we
obtain the number of ions which return to A in a retarding
field, by taking the second intersection and rotating the plane
of B until it becomes coincident with that of A. (4) A is a
circular cylinder surrounded by a thick-walled tube C in
which a narrow gap is cut perpendicular to the axis of the
tube. The problem is to find the number of ions which pass
through the gap and reach an outer concentric cylinder B,
when A and C are at the same potential which is different
from that of B.

The case in which A and B are coaxial circular cylinders of
indefinite length maintained at a constant difference of po-
tential which retards the ions passing from A to B has been
considered by Schottky.^ The solution is given on p. 155
where we saw also that it had been confirmed by experiment.

3. The Latent Thermal Effects.

Loss of Energy due to Electron Emission. — We have just
seen that when electrons escape from a hot body they carry
with them on the average the definite amount of kinetic energy
2/^T, where T is the temperature of the hot body. In addi-
tion, we saw in Chapters II and III that, in order to escape,
each electron had to do an amount of work w against the
forces tending to retain it in the interior of the substance. It
follows that, for each electron which escapes, the hot body will
suffer a loss of energy equal to </> + 2kT, and, Mi is the ther-
mionic current to the hot body, this surface loss of energy ^ will
amount, per unit time, to

U = -(w + 2kT) . . . .(52)

= <^+~t) . ■ . (53)

where <^ is the potential difference through which an electron
has to fall in order to acquire an amount of energy equal to w.

1 " Ann. der Physik," Vol. XLIV, p. loii (1914).

»0. W. Richardson, " Phil. Trans., A.," Vol. CCI, p. 497 (1903),

ENERGETICS OF ELECTRON EMISSION 165

The loss of energy under consideration is analogous to the
heat lost during the evaporation of liquids, and it may, in fact,
be regarded as the latent heat of evaporation of electricity from
the substance in question. On account of the very rapid in-
crease of / with rising temperature the heat lost in this way
will also increase with corresponding rapidity. With sub-
stances like carbon and tungsten this loss of energy should
become equal to, and ultimately exceed, that arising from
electro-magnetic thermal radiation at temperatures below 3000°
C. It is to be borne in mind that energy will only be lost in
this way so long as the electrons are emitted. In the case of
an insulated hot body it will soon cease, as the emission of
electrons is stopped by the positive charge it leaves on the hot
body.

The first experiments to detect and measure this effect
were made by Wehnelt and Jentzsch ^ using the emission from
lime-coated platinum wires. The wire formed one of the two
low-resistance arms of a Wheatstone's bridge circuit through
which a large heating current flowed in the usual way (p. 15).
The resistance and therefore the temperature of the wire could
be kept very accurately constant by controlling the external re-
gulating resistances. The main current also flowed through
a suitable standard resistance. The potential drop along this
was measured by a sensitive potentiometer arrangement which
enabled extremely small variations of the heating current to be
determined. It was found that when the hot wire was charged
'negatively, so as to cause the electron current to flow from it,
it was necessary to increase the magnitude of the heating cur-
rent in order to maintain the resistance of the wire constant.
If Rj is the resistance of the wire, i^ the value of the heating
current when the thermionic current is not flowing, and
h + di^ th® value required to maintain the resistance at R^
when the thermionic current is flowing, the rate of supply of
additional energy necessary to keep the temperature of the
wire constant is

U = Ri[(/\ + di^Y - '?] = 2R,/A, . . (54)

^ " Verb, der Deutsch. Physik. Ges.," 10 Jahrg., p. 610 (1908) ; " Ann. der
Physik," Vol. XXVIII, p. 537 (1909).

r66 EMISSION OF ELECTRICITY FROM HOT BODIES

neglecting 'R.idi^. If this energy is entirely used up in counter-
acting the cooling due to the emission of the electrons, and if
there are no subsidiary disturbing effects, we see from equa-

tion (53) that U will also be equal to i [j> + — (T - Tq)],

where i is the thermionic current and T^ the temperature of
the cold part of the system. The term in To is added be-
cause the electrons carry the corresponding quantity of energy
when they flow into the wire at the cold ends. In the
equation

,•[</, + ^(T- To)] = 2Ri/i^/, . . (55)
ve

all the quantities are known or measurable except ^ ; so that
these experiments should enable 0 to be determined. Unless
special precautions are taken there are in experiments of this
character a number of possible disturbing phenomena which
may seriously affect the results. The most important of these
arise from the direct action of the thermionic current in up-
setting the balance of the Wheatstone's bridge, and in modify-
ing the distribution of temperature along the hot wire. The
conditions which have to be satisfied in order either to elimin-
ate the effects of these disturbing actions or to make them so
small as to be innocuous are discussed in a paper by H. L.
Cooke and the writer.^

Working with the method outlined, Wehnelt and Jentzsch
were able to show that the emission of electrons caused a cool-
ing of the wire at low temperatures. This changed to a heat-
ing effect at high temperatures and with large thermionic
currents. The heating effect was satisfactorily attributed to the
energy communicated to the wire by the positive ions liberated,
by impact ionization, from the gas evolved by the wires when
strongly heated. On the other hand, the phenomena at low
temperatures were not in accordance with the requirements of
the theory. At the lowest temperature (950° C.) the value of
^ found was about ten times as great as that deduced from
the temperature variation of the electron emission from lime,

1 " Phil. Mag.," Vol. XXV, p. 628 (1913) ; cf. also ibid.. Vol. XX, p. 173
(1910).

ENERGETICS OF ELECTRON EMISSION 167

and instead of being constant it diminished rapidly with
rising temperature. Similar results have since been obtained
by Schneider. ^ It now appears that lime was chosen un-
fortunately for the purpose of investigating this effect, as its
behaviour presents abnormalities which are not exhibited by
the highly refractory metals.

The first clear proof of the existence of the cooling efifect
predicted by the theory was given by H. L. Cooke and the
writer^ as a result of experiments made with osmium filaments.
In these experiments Wehnelt and Jentzsch's method was
modified somewhat ; the change in the resistance Rj, due to
turning the thermionic current / oflf and on, was observed when
the heating current / was kept constant This simplifies the
manipulation very considerably, although the numerical re-
duction of the results becomes rather more complicated.
Precautions were taken also to ensure the absence of errors
arising from the efifect of the thermionic current itself on the
Wheatstone's bridge galvanometer and from the alteration in
the distribution of temperature along the filament due to the
Joule effect of the thermionic current. For these matters the
original paper must be consulted. It may be permissible to
point out that a factor i//j has been omitted from the right-
hand side of equation (13), p. 635, and that the same error has
been copied into a later paper on a similar subject [equation
(13'). "Phil. Mag.," Vol. XXVI. p. 475 (iQU)} In all. 37
determinations of ^ were made under conditions as varied as
possible. The experiments involved the following range of
variation of the quantities entering into the reduction formula :
the thermionic current / from 2 x io~^ to 8 x io~* amp., the
heating current i^ from 0-430 to 0687 amp., the resistance R^
from 4-216 to 5*533 ohms, and the potential driving the thermio-
nic current from i2-i to 24-4 volts. All the thirty-seven result-

ing values of «^ + 2 — (T-TJ fell between 4-16 and 6- 1 6

volts, and if five of them, which involved the measurement of
extremely small deflections and are therefore liable to large

» "Ann. der Physik," Vol. XXXVII, p. 569 (191a).
••' Phil. Mag.," Vol. XXV, p. 624 (1913).

1 68 EMISSION OF ELECTRICITY FROM HOT BODIES

observational errors, are neglected, all the remaining thirty-two
lie between 4'59 and 5 '36 volts. Thus the results are quite
consistent and the evidence is definite that there is no large
variation of ^ with T. The mean of all the thirty-seven
values gives

0 = 47 equivalent volts.
The value of b corresponding to this ^ would be
b = 5 4 '600 degrees.

Since the chemical properties of osmium are similar to those
of platinum, it is satisfactory to note that this value of b falls
within the limits of the platinum values on p. 69, Chapter
III.

Measurements of the same kind were also made by H. L.
Cooke and the writer^ using tungsten filaments mounted in
tubes which had been very carefully treated to eliminate gas-
eous contamination. Six measurements gave values of ^ show-
ing an extreme variation of 08 volt, the mean valu"?, after
correction for the error in equation (13') of the paper already
alluded to, being

(f) = 4 '6 3 equivalent volts.
As the data available in this case are more definite than for
osmium it is worth while to consider the precise meaning of ^
a little more closely. As used in the present section <f) denotes
the excess, over the equilibrium value, of the kinetic energy,
expressed in equivalent volts, which an electron inside the
metal has to lose in order to escape with the velocity, and the
kinetic energy, zero. In Chapter II (for example on p. 28)
the symbol <p has been used with a different meaning. It
there denotes the change in ergs in the energy of the system
which takes place when an electron escapes from the hot body
under actual equilibrium conditions at temperature T. Apart
from the difference of dimensions which may be regarded as
accidental, there is thus an important distinction between
the two quantities. To distinguish between them we shall in
this section denote the ^ of Chapter II by ^. Now $ can be

^ Deduced from the relation * = 8*59 x 10 -* 6 ; cf., however, below.
2 "Phil. Mag.," Vol. XXVI, p. 472 (1913).

ENERGETICS OF ELECTRON EMISSION 169

regarded as made up of three parts : (i) <fi the change in
potential energy at the interface, (2) - Kj the internal kin-
etic energy, and (3) + Kj = | >^T the external kinetic energy.
Thus

* = *i - Ki + I /^T . . (56)

In Chapter II, p. 30 et seq., it is shown to follow from
thermodynamics and the magnitude of the Thomson effect in
metals that $ is very nearly of the form

$ = <?o + f/&T, . . (57)

where ^^ varies very little with T. It follows from (56)
that *i - Kj varies very little with T. Again, the smallness
of the specific heats of metals, as well as the quantum theory
considerations in Chapter II, indicates that the energy K^ of
the internal electrons varies little if at all with T ; so that, to
the same extent, the same must be true of ^^ Except for
the difference of dimensions, which we may disregard for the
moment, the <^ of this section is evidently

<^ = «?! - Ki + 2kT, = $0 + 2/&T0, . . (58)
the term in To appearing because we have already subtracted
the small quantity 2^To in deducing <^. This inclusion is
clearly undesirable except from the standpoint of the theory
based on the classical dynamics; but in any event it is un-
important, as the amount so added is comparable with the
errors of measurement. If we disregard it

•^ = *o • . • (59)

From Chapter II, equation (17), /= AT^^-^o'"^ ; so that ^
when corrected for the difiference in dimensions is the numer-
ator in the exponent in this equation. From equation (6),
Chapter III, p. 58, we see that the corresponding value of
the exponent b is

^ = <?o + t T . . . . (60)

Corresponding to (/> = 4*63 equivalent volts, $0 = 5*33 x 10*
degrees and

b = S'62 X 10* degrees . . . (61)
This is certainly a very satisfactory agreement with the values
of b for tungsten deduced from the variation of the satura-
tion current with temperature according to the formula i =

I70 EMISSION OF ELECTRICITY FROM HOT BODIES

AT*^-*/T. Langmuir's values for b under the best vacuum
conditions vary from 5-25 x 10^ to 5-58 x I0^ the lower
values being considered most satisfactory.
^ Cooke and Richardson^ also made experiments on the
cooling effect with the Wehnelt cathode, and were able to con-
firm the conclusion of Wehnelt and Jentzsch that the behaviour
of these cathodes did not conform to the theory. Recently
the action of this source of electrons has been exhaustively
examined by Wehnelt and Liebreich.^ They find that, start-
ing with a freshly prepared coating of lime and platinum, the
emission diminishes with time on first heating, reaches a
minimum, rises again, remains fairly constant for some time,
increases sharply to a relatively high maximum and then falls
away to small values. The precise character of these changes
depends to a considerable extent on the temperature of the
cathode and on the applied voltage, but they were found to
be accompanied by corresponding changes in the magnitude
of the cooling effect. When the emission was small so was
the cooling effect, and vice versa. The measured values of

rf> + 2 — (T - To) varied between the extreme limits 2*24
ve

and I0'66 equivalent volts. To explain these variations
Wehnelt and Liebreich assume that in addition to the cooling
due to the emission of electrons two other effects are present.
These effects, which vary in magnitude with the duration of
heating and with other conditions, are: (i) a heating effect
due to the energy of positive ions received by the cathode,
and formed by impact ionization in the gas liberated from it,
and (2) a cooling effect arising from the volatilization of the
lime which is partly enhanced by the positive ion bombard-
ment. These assumptions are shown to give a satisfactory
account, not only of the variations of the apparent experi-
mental value of ^, but also of the concomitant variations of
the saturation current with lapse of time under different ap-
plied potentials. The peculiar behaviour of lime cannot

1 " Phil. Mag.," Vol. XXVI, p. 472 (1913).

*"Verh. derDeutsch. Physik. Ges.," 15 Jahrg., p. 1057(1913); " Physik.
Zeits.," 15 Jahrg., p. 548 (1914)-

ENERGETICS Of ELECTRON EMISSION 171

therefore be regarded as an argument against the general
theoretical position.

Wehnelt and Liebreich ^ also investigated the cooling ef-
fect from platinum alone and found values for 4> varying be-
tween 578 and 6'04 equivalent volts. If we take 5*9 as the
mean value for ^, and calculate the corresponding value for the
constant b in the emission formula in the same way as was
done with tungsten on p. 169, we find

b = yi X 10* degrees.

This number is not far from the best values of b for platinum
in the table on p. 69. Thus we see that for the metals
tungsten and platinum, and probably also osmium, the values
of b calculated from the cooling effect are in agreement with
those calculated from the temperature variation of the satura-
tion currents.

The writer is indebted to Mr. H. H. Lester, of Princeton
University, whose work has not yet been published elsewhere,'
for the results of a series of determinations of ^ which he has
made with molybdenum, carbon, tantalum, and tungsten, from
measurements of the cooling effect, using the same method as
Cooke and Richardson. The particulars are collected in the
following table : —

Substance.

Number of
Measurements.

Extreme Values

of 0

(in Equivalent Volts).

Mean Value
of <b
(in Equivalent Volts).

Molybdenum
Carbon
Tantalum
Tungsten

II
12

4*498 — 4*6oS
4*177—4*778
4*276 — 4*684

4*540

4-54
4*468

4-451

The value for tungsten is slightly lower than that found
by Cooke and Richardson (p. 168). The most interesting
feature of these results is that they make the values of ^
practically identical for all the elements tested. If it could be
established generally that ^ is the same for all substances
most important consequences would follow, amongst others
the absence of contact electromotive force under good vacuum
conditions.

»"Verh. der Deutsch. Physik. Ges.," loc. cit.

' Since this was written an account of these experiments has appeared in
" Phil. Mag.," Vol. XXXI, p. 197 (1916).

172 EMISSION OF ELECTRICITY FROM HOT BODIES

4. The Heat Liberated During Electron
Absorption.

When a powerful stream of slowly moving electrons is ab-
sorbed by a metal there is a liberation of heat which is the con-
verse effect to that just considered. Naturally, if the electrons
have been allowed to fall through any considerable difference
of potential they will have acquired a corresponding amount
of kinetic energy and this will appear in the form of heat on
absorption. But the effect now under consideration occurs
even when the stream of electrons reaches points just outside
the absorbing surface with zero kinetic energy. It is caused
by the work done on the electrons as they cross the surface
layer, and may be regarded as analogous to the latent heat
liberated during the condensation of vapours.

This effect has been investigated by the writer and H. L.
Cooke.^ Two short osmium filaments heated to a high tem-
perature were used to supply the copious streams of electrons
necessary. The metals to be tested, in the form of very thin
strips, were wound on a very light glass frame so as to ex-
pose as much surface as possible. The frame was insulated
from the osmium filaments and suitably mounted between
them. By applying various small differences of potential the
electrons could be directed from the osmium on to the metal
strip. The strip formed one arm of a very sensitive Wheat-
stone's bridge, and the effect was detected and measured by the
change of resistance and temperature experienced by the strip
as the electrons were being absorbed. The strip was thus
made to perform the function of the bolometer in measure-
ments of radiant energy.

There is, however, one important difference which requires
consideration. The stream of electrons absorbed by the strip
constitutes a current flowing out of that arm of the Wheat-
stone's bridge mesh. This current of itself will cause a deflec-
tion of the galvanometer previously balanced when the
thermionic current was not flowing. The deflection which
thus arises will depend both on the magnitude of the thermi-

1 " Phil. Mag.," Vol. XX, p. 173 (1910) ; Vol. XXI, p. 404 (1911).

ENERGETICS OF ELECTRON EMISSION 173

onic current and on the point at which it is allowed to return
to the Wheatstone's bridge circuit. There is one such point
in each of the adjacent arms for which this deflection is zero,
whether the battery circuit of the bridge is closed or not. In
order to eliminate this difficulty, therefore, all that is necessary
is to provide the resistance of one of the adjacent arms with
a sliding contact connected to the line through which the
thermionic current is returned, and to adjust the position of
the contact until no deflection is caused by turning on the
thermionic current when the main Wheatstone's bridge current
is off. Some other corrections, the chief of which are for the
effect of lack of saturation when the currents are unsaturated
and for the Joule heating effect of the thermionic currents,
together with a number of minor possible sources of error, arc
discussed in the original papers.

We have seen that what is required to be measured in
these experiments is the quantity of heat, which we may de-
note by J, liberated per absorbed electron, when the electrons
have not acquired kinetic energy from an applied electric field.
As a matter of fact it is necessary to employ some potential
difference in order to drive enough electrons from the osmium
to the strip to produce measurable effects ; so that J cannot
be measured directly. The value of J can, however, readily
be deduced by making experiments with different, but suffi-
ciently small, values of the applied potential difference V.
Let V be expressed in volts and J in equivalent volts ; that is
to say, let J be the number of volts through which an electron
would have to fall in order to acquire an amount of kinetic
energy equivalent to the quantity of heat which it is desired
to determine. Clearly, when the potential difference is V,
the heat developed per electron, or per unit thermionic
current, will be proportional to J + V ; so that in order to
determine J all we have to do is to divide the observed de-
flections, for various values of V, by the corresponding
thermionic currents and plot the resulting numbers against V.
A linear relationship should thus be exhibited, and the value
of J in volts should be equal to the intercept on the voltage
axis between the point of intersection of the line through the

174 EMISSION OF ELECTRICITY FROM HOT BODIES

experimental points and the position of zero volts. If the
effect exists this intersection will be on the negative side of
the zero. That these requirements are satisfied is shown by
Fig. 20 which represents the results obtained with platinum.
The points obtained with a platinum strip previously saturated
with oxygen are shown thus : 0, with a platinum strip
saturated with hydrogen thus : 0, and for a fine platinum
wire of circular section thus : %. The points which fall on
the two lines towards the right-hand side have been arbitrarily
moved a distance corresponding to 4 volts in this direction
to avoid confusion. It will be seen that the magnitude of J is
not far from 6 volts and is slightly less for the strip soaked
in hydrogen than for the others.

It is now desirable to consider the interpretation of J a
little more carefully than we have done. Imagine a slab of
the hot metal A at temperature T connected by a wire of the
same material to a parallel slab of the cold metal B at tem-
perature To, the whole being in a suitable vacuous enclosure.
This system is not in equilibrium on account of the difference
of temperature T - Tq, but may be considered to be artificially
maintained in the definite condition just described. The work
done in taking a single electron from A to B along a path
passing across the space intervening between the metals may
be denoted by

"^2 - <V2 - V,) -«/!,. . . (62)

where w^ is the work at the surface of A, w^ that at the sur-
face of B, and Vg and Vi are the potentials at points just out-
side A and B respectively. The work between the same
points for a path along the wire and never passing outside
the metals may be written

^{Pi2+ /^V-^^t} . . . {(>l)

where P12 is a quantity comparable with the Peltier effect at
the junction and o-jj is comparable with the specific heat of
electricity in A. The difference between the symbols and the
corresponding thermoelectric quantities depends on the condi-
tions which are supposed to govern the behaviour of electrons

ENERGETICS OF ELECTRON EMISSION

'75

in metals ; but there is no reason to suppose that the quantities

\v ^

^ \

•^

Fio. 20.

are not of the same order of magnitude. The expressions (62)
and (63) must be equal ; so that

176 EMISSION OF ELECTRICITY FROM HOT BODIES

^1 + <V2 - Vi) = w, + ej/^o-,^ - P12} . (64)

The second term on the right is small compared with w^ ;
so that w^ - Wx has nearly the same value as e(V2 - Vj).

Now consider the heat liberated as each electron passes
from A to B under the conditions of the experiments, when,
however, the externally applied potential difference V is zero.
First suppose that w^ is greater than Wy. A is then electro-
negative to B and V2 - V^ accelerates electrons going from
A to B. The average kinetic energy of the electrons when
they leave A is, as we saw at the beginning of this chapter,
equal to 2^T. At a point immediately outside of B it has
increased to 2^T + ^(Vjj - Vj) and after passing through the
surface it becomes 2k'Y + ^(Vj - Vj) + Wx. If Ki is the
kinetic energy of the internal electrons of B at temperature
Tq, the quantity of heat J liberated by the electron considered
will thus be given by

J = 2/^T + <V2 - VO + Wi - Ki

/•T

On certain views of the behaviour of electrons in metals the
last three terms are equal to - Kg where Kg is the kinetic
energy of the internal electrons in A. In any event they are
not likely to differ seriously from this quantity ; so that to a
sufficient degree of approximation

J = 2kT + ^2 - K^2 = 2/^T + $o^ • (65)

where ^^ denotes the value of the quantity called = on
p. 169 for the substance A.

Now "consider the case when w^<.Wx and A is electro-
positive to B. Vg - Vj will now retard electrons passing
from A to B. This will cause the electrons reaching B from
A with zero potential difference applied externally (V = o) to
arrive at B with the same average kinetic energy as those
which left A had, the only effect of the field being to reduce
the number.^ Their kinetic energy after passing the surface

1 Cf. O. W. Richardson," Phil. M?ig.," Vol. XVIII, p. 697 (1909).

ENERGETICS OF ELECTRON EMISSION 1 7 7

layer will thus be 2^T + Wj and the heat liberated

J' = 2/feT + Wi - Ki = 2/feT + <^o' . (66)
where ^0^ is the value of $0 for the substance B.

It thus appears that if the hot metal A is electropositive
to the cold metal B, the magnitude of J is determined by that
of #0 for the cold metal B. In this case the value of $0 is
greater for B than for A. If, on the other hand, the hot
metal A is electronegative to B, the magnitude of J is deter-
mined by that of $0 fo"* the hot metal A. In this case, how-
ever, the value of $0 is less for B than for A Thus the heat
liberated at the cold metal tends to be as great as possible, in
accordance with the principle of increase of entropy, and the
value of $Q deduced from these measurements is the value be-
longing to that metal of the pair for which this quantity is
greatest, quite apart from whether the metal functions as the
receiver or emitter of electrons.

The values of ^^ calculated from the values of "^" in the
papers referred to are collected in the following table : —

Platinum (wire) in Oj

Platinum (strip) in H,

Gold .
Nickel
Copper

Phosphor bronze .
Palladium .
Silver .
Aluminium .

Iron

Mean ♦().

5-40
5-66

6'65 X lo*
6-86 X io<

470

574 X 10*

6-86

—

5-24
6-69
5-67

5-57
5'oo

—

7-25

—

Metal. Actual Values of <(o-

Platinum (strip) in Oj 6-31, 5-20, 5-47, 5-43, 5-35, 5-34

574, 5-47, 6-21, 5-21

r 5-04, 4-10, 4-35, 4-48, 4-84, \

\ 4'2i. 373, 5"38, 5'54, 5"6o /

6"39, 7*oi, 6-68, 7'89, 7-2i, 6*oi

5'04, 5"23. 5*46
7*2i, 7'0i, 671, 671, 5*6x, 6-86

5-67
5*89, 5*29
4-91, 5-68, 4-01, 5-31, 5-II

7*45, 675, 5-15, 775. 8'45
( 4-80, 4-03, 4-17, 470, 5-39, 5-39, \ _

\ 6-12, 6-43, 6-34, 7-37 / ^ '♦^

The values of 4^0 ^''^ ir^ equivalent volts and the values of
b in degrees centigrade. Unfortunately, the experimental
numbers show a good deal of variation for each individual
substance. Since the publication of those numbers the
authors have spent a good deal of energy trying to improve
the technique of the measurements, so as to get more accurate
results, without any apparent success. The strips become dis-
coloured during the experiments and the difficulties may be
due to changes in the radiating power of the surface in the
course of an experiment, and also to the discharge wandering

178 EMISSION OF ELECTRICITY FROM HOT BODIES

from one part of the strip to another. It is possible that
better results might be obtained by using tungsten as a source
of electrons, as it is less volatile than osmium. As the results
stand it is questionable whether much weight can be attached
to the differences of $o shown in the last column but one ; so
that it may be that the values would show very little differ-
ence if they could be determined more accurately. This is to
be expected on the theory outlined above, since all the metals
below gold are probably electropositive to osmium and should
give the value of ^^ characteristic of that metal. The values
for gold and platinum also are not likely to differ much from
that for osmium. Thus the numbers support the theory so
far as they can be relied on. At least it is satisfactory to note
that the values of $o are of the expected magnitude; and
that the calculated values of b for platinum, for which metal
the present data are much the most consistent and reliable,
agree with the best values of that quantity as deduced from
the temperature variation of the emission and given in the
table on p. 69.

CHAPTER VI.

THE EMISSION OF POSITIVE IONS BY HOT METALS.

The older experiments referred to in Chapter I showed that
positive ions are liberated by hot metals under certain condi-
tions. Thus, in 1873, Guthrie found that an iron ball in air
at atmospheric pressure allowed positive but not negative
electricity to leak away from its surface at a dull red heat.
This experiment shows that positive ions are liberated at the
surface of the metal but that negative ions are not ; it does not
show whether the positive ions arise from the interaction of
the metal and the air, or whether they result merely from the
high temperature of the metal. To determine this question it
is necessary to make similar experiments in a vacuum. Such
experiments, using electrically heated wires, were made by
Elster and Geitel, who found that freshly heated metals, in
general, emitted only positive ions when the temperature was
not too high, and that the effect occurred both in a vacuum
and in an atmosphere of various gases. At higher tempera-
tures an emission of negative ions of the kind already con-
sidered accompanies this emission of positive ions ; so that an
insulated metal then discharges electrification of either sign.

These and many other experiments have abundantly shown
that there is an emission of positive ions from freshly heated
metals in a vacuum which has nothing directly to do with the
presence of a surrounding gaseous atmosphere. The bearing
of occluded gases on this emission is a different question which
will be considered later (p. 205). The present chapter will be
devoted to the conditions affecting this emission and the pro-
perties of the ions liberated thereby. One of the important
features of the phenomenon, discovered by Elster and Geitel, is
its transient character. If a metal is heated in vacuo at con-

179

i8o EMISSION OF ELECTRICITY FROM HOT BODIES

stant temperature, the positive emission is greatest at first and
diminishes with time to smaller and smaller values. In this
respect its behaviour affords a strong contrast to that of the
negative emission. So far as the writer has observed there is
no limit to the decay of the positive emission in a good
vacuum ; so that the property is one which characterizes some
exceptional condition of metals which have not previously been
heated in vacuo, and is not a characteristic of the metal as
such. It is possible that there are small positive emissions of
a lower order of magnitude which do not decay with time, and
which are definitely characteristic of the metals themselves,
but there is no convincing evidence that they have yet been
discovered.

In addition to the effects immediately under discussion
there is an emission of positive ions from metals heated in
atmospheres of various gases which is probably of different
origin and which, at any rate, is much more permanent in
character. This will be considered in Chapter VII.

The Decay of the Emission with Time.

The variation with time of the thermionic current from a
positively charged platinum wire in a vacuum at a constant
temperature has been examined by the writer.^ The applied
potential difference was constant and sufficient to produce
saturation in the later stages of the experiments (see p. 1 82).
The precise form of the current time curves varies from one
specimen of wire to another. It also depends on the treat-
ment of the wire and the temperature during the experiment.
Fig. 21 exhibits some of the characteristic features. The cur-
rent i decays rapidly at first and then more slowly, apparently
approaching a constant value i^ asymptotically. The curve
shown can be represented by the equation

i - i, = Ae-^\ .... (I)

when t is the time, and A and k are constants. This formula
can be deduced from the assumption that the ions which carry
the part / - 4 o^ ^^^ current are produced by the decomposi-

1 " Phil. Mag.," Vol. VI, p. 80 (1903).

EMISSION OF POSITIVE IONS BY HOT METALS i8i

tion of some substance present in the wire, if it is admitted
that the rate of decomposition is proportional to the amount
of the substance present. This interpretation is a possible,
though not a necessary one. Similar results might follow if
the active substance were disappearing through evaporation or
diffusion. More complete experiments have shown that the
part /q of the current is not constant. It also decays with

240

TiMi IN Minutes
Fig. 21.

120

time in the same general way as the initial part, but much
more slowly.

Often the time changes are more complex than those
shown in Fig. 2i, the quick initial drop being followed by a
later rise to a maximum, after which the emission shows the
final slow decay. An example of this type of change, taken
from a paper by the writer,* is shown in Fig. 22. These
effects have a superficial resemblance to radio-active changes
and may be interpreted in a somewhat analogous manner.

* " Congr^s de Radiologic," Liige, C. R., p. 50 (1905).

1 82 EMISSION OF ELECTRICITY FROM HOT BODIES

70
60
SO
40

■

r—

*><

-**-

20 30
Time

40 SO

It is probable that there are at least two substances concerned.
One of these A may be supposed to decompose, emitting the
ions which cause the large initial current which decays quickly,

whilst a second substance
B decomposes with little
or no emission, but forms
a third substance C which
is relatively more active.
It is not supposed that
these changes have any-
thing more than a formal
analogy with radio-active
processes ; it is probable
that they are of a chemical
character and that the emis-
sions are characteristic of
Fig. 22. the various chemical pro-

ducts. The conditions under which the intermediate hump ap
pears have been insufficiently studied. So far as the writer's ^
observations go their presence is favoured by relatively low
temperatures. Similar effects have been observed by Sheard ^
at atmospheric pressure (p. 229).

Current and Electromotive Force.

The rate of decay of the initial emission just referred to
increases rapidly with rising temperature. It is very small
at the temperatures at which the emission is conveniently
measurable with a sensitive electrometer. Experiments made
at such relatively low temperatures enable the dependence of
the thermionic current on conditions such as the magnitude
of the applied electromotive force to be investigated, without
having to consider complications arising from independent
changes of the emission with the time.

The experiments which have been made to measure the
current, with different applied potentials, from a positively
charged hot wire to a suitable electrode in a good vacuum

1 C. R., Li^ge, loc. cit.

"•Phil. Mag.," Vol. XXVIII, p. 170 (1914).

EMISSION OF POSITIVE IONS BY HOT METALS 183

under these conditions have shown that the relation between
current and potential difference is surprisingly complicated.
The first observations, made by the writer,' indicated that the
current was proportional to the voltage from + 40 to + 400
volts. This result is very surprising because the currents are
very small, there are no negative ions emitted by the hot wire,
and the positive ions, being of atomic dimensions, are so mas-
sive that their motion is unaffected by the presence of the
magnetic field due to the current used to heat the wire.
Thus all the conditions, namely : spatial density of the ions,
recombination, and deflexion by the magnetic field, which
may in general operate to prevent saturation, are absent.
We should, in fact, expect these currents to be saturated
by the application of any positive potential sufficient to
make the negative end of the hot wire positive to the col-
lecting electrode after allowing for the drop due to the
heating current.

The phenomena usually observed with voltages under 40
are, to a certain extent, more in line with expectation. Thus
the writer^ found that with a new wire in air at O'OOIS mm.
the current increased as the potential was raised from o to
about 3 volts where it showed signs of saturation. On in-
creasing the potential from 3 to 40 volts there was a steady
decrease in the value of the current. Thus under certain cir-
cumstances the currents may diminish with rising voltage.
This statement refers only to the relatively steady values
which are obtained after the potentials have been applied for
a few minutes. The initial currents are usually larger if the
potential has been raised, and sometimes smaller if it has been
lowered, immediately before the observation.

Further experiments on the subject have been made by
the writer and C. Sheard.^ The current from a hot platinum
wire at various voltages was measured in three different types
of apparatus at pressures recorded by the McLeod gauge as
under 00002 mm. With new wires the current grew to a
maximum as the potential was increased from o to something

»" Phil. Mag.," Vol. VI, p. 80 (1903).

»" Phil. Trans., A.," Vol. CCVII, p. 11 (1906).

» " Phys. Rev.," Vol. XXXIV, p. 391 (1912).

1 84 EMISSION OF ELECTRICITY FROM HOT BODIES

below 5 volts ; it then usually diminished a little, and finally
increased, being roughly proportional to the potential from
+ 40 to + 400 volts. So far these results confirm those
already described. In some cases, however, the drop in the
current after passing 5 volts was not observed. The increase
from 40 to 400 volts was found gradually to die away as the
heating continued. The writers concluded at the time that
this part of the current was due to the bombardment of the
wire by electrons liberated by the impact of the positive ions
on a layer of gas at the surface of the negative electrode. It
is questionable, however, whether this interpretation can be
considered to be established definitely without further experi-
ments. It appeared that after the increased current at high
potentials had been destroyed by continued heating it could
be restored, to a greater or less extent, by the following
agencies: (i) heating the positively charged wire to a higher
temperature than any previously employed, (2) allowing a
discharge of negative electrons to pass from the hot wire
to the cold electrode, and (3) admitting air to the apparatus.
However, later experiments by H. H. Lester indicate that
the effectiveness of these agents is not always to be relied
on. The observed effects, in fact, may be due not to the
causes mentioned but to some unknown factor which was
altered at the same time.

It is evident that the drop in the current sometimes
observed when the potential is increased beyond 5 volts, and
the large increase above 40 volts, still require explanation.
These phenomena are shown only by new wires when first
heated at a low temperature ; but similar or related effects are
exhibited in a gaseous atmosphere as well as at the lowest
pressures (see p. 231). The experimental investigation of
these effects is extraordinarily difficult as it is very hard to
reproduce the same conditions in successive experiments.
Similar effects, but usually not so well marked, are often
exhibited by the negative (electronic) emission from freshly
heated wires. The difficulty of attaining saturation of the
electron currents which is peculiar to new wires has already
been referred to (p. 60).

EMISSION OF POSITIVE IONS BY HOT METALS 185

Revival of Old Wires.

A wire which has lost the power of emitting positive ions
through continued heating in a vacuum can be revived in a
number of ways, some of which give important indications as
to the cause of the emission. The various methods will be
considered in order.

1. By distillation. The writer^ found that if an old wire
A was mounted near a fresh wire B, and B was heated and
charged positively, A being cold, the passage of the thermionic
current from B to A caused A to re-acquire the power of
emitting positive ions when heated again. The same thing
occurred, but to a smaller extent, if B was negative with
respect to A or if they were at the same potential. These
experiments indicate that the emission is, at least in part, due
to a substance which may be distilled from one metal to
another. The fact that the effect is greatest when the wire B
is positively charged indicates that the ions emitted by B are
either themselves re-emitted or cause the formation of new
ions when A is heated afterwards.

2. Effect of a luminous discharge.^ The power of emit-
ting positive ions on subsequent heating is restored if an old
wire is placed in a tube through which a luminous dis-
charge is caused to pass in various gases at a low pres-
sure. The effect is greatest if the wire is close to the cathode
and is inappreciable at distances exceeding a few centi-
metres. It also disappears if the wire is shielded from a
direct view of the cathode by a solid obstacle, indicating that
the revival is caused by something projected from the cathode.
However, this seems to be only part of the story because
separate experiments showed the wire was revived when it
was itself made the cathode during the passage of the dis-
charge. It seems likely that the sputtering of the surface of
an old wire under these conditions exposes fresh material
which has not lost the power of positive emission.

The reviving effect produced by an auxiliary cathode

1 " Phil. Mag.," Vol. VI, p. 86 (1903).

» O. W. Richardson, " Phil. Mag.," Vol. VIII, p. 400 (1904).

1 86 EMISSION OF ELECTRICITY FROM HOT BODIES

occurred with cathodes of platinum, aluminium, and car-
bon when the gas was either air, oxygen, or nitrogen. The
effects in hydrogen were very small. At moderate pressures
the effect increased as the pressure diminished ; thus in air
when the pressure was reduced from 0*8 to 0*0025 mm., and the
discharge passed for a given time, the quantity of electricity
emitted when the wire was subsequently heated was increased
by a factor of about 300. By a kind of fractional distillation
of the imparted emissibility it was possible to show that the
effects were due to the formation on the wire of two distinct
substances.

The bulk of the observations which have been made with
this effect indicate that it is intimately connected with the
sputtering of metal from the surface of the cathode. On the
other hand, similar experiments made by Garrett ^ on the effect
of a discharge in carbon dioxide on the emission of positive
ions from aluminium phosphate (see p. 253) led him to con-
clude that the revival occurred only when fresh gas had been
admitted to the apparatus.

3. The writer ^ observed that the emission from an old wire
was enormously increased if the walls of the glass tube in which
it was mounted were slightly heated. This effect occurs if
the glass and platinum are carefully cleaned with acid and
dried before testing. In a particular experiment it was found
that warming the glass walls with a bunsen burner for about
two minutes increased the current from the positively charged
hot wire from 2*2 x lo"^^ amp, to 5 x io~^ amp. The effect
is not caused by ordinary gases expelled from the glass by
heating, as the pressure rose only from 0*0005 to O'OOi mm.
in this experiment, and the positive emission caused by any of
the commoner gases at these pressures is negligible in com-
parison with the observed currents.

4. Exposure to gases at high pressures, Klemensiewicz *
found that an old wire is revived by exposure to atmospheres
of hydrogen, nitrogen, or oxygen at pressures of 50 to 100 at-

1 " Phil. Mag.," Vol. XX, p. 572 (1910).

2 " Phil. Trans., A„" Vol. CCVII, p, 19 (1906).

3 " Ann, der Physik," Vol, XXXVI, p. 796 (191 1).

EMISSION OF POSITIVE IONS BY HOT METALS 187

mospheres at a temperature in the neighbourhood of 200° C.
He concludes that the initial ionization from fresh wires is
therefore due to absorbed gases (see p. 205).

5. Heating in a gaseous atmosphere. Various observers
have recorded that old wires are revived when heated for a
short time in an atmosphere of various gases or in a bunsen
flame.

6. Straining. The writer ^ found that a manganin wire was
revived when subjected to the strain caused by passing a cur-
rent through it in a varying magnetic field.

The processes just described all give rise only to effects of a
somewhat temporary character. The increased emission rapidly
disappears when the exciting agency is no longer operative
and the wire is subsequently heated in a vacuum. In addition
to the effects enumerated, an old wire may exhibit an increased
emission of a comparatively permanent character when it is
immersed in a gaseous atmosphere. The effects which then
arise will be considered fully in Chapter VH.

It will be seen from the foregoing list that almost any
change which may be made in the condition of an old wire
restores, to some extent, its power of emitting positive
electricity. There are, however, two processes which might
conceivably be expected to produce such an effect and which
do not do so. An old wire is not revived either by exposure
when cold to dust-free air at atmospheric pressure or by being
allowed to stand in the cold for long periods of time in a
vacuum. At one time it was thought that the first of these
agencies did produce an effect,^ but further investigation '^
showed that it was due to other causes. Experiments ' made
to test the second point have only extended over a period of
three months, but there is no definite reason for expecting
that longer intervals would be much more likely to lead to
a positive result.

1 " Roy. Soc. Proc., A.," Vol. LXXXIX, p. 521 (1914).
•O. W. Richardson, " Phil. Mag.," Vol. VI, p. 90 (1903) ; Vol. VIII, p. 410
(1904).

»0. W. Richardson, " Congris de Radiologic, C. R.," p. 53, Liige (1905).

1 88 emission of electricity from hot bodies

Variation of Emission with Temperature.

" We have seen already that at very low temperatures the
rate of decay is so small that the initial positive emission can
be regarded as a function of the temperature. The first ex-
periments to measure the positive emission at different low-
temperatures were made by Strutt.^ The currents were
measured with an electroscope and the electrostatic capacity
of the system was quite small. Thus by taking the deflexions
over rather long intervals of time very small currents could
be measured. The following emissions were investigated :
copper in air, copper oxide in hydrogen, silver in air, silver in
hydrogen, and copper oxide in air. In each case the pressure
of the gas was l 'O cm. The following values given by a silver
wire in air may be considered typical, as there is no striking
difference in the results given by the different materials ex-
amined : —

Temperature °C.

194

210

217

227

240

258

Current

0-2

0-84

1'46

5-0

6-2

45-6

If the capacity, which is not given, is taken to be 10 cm.
the unit of current would be about 3 x 10 ~ ^* amp. In each
case measurable effects were obtained in the neighbourhood of
200° C. and the currents increased very rapidly with rising
temperature. The temperature at which a current of 10 units
was obtained was lower with silver wires in air and hydrogen,
and with an oxidized copper wire in air, than with a clean
copper wire in air or an oxidized copper wire in hydrogen,
indicating that chemical action is unfavourable to the emission
rather than the reverse.

The writer^ pointed out that the currents observed by
Strutt followed the formula i = AT*^"*'"^, with A and b con-
stants, which, as we have seen, governs the variation of the
negative emission with temperature. It was also pointed out
that the same formula also covered the following cases : (i)
the positive emission from a wire revived by the electric
discharge, when measured at temperatures such that the time-

1 " Phil. Mag.," Vol. IV, p. 98 (1902).
^" B. A. Reports," Cambridge, 1904, p. 473.

EMISSION OF POSITIVE IONS BY HOT METALS 189

rate of decay is small (p. 182); (2) the positive emission from
the alkaline earth oxides heated on platinum at atmospheric
pressure as observed by Wehnelt,* and (3) Owen's 2 observa-
tions on the positive emission from the Nernst filament at low
pressures. In fact the formula has been found to cover all
cases of emission of both positive and negative ions from
solids in which the emission can be considered to be a definite
function of temperature.

The value of b for the initial positive emission is much
smaller than that of the corresponding constant when the
formula is applied to the emission of electrons. Thus Strutt's
numbers for silver in air give b = 134 x 10* degrees C.
This is less than one-fourth of the value of the corresponding
quantity for the electronic emissions for most of the elements
given in the table on p. 69. Thus, if they could be com-
pared at the same temperature, the negative emission would
be found to increase much more rapidly than the positive;
so that, apart from the decay of the positive emission with
continued heating, there is an additional reason why the
positive emission should inevitably be swamped by the nega-
tive at high temperatures.

The Kinetic Energy of the Ions.

The distribution of kinetic energy among the positive ions
emitted from a heated platinum strip was first examined by
the writer,^ using the methods described on p. 150 in con-
nexion with the same problem for the energy of the negative
electrons. It was found that the results were in agreement
with the view that the distribution of velocity among the
positive ions was in accordance with Maxwell's Law and that
their average kinetic energy was the same as that of the mole-
cules of a gas at the same temperature as the hot metal. As
in dealing with the negative electrons, this conclusion was
established both by a consideration of the comparative magni-
tudes of the current through the slit at different distances

» " Ann. der Physik," Vol. XIV, p. 425 (1904).
••• Phil. Mag.," Vol. VIII, p. 249 (1904).
*Ibid., Vol. XVI, p. 890 (1908).

iQo EMISSION OF ELECTRICITY FROM HOT BODIES

from the central position, by the actual magnitude of the
current in the central position through a slit of given width, and
by the inferred value of the gas constant R deducible from the
experimental results on the assumption that the ionic charge
is the same as that of a monovalent ion in electrolysis. The
three methods of determining R referred to on p. 152 led to
the respective values 4*0 x 10^, 3*3 x lo^ and 5-4 x lo^ The
mean of these is 4*2 x 10^ as against the theoretical value
3 "7 X I0^ When all the possible sources of error and the
limitations of the apparatus used are taken into consideration
this agreement is as good as could reasonably be expected.

The experiments just described supply us with information
about that part only of the kinetic energy which depends on the
component of velocity of the ions parallel to the emitting sur-
face. The investigation was extended to include the normal
component of the velocity by F. C. Brown,^ using the method
described on p. 141. The current i between parallel plates
against an opposing potential difference V was found, as with
the negative electrons, to satisfy the equation

logi = _ -^V, ... (2)

required by Maxwell's Law and deduced on p. 1 44. The values
of R varied from 3-5 x 10^ to 4-0 x lo^ the mean being
3 '6 X 10* instead of 3*7 x 10'. Brown also found that the
results of the experiments were independent of the pressure of
the surrounding gas between the limits 0*009 n^i^' ^'^d 28 "O
mm. These experiments were limited to platinum, but in a
later paper Brown ^ extended the observations to cover a large
number of substances, using the same general method. Where
possible the materials tested were in the form of discs or strip,
but in some cases thin wires or filaments had to be used.
Generally speaking, wires or filaments were found to give
values of R higher than the normal, probably owing to distor-
tion of the electric field near the hot metal. An osmium
filament, however, gave an abnormally low value of R
(2*5 X 10^), but this was attributed by Brown to the presence

1 " Phil. Mag.," Vol. XVII, p. 355 (1909).
^Ihid., Vol. XVIII, p. 649 {1909).

EMISSION OF POSITIVE IONS BY HOT METALS 191

of electrons, which modify the conditions affecting the motion of
the ions. The final values of R and the data leading up to
them are collected in the following table : —

Material Tested.

Form of
Emitter.

Absolute
Temperature.

Current »o

(when V = o)

1 = 10-1' amp.

Pressure
(mm.).

R X 10-

Gold I

. disc

/1030I
I 973/

I'O

0*007

4*2

Gold II

• »i

riigo)
\"63/

6o'o

O'OI

3 '9

Silver I .

1020

0-8

0-002

3'o

Silver II .

«i

1 150

35 -o

o*oo8

2*9

Palladium .

1170

25*0

0*04

3 '4

Nickel

strip

1120

2-5

0*003

3*6

Iron I

disc

1 100

i-o

—

4*6

Iron II

1 100

0-8

0*005

5*2

Iron III .

1240

0*01

4 '4

Platinum I .

wire

1695

—

5'i

Platinum II

disc

1293

5-0

0*009

3*5

Tungsten .

filament

1150

I'O

0*0003

5"i

TanUlum I

»t

1050

0*0005

9*6

Tantalum II

strip

1050

I'O

0'002

3*o

Osmium

filament

1120

3-0

2*5

Aluminium phos

phate I .

disc

1230

loo-o

—

3-9

Aluminium phos-

phate II .

1170

I20*0

0*006

3'4

If the values with wires and filaments are disregarded as
not fulfilling the conditions laid down by the theory of the ex-
periments, the average of the remaining numbers in the last
column is R X 10 " ' = 3*8, instead of 37. The values for a
given metal with a given form of radiator agree better with
one another than do the values when different metals are com-
pared. Thus all the values for iron are distinctly high and for
silver distinctly low. The difference between iron and silver
is greater than could be expected from any obvious source of
experimental error, and Brown concludes that there is a real
difference in the value of R for the ions from different metals.
It is questionable, however, whether this inference can be ac-
cepted without further experimental support. The difference
between the results for a strip and a filament of tantalum is
much greater than the difference given by discs of iron and
silver, showing that relatively small differences in the geome-
trical arrangement may make very great differences in the final
values. There is also the difficulty arising from the presence
of negative electrons in some instances, a factor which is very
difficult either to control or allow for. The temperature.

192 EMISSION OF ELECTRICITY FROM HOT BODIES

too, IS difficult to determine with an apparatus of the type
used. Taking all the circumstances into account it would ap-
pear that the only inference which can be drawn with certainty
from these experiments is that the distribution of energy is not
far from that required by Maxwell's Law in the case of the
positive ions from all the substances examined.

It is necessary to add that Schottky^ has recently an-
nounced that he has obtained evidence of much greater values
for the energy of the positive ions emitted by hot bodies than
those given by the foregoing investigations. As no details are
given it is impossible to state what is the probable cause of
this discrepancy.

The Charge of the Ions.

If we regard it as inherently probable that the distribution
of velocity among the emitted ions is in accordance with
Maxwell's Law, the foregoing experiments may be used to
demonstrate that the charge of the positive ions is equal to
that of an electron or of a monovalent ion in electrolysis. In
some of the experiments with platinum strips which had been
heated for a long time, the writer^ found that the spreading
out of the ions was abnormally small. The results could be
reconciled with either of the two following hypotheses :
(i) that the charge was equal to e but that the kinetic energy
had only half the normal value, and (2) that the kinetic
energy had the normal value but that the charge was doubled.
Of the two alternatives the latter is more likely to be true.
At the same time enough experiments have not been made on
this particular subject to make it certain that the observed
effect is a real one. Bending outwards of the strips tested or
the appearance of electrons, both of which tend to occur
with continued heating, would produce effects in the direction
of those observed and might be capable of accounting for the
phenomena. Until more detailed experiments are forth-
coming it is not desirable to attach too much weight to this
particular piece of evidence of the occurrence of ions with

1 «' Ann. der Physik," Vol, XLIV, p. 1030 (1914).
» " Phil. Mag.," Vol. XVI, pp. 900, 903, 906 (1908).

EMISSION OF POSITIVE IONS BY HOT METALS 193

multiple charges in the positive emission from hot metals.
Another point which tends to make this evidence doubtful is
that the value of e/w for these particular ions, which was
measured at the same time as the energy, would make their
electric atomic weight equal to about 100, a value which
would be difficult to harmonize with that for any substance
likely to be present.

A direct attempt to measure the charge of the ions from
hot bodies at atmospheric pressure has been made by Pome-
roy.^ He concluded that the positive ions emitted by a
platinum strip had a charge 2e on first heating, but that the
average value of the charge gradually fell to e as the heating
was continued. The method used was one due originally to
Townsend, but in applying it the importance of the mutual
repulsion of the ions has been insufficiently considered,'^ and
it is doubtful what interpretation ought to be put on the
results obtained. In any event, the conditions affecting the
origin and motion of the positive ions in these experiments
are quite different from those present when the kinetic energy
and specific charge (e/w) have been measured.

The Specific Charge and Electric Atomic Weight

OF THE Ions.

In discussing the specific charge (e/w) for the positive
ions it is convenient to introduce a related quantity which we
may call the electric atomic weight (M) of the ions. The
last-named quantity is obtained when we divide the specific
charge of a monovalent element of unit atomic weight, the
value of which is 9649 E.M. units, by the specific charge of
the ions under consideration. If the charge of a positive ion
is equal to that of an electron, and there are numerous indica-
tions that such is the case, the electric atomic weight is, if we
neglect the mass of the electron compared with that of the
atoms, equal to the chemical atomic or molecular weight of
the ions. In any event, even if the charge is a multiple of c,
the electric atomic weight is, to the same close approximation,

1 •• Phil. Mag.," Vol. XXIII, p. 173 (1912).
« Townsend, «♦ Phil. Mag.," Vol. XXIII, p. 677 (1912).
13

194 EMISSION OF ELECTRICITY FROM HOT BODIES

equal to the chemical equivalent weight (in terms of O = 1 6)
of the same ion in electrolysis. Thus the determination of
elm or M is of the utmost importance if we wish to discover
the structure of the ions in question.

The first experiments to measure these quantities for the
positive ions from hot bodies were made by Sir J. J. Thomson ^
who used the method of crossed electric and magnetic fields
described on p. 8. If ^is the distance between the wire and
the receiving plate, H the magnetic intensity, and V the dif-
ference of potential just necessary to drag the ions across in
the presence of the magnetic field, then

elm = 2V/H2^2 .... (3)
This formula applies ^ even if the electric field is not uniform,
a point not brought out in our earlier discussion. It assumes,
however, that the ions set out with negligible velocities, and
this is not quite correct. The experiments were made with
wires of iron and platinum which had been heated for a long
time in a vacuum. It was found that the behaviour of the
currents in a magnetic field was very capricious. In some
cases the thermionic current was unaffected by a magnetic field
of 19,000 gausses. When the currents were sensitive to the
magnetic field Thomson ^ describes the phenomena occurring as
follows : "When the potential difference between the hot metal
and the plate connected with the electrometer was small, say 3
or 4 volts, the leak was very nearly stopped by the magnetic
field ; with a potential difference of 10 volts the leak was reduced
by the magnetic field to about one-quarter of its original value,
the effect of the magnetic force upon the leak diminished as
the potential difference increased but was appreciable until this
reached about 1 20 volts. Thus in this case we see that while
some of the carriers can reach the plate under a difference of
potential of 10 volts, there are others which require a potential
difference of 120 volts to do so." With the dimensions of the
apparatus used and with H = 19,000, for ions which are just
stopped when V = 10, ejjn = 60 and M = 161, for those just

^ " Conduction of Electricity through Gases," 2nd ed., pp. 145, 217. Cam-
bridge (1906),

* Thomson, loc. cit., p. 219. ' Loc. cit., p. 220.

EMISSION OF POSITIVE IONS BY HOT METALS 195

stopped when V = 120, elm = 720 and M = 13-4, From
these numbers Thomson concludes that the ions are a mixture
of atoms of platinum and of the gas. The experiments were
made in air, at 0*007 ^^- pressure. If the atoms of the ele-
ments under consideration carried a charge e the values of
M would be 192 and 14 (or i6) respectively. Since more than
half the current was stopped with 10 volts, the experiments
indicate that the lighter ions carried the greater part of it.
The carriers of the current in the condition in which it was un-
affected by the magnetic field, under low potential differences
in the neighbourhood of I or 2 volts, are attributed to charged
particles of platinum dust sputtered from the wire. Similar
experiments made with iron wires gave elm = 400 and
M = 24.

A fuller discussion of the interpretation of the numbers
above will be given later (p. 206). Without going into detail
it is clear that most of the ions under consideration are of
atomic magnitude.

Measurements of elm and M for the positive ions from hot
metals have been made by the writer ^ by a different method.
The apparatus, which is similar to that used in investigating the
distribution of the tangential component of emission velocity
(p. 147), is shown diagrammatically in Fig. 23. The part on
the left-hand side of the dotted line FF represents a section,
by the plane of the paper, of two parallel metal plates AA and
BB. The plates AA are fixed, and separated by a narrow slit
of constant width running perpendicular to the plane of the
figure. A narrow strip c of the metal to be tested is shown in
transverse section. It almost fills the slit and its upper sur-
face is flush with that of the plates AA. The upper plates
BB also are divided by a narrow slit a parallel to the former.
Behind this is a box-shaped electrode indicated by E. The
plates BB and the electrode E are rigidly bolted together, BB
and E being insulated from one another. The rigid system
BBE can be moved backwards and forwards through small

J "Phil. Mag.," Vol. XVI, p. 740 (1908); "Roy. Soc. Proc, A.," Vol.
LXXXIX, p. 507 (1914) ; cf. also C. J. Davisson, «• Phil. Mag.," Vol. XXIII,
p. 121 (1912).

13*

196 EMISSION OF ELECTRICITY FROM HOT BODIES

measured distances in a horizontal line by the accurate screw
shown on the right. The parts ABE are all enclosed in a
glass tube permitting the attainment of a high vacuum. In
the final form of the apparatus the screw was provided with a
micrometer head and cyclometer attachment on the horizontal
axis. Both these were enclosed in the glass tube and read from
outside, the turning being effected by a right-angled bevel-
gear operated through a ground glass joint in a side tube.
The central region between the plates can be placed in a very
uniform magnetic field of measured strength running perpen-

0<=^

Fig. 23.

dicular to the plane of the paper. A suitable potential dif-
ference V is applied between AA and BB so as to drive the
ions on to the upper plate.

There are two ways of using the apparatus. These, for
convenience, will be called the slit method and the balance
method respectively. The figure shows the electrical con-
nexions for using the slit method. Initially the keys R and
T are depressed ; so that the electrometer N, capacity M, and
BB and E are all connected to earth. On breaking T the
charge passing through the slit into E flows into the electro-
meter, whilst that received by the plates BB flows into the

EMISSION OF POSITIVE IONS BY HOT METALS 197

capacity. When a suitable deflexion has accumulated, the
compound key R is taken out, thus breaking both currents.
The steady deflexion of the electrometer thus measures the
quantity of electricity which has passed through the slit. The
key S is then depressed ; so that M and N are connected to-
gether. After the electrometer has come to rest the new
steady deflexion will measure the quantity of electricity re-
ceived both by the slit and the plates during the identical time
interval in which the quantity previously measured passed
through the slit. These measurements are repeated for dif-
ferent horizontal displacements x of the slit from the central
position. The procedure by this method in fact is the same
as that followed in getting the distribution of the tangential
component of velocity, and described in Chapter V. The chief
difference between the two experiments arises from the pre-
sence of the magnetic field. If the ions all have the same
value of elm, and if the magnetic field is not too large, the only
effect of its presence is to displace the resulting curve, which
connects the proportion passing through the slit with x and is
similar to Fig. 18, bodily to the left or to the right according to
the direction of the magnetic intensity H. There is no dis-
tortion of the curves unless the ions are a mixture having dif-
ferent values of ejm. In that case, if there is sufficient difference
in the values of ejm for the constituents, the curve which has
a single maximum in the absence of a magnetic field develops
two humps when the field is applied. Thus this method en-
ables us to form a judgment as to the homogeneity of the ions.
When the ions are homogeneous the value of ejm is given by
the formula

V =^— ... (4)

\{ X is the displacement of the maximum caused by the field
H, and z is the distance between the plates. This formula is
only an approximation, but it is correct to about 05 per cent
under the conditions of the experiments.

The measurements when the balance method is used are
much simpler. E is connected to one of the plates BB. These
are insulated from each other and connected to the alternate

198 EMISSION OF ELECTRICITY FROM HOT BODIES

pairs of quadrants of the electrometer, all four quadrants being
insulated. Under these conditions the electrometer will not
deflect if the potentials of each pair of quadrants change at
equal rates. This happens when the dividing line between
the upper plates is at the value of x corresponding to the
maximum. If the screw is turned a little one way the electro-
meter deflects to the right, if in the other way to the left.
The position of zero deflexion can be determined easily with
precision, and two experiments with H in opposite directions
are all that is required to determine the corresponding displace-
ment ix of the maximum required in equation (4). Thus this
method enables e\tn to be measured very rapidly. On the
other hand, it does not tell anything about the homogeneity of
the ions under investigation ; so that it is advisable to restrict
its application to cases in which the homogeneity of the ions
has previously been established by experiments using the slit
method, provided the latter method can be applied. The be-
haviour of the curves in a magnetic field indicates that as a
general rule the ions which carry the large initial current from
hot metals are very homogeneous. This conclusion is also
supported by the fact that the value of e/w given by the
measurements often remains constant over long periods of
time (see below, p. 201).

The first experiments by the slit method, made partly in
collaboration with E. R. Hulbert,^ gave the values shown in
the next table : —

Value of e/m.

Substance. (E.M. Units per Gm.)

Value of M (0=i6).

Platinum .... 361

26-8

Palladium

317

30-5

Copper

342

28-3

Silver

322

30-0

Nickel

357

27-1

Osmium

395

24-5

Gold .

206 -> 418

47 -»23-i

Iron .

726 -> 457

13-3 -> 211

Tantalum

186 -> 376

52 -5- 257

Tungsten

230

42-1

Brass .

336

28-8

Steel .

322

30*0

Nichrome

395

24-5

Carbon

333

29*1

1" Phil. Mag.," Vol. XX, p. 545 (1910).

EMISSION OF POSITIVE IONS BY HOT METALS 199

With the apparatus as it was used in these experiments
there are two sources of error of unknown magnitude, arising
respectively from lack of uniformity of the electric field, and
from the bowing of the strip due to its expansion. It was at-
tempted to correct for these by using the same method and ap-
paratus to measure the value of tjm for the negative electrons
from platinum. It is probable that this method overdoes the
correction, since the electrons come off at a higher tempera-
ture than the positive ions ; so that the corresponding errors
would be greater in this measurement. The true values ofejm
are probably smaller, and of M greater, than those given in
the table. The values have been corrected for an erroneous
value of €/m for the negative electrons which was used in the
original papers.

The behaviour of tungsten was found to be erratic and the
values given are relatively less reliable than the others. With
gold, iron, and tantaluni the numbers obtained on first heating
were different from those obtained later. The later values
persisted for a considerable time, until the emission disappeared
or the material melted, in fact. No definite change of e/m
with time was noticed with the other substances. Excluding
tungsten the relatively permanent values of M all lie between
21*1 and 30*5, the average being 26*9.

No great accuracy is claimed for the numbers found, on ac-
count of the reasons given above. At the same time a number
of important inferences can be drawn from them. They show
that the ions are not atoms or molecules of the elements con-
cerned, since the values of M all lie between 20 and 30,
whereas the atomic weights range from 12 for carbon to 192
for platinum. The similarity of the values indicates that the
majority of the ions arise from some impurity common to all
the metals. This impurity cannot be hydrogen or any light
gas with an electric atomic weight below 20, as the values
of M are too high for such bodies. The ions might be charged
atoms of sodium or potassium or charged molecules of nitrogen,
oxygen, or carbon monoxide or a mixture of these. To dif-
ferentiate these various possibilities it was necessary to increase
the accuracy of the experiments.

200 EMISSION OF ELECTRICITY FROM HOT BODIES

Substantial improvements in this respect have recently
been effected by the writer,^ Probably the most important
source of error in the old experiments arose from the bowing
of the strips when heated. This has now been eliminated by
keeping them under a slight but sufficient tension. Since the
distance z between the plates enters into the formula for e/»/
through its fourth power, it is important that it should be
capable of accurate and reliable measurement. This was ac-
complished by enlarging the apparatus and improving the
technique in various ways. Another point to which insufficient
attention had previously been paid was the accurate measure-
ment of the magnetic field under the actual experimental con-
ditions. Finally, any lack of uniformity in the electrostatic
field was almost completely eliminated by reducing the gap
between the edges of the strip and the sides of the slit almost
to the vanishing point. The measurements were ultimately
checked by comparing the values of M given by the metals
tested with those given by the ions from potassium sulphate.
These ions are known on independent grounds to be atoms of
potassium which have lost an electron (Chapter VIII). The
apparatus as improved has one disadvantage. It restricts the
number of metals which can be experimented with. Most of
those in the previous table were found either to yield or break
under the tension required to keep the strips taut, at the tem-
peratures at which the emission became copious enough con-
veniently to make measurements with.

Most of the measurements with the improved apparatus
were made by the balance method, as this enabled any changes
in elm with lapse of time to be followed readily. The two
methods, however, were compared in independent experiments
and were found to give identical results when the emission
was homogeneous, and was not changing in character with
lapse of time. With platinum strips the ions given off during
the first twenty hours or so of heating were found to be very
homogeneous and to have a value of M very close to 40.
In the later stages there were indications of ions for which M
was near 23, and sometimes also values of M between 50 and
1 " Roy. Soc. Proc, A.," Vol. LXXXIX, p. 507 (1914).

EMISSION OF POSITIVE IONS BY HOT METALS 20i

60 were obtained in the last stages of heating just before
the strips broke. The variation of M with the time of
heating is exhibited in Fig. 24, where the points marked thus :
X represent some of the values given by a particular strip at
times extending over twenty-eight hours. The final high
values are a little uncertain as the strips never last long after
these values have begun to appear. The points thus \ in
the figure represent values of M given by another strip, and
the circles are values given by the ions from potassium sul-
phate. In all the measurements the strips were kept at the

2Cy

Positive Ions

±t

Pt Strip ♦ t
Pt Strip # 2

KjSO^

K +

^^-

s--ir

Na+

■^

4. 8 12 16 20 24

Time heated (hours)

Fig. 24.

lowest temperature at which the currents were large enough
for convenient measurement. This involved gradually increas-
ing the temperature during any one experiment, on account of
the decay of the emission with time.

It appears from these experiments that most of the ions
given off by platinum have an electric atomic weight which is
indistinguishable from that for the ions from potassium sul-
phate, that in the later stages ions for which M is very near to
the sodium value (23*05) also appear, whilst finally, there are
fleeting indications of the presence of ions with M in the
neighbourhood of the atomic weight of iron (56).

202 EMISSION OF ELECTRICITY FROM HOT BODIES

The ions with M close to 40 were found not only to
constitute the whole of the emission from freshly heated cleaned
platinum. They were found also to carry the emission from a
platinum strip when revived by heating in air and in a bunsen
flame, the greater part of the initial emission from iron and
manganin strips, and the whole of the emission from a man-
ganin strip due to revival by mechanical straining. Some of
the data collected in various experiments to test the points
mentioned are exhibited in the following table. Incidentally
they demonstrate the very considerable accuracy with which
e/w and M can be measured with the apparatus used, and the
high degree of consistency of the different experiments : —

Material and Treatment.

Duration of
Observations.

Number

Measurements.

Extreme Values
of M.

Mean
Value
of M.

Platinum, clean but not

specially cleaned .
Platinum, cleaned with

5 hours

3975— 40'2

40*0

acids, etc.
Platinum, cleaned with

520 minutes

39-1— 41-6

40* I

acids, etc.
Potassium sulphate .
Manganin strip, cleaned

with reagents
Iron, cleaned with re-

36 hours
280 minutes

4 hours

10
13

38 — 40*1
39-2— 4I-I

39-3— 41-4

39-1
40-2

40-0

agents ....
Iron, cleaned with re-

55 minutes

39-8— 40-0

39'9

agents ....

315 minutes

38-3— 42-1

40*1

Platinum, emission re-

stored by heating in air
Platinum, emission re-

160 minutes

37'9— 39-8

39-0

stored by heating in
bunsen flame

133 minutes

39-0—407

40-0

Manganin, emission re-
stored by straining

—

39-4

The table does not include the exceptional values already
referred to, which were given by platinum strips which had
been heated for a long time.

In the case of iron low values in the neighbourhood of the
atomic weight of sodium were sometimes got at first, as well
as values considerably above 40 in the last stages before the
strips broke. These also have been omitted.

The experiments just described prove that the initial posi-
tive emission from hot bodies cannot be ascribed to charged
atoms or molecules of any of the commoner gases which are
likely to be present as impurities. The values of M for these
are respectively : —

EMISSION OF POSITIVE IONS BY HOT METALS 203

CO^. - 28, H+ =» I, H2+ =■ 2, COj^. = 44, N^ = 14, Nj^ = 28,

O^ = 16, and O2+ = 32.
The experimental determinations are much too accurate to
admit of any of the bodies enumerated. The only admissible
substances whose presence is at all likely are, K^ «= 39' I,
Ar^ = 39*9, or Ca^ = 40-07. The mean values of M would
agree better with Ar or Ca than with K ; but as the same is
true for the ions from potassium sulphate, which there are good
reasons for believing to be atoms of potassium, it seems most
reasonable, on the evidence, to attribute these ions to the pres-
ence of potassium, and to assume that the method used tends
to give values of M about 2 per cent too high.

Nature of the Ions.

As the view which attributes the positive ions that carry
the initial emission from hot bodies to the presence of gaseous
contamination has acquired a good many adherents, it is per-
haps desirable to consider a little more fully the arguments
which have been advanced in support of such a position, and
the reasons for considering them insufficient. The principal
facts which have been held to support, or even by some
authorities to establish, the gaseous origin of the ions in ques-
tion, will be found enumerated in the following list : —

1 . A wire which has lost the power of emission owing to
continued heating in a vacuum is found to regain this property
to a considerable extent if it is heated in a bunsen flame or in
air at atmospheric pressure.

2. A similar recovery takes place when the wire is exposed
to various gases at a pressure of 50 to 100 atmospheres^ at a
relatively low temperature (about 200° C).

3. When most metals are first heated in a vacuum there is
a considerable evolution of gas, the bulk of which usually con-
sists of hydrogen, carbon monoxide, and nitrogen.

4. When a wire has been heated in a vacuum for a long
time, so that the emission has become too small to measure,
there is an emission in different gases, which seems to be a

^Z. Klemensiewicz, "Ann. der Physik," Vol. XXXVI, p. 796(1911); cf.
also p. 1S6, ante.

204 EMISSION OF ELECTRICITY FROM HOT BODIES

definite function of the nature and pressure of the gas (see
Chapter VII). This phenomenon has been most completely
studied in the case of platinum in an atmosphere of oxygen.
The facts have been explained by the writer ^ on the hypothe-
sis that the metal adsorbs or absorbs the gas, which it re-emits
in the form of charged atoms. It has been suggested by
various writers that the initial emission is an intensification
of this phenomenon, owing to the presence of much larger
amounts of gas in the original metal.

5. Horton ^ has found that carbon monoxide has a greater
power of stimulating the emission of positive ions both from
hot platinum and from heated salts than the other common
gases, with the exception of hydrogen.

6. Determinations by Garrett ^ of e/w for the positive ions
emitted by aluminium phosphate when heated, led him to
conclude that about 10 per cent of them were charged atoms
of hydrogen.

7. The experiments of Sir J. J. Thomson, described on
p. 194, led him to conclude that the positive ions from
hot platinum consisted of a mixture of charged atoms of
platinum and of the surrounding gases. More recently
Thomson * has returned to this question and has examined
the positive ions from hot platinum by the same method as
that used by him in investigating the positive rays. Most of
the ions were found to have a value of M equal to 27, and he
concludes that they are charged molecules of carbon mon-
oxide. After the platinum had been soaked with hydrogen
the average value of M was reduced to 9, indicating the
presence of charged atoms or molecules of hydrogen also.

In weighing this evidence it is essential to realize that the
portion enumerated under (i) to (5) is indirect so far as the
structure of the ions is concerned. It may be of great
importance in arriving at an understanding of the processes
concerned in the emission of the ions, but it has only a

1 " Phil. Trans., A.," Vol. CCVII, p. i (1906).
2" Camb. Phil. Proc.," Vol. XVI, p. 89 (1911).
3 " Phil. Mag.," Vol. XX, p. 582 (1910).
< " Camb. Phil. Proc," Vol. XV, p. 64 (1908).

EMISSION OF POSITIVE IONS BY HOT METALS 205

secondary bearing on the question of material composition.
For this purpose determinations of M give an immediate and
final answer, provided that they are sufficiently accurate and
do actually refer to the ions under discussion. At the same
time it is necessary that the interpretation to which they lead
should not be incompatible with the various points enumerated.
I shall now show that none of the evidence really conflicts
with the view that the initial positive ionization from hot
metals consists of charged atoms of the alkali metals, and
chiefly of atoms of potassium.

In the first place direct measurements of M for the emis-
sion from platinum revived by heating in air and in a bunsen
flame have consistently given values between 39 and 40, indi-
cating that this emission has the same composition as that
from a fresh wire, and that it does not consist of atoms or mole-
cules of the various gases in which the heating has taken place.
In conjunction with the fact that similar values are given by a
strip revived by straining, this indicates that the effect of heat-
ing in gases consists in opening up the structure of the material
and allowing access to the surface by alkaline impurities pre-
viously imprisoned. The effect of gases at high pressures is
probably a direct mechanical one, although there are a number
of actions which might affect the phenomena under these con-
ditions. In any event there is no reason for presuming that
the ions subsequently emitted consist of atoms or molecules of
the gases used, in the absence of direct evidence to that effect
and in the presence of direct evidence to the contrary.

With reference to (3) and (4) the writer ^ has measured sim-
ultaneously the quantity of gas and of positive electricity
emitted on heating a new wire. Apart from the fact that both
emissions were greatest at first and decayed with time, there
was no evidence of a close correspondence between them. If
the effect of heating in gases is due to the opening up of the
metal by their solution or diffusion, (5) would be expected, as
the gases carbon monoxide and hydrogen are notable for their
power of diff"using into metals. Their chemical activity may
also be a factor, as the positive emission from some salts has

* •• Congris de Radiologic, C. R.," Li^ge, p. 50 (1905).

2o6 EMISSION OF ELECTRICITY FROM HOT BODIES

been found to be increased in the presence of reducing gases.
The experiment of Garrett (6) has only an indirect bearing on
the present question as it refers to a salt and not to a metal ;
but, in any event, it has not been confirmed as a fact by
more recent and very careful experiments by Davisson.^ The
writer's experiments have afforded no evidence of the occur-
rence of hydrogen ions in the initial positive discharge from
hot metals.

At first sight Thomson's experiments (7) appear to offer
an immediate contradiction to the position now being main-
tained. His values of M are certainly quite different from
those found by the writer, and there does not appear to be any
likelihood that the differences can be attributed to errors in the
measurements under comparison. There is, however, a very
important difference in the conditions under which the experi-
ments were made. Thomson used wires which had been
heated for a long time in a vacuum before testing ; so that
presumably all, or almost all, the initial ionization would have
been given off. Under these conditions there is no reason to
expect that the values obtained would be those belonging to
the carriers of the large initial emission.

If this is the explanation of the difference it follows that
Thomson's measurements refer either to the positive emission
due to the residual gases referred to under (4) or else to a per-
manent emission characteristic of the metal, and not, since the
values of M are different, to remaining traces of the initial
emission. Thomson's first experiments with platinum were
made in an atmosphere of oxygen at o 007 mm. pressure, and
the majority of the ions were found to have a value of M near
14. We shall see in the next chapter that there is a consider-
able amount of indirect evidence indicating that the emission
in an atmosphere of oxygen referred to under (4) is carried by
charged oxygen atoms. This would agree well with the value
obtained by Thomson. Again in the later experiments the
value M = 27 was found at first, when the only gas whose
presence could be detected spectroscopically was carbon mon-
oxide, for which M = 28. After the platinum had been heated
1 " Phil. Mag.," Vol. XXIII, p. 121 (1912).

EMISSION OF POSITIVE IONS B V HOT METALS 207

in hydrogen the average value of M was reduced to 9, indicat-
ing that some of the current was now carried by hydrogen
ions. Thus these experiments furnish very definite evidence
that when the initial emission has been got rid of, there is an
emission in different gases of such a nature that the carriers
are formed from the molecules of the gas.

In the first of the experiments referred to, Thomson also
found indications of ions for which M had a value very close
to the atomic weight of platinum. This rather indicates the
existence in an old wire of an emission which is a property of
the pure metal itself. Hitherto no other evidence of an emis-
sion of this kind has appeared, but it may be small and usually
masked by the other kinds of emission to which reference has
been made. The writer has several times attempted to detect
the presence of ions for which M has values corresponding to
the atomic weight of the metal or to the atomic or molecular
weights of the traces of gas present, but has never succeeded
in doing so. The method used was the same as in measuring
M for the initial ionization. This method is admirable where
currents of considerable size are available and where all the
ions are alike. It is not suitable when the currents are small,
as with wires which have been well glowed out, and it is quite
incapable of detecting small quantities of one kind of ion
mixed with large quantities of another. In these cases the
methods used by Thomson have decided advantages. It
would appear that there is room for more experiments on this
subject, particularly by the canal ray method of measuring M.

In Chapter VIII we shall see that the view which attributes
the large initial ionization to contamination by the alkali
metals or their compounds receives indirect support from the
very large emissions to which the compounds of these elements,
and especially of potassium, give rise. This view also ac-
counts for the large emission, described on p. 186, which is
obtained when the walls of the glass tube containing the hot
metal are heated. As there was no appreciable increase of
gas pressure in this experiment the most likely agent would
appear to be traces of salt vapours distilled from the glass.

2o8 EMISSION OF ELECTRICITY FROM HOT BODIES

The Quantity of Electricity Emitted.

Since the emission from a fresh wire, heated at a constant
temperature, after a while practically comes to an end there
is a definite total quantity given off under these conditions.
Nine wires,^ each about 5 cm. long and 001 cm. diameter,
heated to various temperatures between 600 and 800° C. all
gave off about io~^ coulomb. A strip ^ O'l cm. wide, about
I cm. long, and whose weight was 005 5 gm. when heated at
various temperatures up to 700° C, gave off about 2 x io~^
coulomb. The amount obtained does not vary much with
the temperature of heating, but there are some indications
that it rises a little with rising temperature. The ratio of
the mass of matter given off in the form of ions to the mass
of the platinum heated is comparable with io~^, according to
these numbers. The subject might repay further examination.

^ C. R., Liege, loc. cit.

3 "Roy. Soc. Proc, A.," Vol. LXXXIX, p. 507 (1914).

CHAPTER VII.

THE EFFECT OF GASES ON THE LIBERATION OF POSITIVE
IONS BY HOT METALS.

Almost all the experiments on the effect of gases on the
emission of positive ions by metals have been made with
platinum. This material has been used on account of its
high melting-point, its chemical inertness, its mechanical
suitability, and its other practical advantages, and not because
it is believed to possess peculiar powers in respect to the
phenomena under consideration. In fact it has been rather
generally assumed that its behaviour may be regarded as
typical of that of metals in general. As there is no certainty
that this is the case it is probable that other metals would
repay investigation in this direction.

The first systematic quantitative experiments bearing on
the subject of this chapter were made by H. A. Wilson,^ who
measured the currents between two concentric cylindrical
electrodes of platinum heated in air at atmospheric pressure.
The inner electrode was a tube of 03 cm. outside diameter,
and the outer electrode a tube of 0*75 cm. inside diameter.
The heating was accomplished by placing the outer tube in
a gas furnace. In this way the temperature of the electrodes
could be kept within 5° of any desired temperature up to
1400° C. In general the inner electrode was the colder, but
the difference of temperature could be reduced by blowing a
current of air in the space between them. By blowing cold
air down the inside of the inner tube its temperature could be
made much lower than that of the outside electrode.

The currents were measured under varying potential dif-

»" Phil. Trans., A.," Vol. CXCVII, p. 415 (1901).

209 14

2IO EMISSION OF ELECTRICITY FROM HOT BODIES

ferences at a constant temperature and under constant potentials
at different temperatures. With a given potential difference
and temperature it was found that the current was always
greatest, except at very low potentials, when the outer tube
was positive. With the outer tube positive there was no in-
dication of an approach to saturation except when the inner
tube was cooled by blowing air through it. With the outer
tube negative the current exhibited very little increase between
lOO and 400 volts except when the inner tube was artificially
cooled. Under constant potential differences the currents
increased rapidly with rising temperature, of which the loga-
rithm of the current was very close to a linear function.

With the arrangement used there are a large number of
possible sources of ionization. These include volume ioniza-
tion of the hot air, formation of positive and negative ions by
interaction between the gas and the electrodes, and the emis-
sion of ions of both signs from the electrodes which would
take place if no air were present. Inasmuch as the currents
with large potential differences were much greater when the
larger and hotter electrode was positive it is reasonable to
suppose that the observed effects were mainly due to the
emission of positive ions by the hot platinum, either of itself
or by interaction with the gas. We have seen that the emis-
sion from freshly heated platinum wires decays with time,
rapidly at first and then more slowly, when the wires are
heated in a vacuum. Wilson noticed effects analogous to both
of these when the tubes were heated at atmospheric pressure.
The readings taken before the quick decay had occurred were
disregarded ; but inasmuch as the currents at constant tem-
perature and potential fell off slowly but continuously during
the course of the experiments it seems unlikely that the effects
due to the initial emission from the hot metal were elimin-
ated. This conclusion is supported by the large magnitude of
the current-densities obtained. These were easily measured
with a galvanometer, and were very much larger than those
obtained later by the writer when a well-glowed-out platinum
wire was heated in air at atmospheric pressure (see p. 218).

By assuming that the ions were formed by the dissociation

EFFECT OF GASES ON POSITIVE IONS 2 1 1

of the gas at the surface of the platinum and applying the
formula ^

?/---") = log I^Lii^L],

2VT, V ^U,M-;r,2Tj

where q is the heat of dissociation, and x^ and x^ are respec-
tively the fractions of the gas dissociated at the absolute
temperatures Tj and Tj, Wilson found values for g in the neigh-
bourhood of 6o,0(X) calories. This investigation is note-
worthy as it forms the first attempt to estimate the energy
changes involved in the emission, from the rate of variation of
the currents with temperature. More recently Wilson ^ has
shown that his numbers for the approximately saturated
currents obey the formula / = AT*^"*'^ with d = 25,000 de-
grees centigrade.

The effect of oxygen, air, nitrogen, helium, and hydrogen
on the emission of positive ions from platinum has been ex-
amined in some detail by the writer.^ A thin platinum wire,
electrically heated and arranged in the form of a loop, was
mounted in a glass tube alongside an insulated platinum
plate, and the current which flowed from the wire to the plate
was measured Considerable attention was paid to the
cleanliness of the tube and the purity of the platinum and of
the gases used. Before commencing the measurements the
platinum wires were glowed out for long periods in an oxygen
vacuum until the initial positive emission had become very
small and showed no appreciable recovery on standing. On
letting in small quantities of oxygen and other gases it was
then found that there was a small emission which was a definite
function of the pressure and nature of the gas and of the tem-
perature of the wire. The magnitude of the currents dealt with
is indicated by the following numbers which refer to one of
the earlier experiments made before the initial emission had
entirely disappeared. The wire under test was 7 cm. long
and O'Oi cm. in diameter. The positive emission on first

* Van't Hoff, " Lectures on Theoretical and Physical Chemistry," Vol. I,

p. 145-

«'• Phil. Trans., A.," Vol. CCVIII, p. 248 (1908).
» Ibid., Vol. CCVII, p. I (1906).

14*

212 EMISSION OF ELECTRICITY FROM HOT BODIES

heating at 804° C. was found to be 1*62 x 10 "^ amp., the
pressure given by the McLeod gauge being 0*00005 mm.
This current decayed to one-half its value in 10 minutes and to
one-tenth in about an hour. Even after heating in vacuo for
several hours a day, at temperatures in the neighbourhood of
800° C, for about two weeks the wire still gave small currents
under the best available vacuum conditions. Thus at 00003
mm. pressure a saturation current of 9'6 x lO"^' amp. was
obtained at 721° C. when the wire was charged positively.
On letting in oxygen to a pressure of 0*045 "f^n^- ^^^ keeping
the temperature constant the current increased to i '8 x lO"^^
amp. It was found that the small current which did not de-
pend on the pressure of the gas gradually disappeared with
continued heating, whereas the additional current caused by
the gas did not. It thus appears that with wires which have
been heated in a vacuum for a long time there is a positive
emission which is a definite function of the pressure of the sur-
rounding gas.

Under the conditions of these experiments saturation was
attained, except in some of the gases at high pressures, by the
application of moderate potentials. Even in the exceptional
cases there was a close approach to saturation. Most of the
experiments were made at temperatures so low that there was
no current when the wire was charged negatively. In these
experiments, therefore, the currents are due entirely to ions
emitted by the hot electrode. None of the observed effects
are due to volume ionization of the gas or to the emission of
ions of opposite sign from the collecting electrode. The con-
ditions are thus much simpler than where two hot electrodes
are employed with hot gas in between, and the results are cor-
respondingly easier of interpretation. Inasmuch as the initial
emission was allowed to decay before the measurements were
made, and the currents measured only appeared when gas was
admitted and disappeared when it was removed, it is clear that
these effects are something quite different from the initial
emission from freshly heated wires which was considered in
the last chapter. We shall now proceed to describe in more
detail the phenomena exhibited in the different gases.

EFFECT OF GASES ON POSITIVE IONS

213

I. Oxygen. — The currents with the wire charged positively
were found to saturate very readily at all pressures up to
atmospheric. At high pressures and low temperatures the
emission exhibited a curious instability ; the current under
apparently constant conditions kept suddenly increasing to a
temporary high value and then returning to about the original
level. The cause of this instability has not been discovered,
but on the assumption that it is due to some secondary pheno-
menon, the minimum values of the currents were taken to
represent those due to the direct action of the gas. This diffi-
culty was not encountered to any considerable extent at low

3
O

•33 -67 10

Pressure : mms.
Fig. 25.

1-33

pressures at any temperature or at high pressures when the
temperature was high.

At low temperatures the saturation current was nearly pro-
portional to the square root of the pressure, when this was under
I mm. At higher temperatures, in the neighbourhood of
1100° C. to 1200° C, the current was almost proportional to
the pressure over this range. At all the temperatures there
was very little variation of current with pressure at high pres-
sures (200 to 800 mm.). The behaviour at 828° C. for pres-
sures below I mm. is shown in Fig. 25.

The variation with temperature of the saturation current at
a constant pressure of i'47 mm. was also examined. The
superficial area of the hot wire used was 0*223 sq. cm. and its

214 EMISSION OF ELECTRICITY FROM HOT BODIES

diameter O'Oi cm. The currents obtained are shown in the
next table. The electron currents with the wire charged to
- 40 volts are added for comparison. These are probably
somewhat greater than the corresponding saturation currents
owing to the occurrence of some ionization by collision.

Temperature

Positive Emission

Electron Current

(Centigrade).

(Amperes).

708

1-6 X lO-i"

—

770

67 X io-i=»

—

826

i'5 X 10 -"

—

883

3'2 X 10-^^

IT X I0-"

940

5-8 X 10- "

67 X 10 -"

999

!•! X 10-^"

8-0 X 10 -"

1058

3-8 X 10-"

6-2 X 10-^'

ziig

6-4 X 10 -"

3*2 X 10 -"

Z181

IT X I0-'

3'3 X 10-^"

1227

17 X 10-8

1-6 X 10-'

At the lower temperatures the negative emission is negli-
gible compared with the positive but increases more rapidly
with the temperature ; so that at this pressure the two currents
are equal at about 1230° C. The values for both emissions
satisfy the equation / = AT*^'*'^ with different values of the
constants. The value of b for the data referring to the posi-
tive emission is 1*52 x io*° C. The values of the positive
emission per unit area from four wires of various sizes which
had undergone different treatment were determined at i -5 mm.
pressure at 770° C, and 880° C. They were found all to be
the same at the same temperature within the limits of the ex-
perimental error, indicating that the emission caused by oxygen
is due to the platinum itself and not to some adventitious im-
purity. One of the wires was subsequently heated strongly
in hydrogen and the treatment was found to reduce the per-
manent emission in oxygen by a factor of nearly four. This
effect may, however, be caused by a change in the crystalline
structure of the platinum which is known to be brought about
by this treatment.

When the temperature of the wire was kept constant and the
pressure of the oxygen raised it was found that the emission was
too low at first and gradually increased to the final steady value.
Similarly, when the pressure was reduced the observed emis-
sion was too high initially. These phenomena indicate that
the emission is not due directly to an interaction between the

EFFECT OF GASES ON POSITIVE IONS 215

hot metal and the surrounding gas, but rather that it arises
from the gas which is either dissolved in, combined with, or
adsorbed by the metal. Any of these processes would be ex-
pected to take some time to reach a condition of equilibrium
after an alteration in the pressure of the gas had been made.
The definitely established facts as to variation of this emission
with temperature and pressure can be accounted for if we
adopt the hypothesis that the emission at constant temperature
is proportional to the number of oxygen atoms held in the
surface layer of the platinum at any instant. This hypothesis
may be formulated quantitively as follows : —

Let a be the total number of platinum atoms per unit area
of the surface which are available for combination with oxygen,
and let x be the number which are combined with oxygen
atoms at any instant ; the number of free platinum atoms is
then a - X. If / is the partial pressure of the dissociated
'oxygen, the free oxygen atoms will become entangled at a rate
proportional to/ x {a - x), and will be liberated from the sur-
face layer at a rate proportional to x. Thus, if t is the time,

^ = Apia - x)- Bx,
where A and B are constant at a given temperature. The

'i^X

state of equilibrium is determined by — = o ; so that

A/>a a/jP)

Ap+B~ b +/(P)' • • ^^

where b = B/A and p = /(P), P being the total pressure of
the external oxygen. On this theory the emission is propor-
tional to X multiplied by a factor of the form ATV"*!/^, with
A, X, and b-^ constant, representing the rate of the reaction by
which the positive ions are ejected. At high pressures / (P)
becomes large compared with b ; so that x approaches ajb
asymptotically at all temperatures. The emission will thus
become independent of the pressure at high pressures whatever
the temperature. This was found to be the case. At low
temperatures the dissociation will be small even at low pres-
sures; so that/(P) will be nearly proportional to P'''. Thus

2i6 EMISSION OF ELECTRICITY FROM HOT BODIES

at low temperatures and pressures the emission should be
closely represented by the formula

^ ^ + pi/v ... (2)

where a and yS are constant at constant temperature. As a
matter of fact, if this formula holds for low pressures, it would
be expected to be fairly near the truth at high pressures also,
since the precise form ofy"(P) makes very little difference when
P is large. That this formula covers the experimental values
almost within the limits of experimental error, at low tempera-
tures, for the range from 0*003 "i"^- to 760 mm., is shown by
the numbers in the next table. The observations were made
at 820° C. ; the calculated numbers were deduced from (2),
using a = 5 '6 x lO"" amp., and fi = 4*0 (mm. of mercury)''*.

Pressure P.

pi/a

Calculated Emission

Observed

Mm. of Mercury.

.• = aP'/*/(/3+Pl/2)

Emission.

0*003

0-055

075

1*0

0*017

0-41

5-2

5*9

1*5

1'22

13-2

3*1

1-76

17-1

6'i

2-47

21-3

207

107

3-27

23*5

i7'o

4-12

a8-4

26*5

5-48

32*3

7-28

36-5

9-85

39'5

200

14-3

43*7

399

467

49*3

587

24*2

48-3

50-5

766

277

53-5

Experiments at a lower temperature (730° C.) gave at least as
good an agreement with (2), using a = i '2 x io~" amp. and
/S = 3"9 (mm. of mercury^'^

At a higher temperature (i 170° C.) the experimental values
did not agree with equation (2) at low pressures, but were
found to be in excellent agreement with

/ = 7P/(S + P) ... (3)

from 0'[4 to 89 mm., with 7 = 3-8 x io~^ amp. and 6 = 4*8
mm. of mercury. This result is to be expected if the greater
part of the oxygen near the surface of the metal is dissociated
at this temperature and at the lower pressures, because /(P)
would then be more nearly proportional to P than to P''^. It

EFFECT OF GASES ON POSITIVE IONS

217

is only at the lowest pressures that the dissociation need be
relatively complete as the formula is not very sensitive to the
form of/(P) at the higher pressures.

Nitrogen. — At low temperatures the positive emission in
this gas was smaller than in oxygen and more nearly compar-
able with the negative emission. Perhaps for this reason
higher voltages were required to attain saturation than in
oxygen at similar pressures when the wires were positively
charged. This is shown by the upper curve in Fig. 26 which
represents the relation between current and electromotive
force for the positive emission in nitrogen at atmospheric
pressure and 920° C. When the pressure was changed at

300 400 500

Pressure: mms
Fig. 26.

constant temperature the emission increased rapidly with
rising pressure at low pressures. The rate of increase of
emission with pressure diminished very greatly at higher
pressures but not so much so as with oxygen. There was no
tendency for the emission to approach a constant value at
pressures in the neighbourhood of atmospheric, but a regular
linear increase of emission with pressure was observed from
about 30 to 800 mm. The variation of current with pressure
at 920° C. is shown in the lower curve of Fig. 26. In these
experiments there was a small current at low pressures which
was independent of the pressure.

The variation of the saturation current with temperature
in nitrogen at 2*8 mm. pressure is shown by the following
numbers: —

2i8 EMISSION OF ELECTRICITY FROM HOT BODIES

Temperature
(Centigrade).

Saturation Currents

(Amperes per sq. cm.)-

+ vt Emission. - vt Emission.

827

3-0 X 10 -1* 4'4 X 10- 1*

90&

17 X 10-" 5-8 X lo-i'

907

3'8 X 10-" 1-5 X 10-"

984

276 X 10-11 3*5 X 10-11

1071

99 X 10-11 ^.7 X lo-i"

Both the positive and negative emissions follow the
formula i = AT*^"*'^ ; for the positive emission the value of b
is 3-56 X io*° C. and for the negative 5 '6 x io*° C. The
positive emission increases less rapidly with temperature than
the negative emission, but more rapidly than the positive
emission in oxygen. Thus, if the same laws continue to
operate, the positive emission in nitrogen should exceed that
in oxygen at high temperatures. The temperature at which
the two emissions become equal should be lower at atmos-
pheric pressure than at pressures of about i mm.

Air. — With some reservations the behaviour of the positive
emission in air is intermediate between that in oxygen and that
in nitrogen. Thus when the electromotive force is varied the
approach to saturation is observed at a lower potential than in
nitrogen but at a higher potential than in oxygen. Again the
saturation current at constant temperature increases with
pressure at high pressures less rapidly than in nitrogen but
more rapidly than in oxygen. The values of the currents at
atmospheric pressure from a wire whose effective area was
0-66 sq. cm. are shown in the next table. The currents were
approximately saturated.

Temperature

Current (Amperes).

(Centigrade).

Positive Emission.

Negative Emission.

8X2

9'3 X 10 -"

—

893

2-2 X lo-ii

3*3 X 10 -1*

900

5'2 X 10-11

5*3 X lo-i*

978

3*3 X lo-i"

3'2 X lo-i'

1064

8-0 X 10 -i«

4*2 X 10-12

1 150

2*0 X 10 -*

3-8 X 10-11

1236

67 X 10-8

2*6 X 10- 1"

These currents follow the usual formula for the temperature
variation; the values of b being, for the positive emission,
2*46 X 10* ° C, and for the negative, 4-49 x 10* ° C. The value
for the positive emission in oxygen at atmospheric pressure
was 1-52 X 10* ° C, and for nitrogen, 3 "56 x 10* ° C. Thus the
value of b for the positive emission in air at atmospheric

EFFECT OF GASES ON POSITIVE IONS 219

pressure is nearly equal to the mean of the values for oxygen
and nitrogen at the same pressure.

Although the foregoing considerations show that the phen-
omena observed in air are to a certain extent a compromise
between those exhibited in nitrogen and oxygen respectively,
the emission in air is not equal to the sum of the effects due
to the nitrogen and oxygen present supposed to act independ-
ently. Thus at a certain temperature the wire, when heated
in the gases at atmospheric pressure, gave emissions propor-
tional to the following numbers : nitrogen 29, oxygen 290,
air 70. The emission in oxygen at a pressure equal to its
partial pressure in the atmosphere is only about 10 per cent
less than at atmospheric pressure ; so that the oxygen alone
which was present in the air should have given an emission of
about 260 in tlie units used. Adding in the effect of the
nitrogen, the principle of simple superposition of the effects
would give an emission equal to about 280, instead of the ob-
served value 70. It thus appears that the nitrogen does not
act merely as a diluent of the oxygen, but has a distinct in-
hibiting effect on the more active gas. It is possible that it
does this by combining with platinum atoms which would
otherwise be free to take up oxygen ; but there are clearly
a number of other ways in which the observed effects might
arise.

Helium. — Only a few experiments have been made with
this gas ; but the results are of particular interest since they
indicate the existence of a positive emission caused by a gas
which is believed to be incapable of acting chemically on the
hot body. The gas was freed from impurities by subjecting
it, in a tube connected with the testing bulb, to a luminous
discharge from a cathode of sodium potassium alloy. After
this treatment the following values of the currents at different
pressures were observed when the emission had assumed a
steady condition at 907° C. : —

Pressure (mm. of mercury) . . . 0*07 O'yi 2*4
Current (1 = 3-3 X 10-" amp. persq. cm.) 18 54 130

At this temperature and at a pressure of 2 mm. of mer-
cury the positive emission in helium appears to be about

2 20 EMISSION OF ELECTRICITY FROM HOT BODIES

twice that in nitrogen and one-fortieth that in oxygen under
like conditions.

Hydrogen. — The emission in this gas at low temperatures
is difficult to investigate, as it changes very slowly with time
after any alteration in the conditions has been made, and the
final equilibrium value takes an inordinate length of time to
become established. At 900° C. and 3-8 mm. pressure the
steady positive emission was found to be 7 x io~^^ amp.
cm. "^. This is about one twenty-fourth of the value in
oxygen at the same temperature and pressure. At 1 300° C.
H. A. Wilson^ found the following values for the currents
from a positively charged wire at different pressures : —

Pressure (mm. of mercury) . 9 156 766

Current (i = 10 -* amp.) .4 24 40

Thus at this temperature the positive emission from platinum
in hydrogen appears to resemble that in oxygen and nitrogen
in so far as it varies only rather slowly with the pressure at
high pressures.

The following values of the approximately saturated cur-
rents at a pressure of 1*9 mm. and different temperatures
were found by the writer : —

Temperature, centigrade . . 860 1017 1181

Positive emission (amps, per cm.'') 2-5x10-" 1*3 x 10-^" i*i2xio-*
Negative „ ,, ,, ,, 4-7x10-^" — i-i x 10-*

The values of b calculated from these data are 1 79 x
io*° C. for the positive emission and 474 x io*° C. for the
negative. Experiments at a higher pressure (226 mms.) led
to the following numbers : —

Temperature, centigrade .

860

1017

1097

II8I

Positive emission (amps.

per cm.2) .

4'i X 10-"

3-8x10-"

—

1-4 X 10

Negative emission (amps.

per cm.") .

i-ox 10-''

—

1-25 X 10-^

2-8 X 10

From these data ^5 = 2*85 x 10^ ° C. for the positive emission
and 278 X 10* ° C. for the negative. In hydrogen the value
of b for the positive emission increases with increasing
pressure, thus exhibiting the contrary behaviour to that for the
negative emission.

1 '♦ Phil. Trans., A.," Vol. CCII, p. 243 (1903). _

EFFECT OF GASES ON POSITIVE IONS 221

Hydrogen Diffusing into Air,

The positive emission from platinum in air when hydrogen
is diffusing out of the platinum has been examined by the
writer,^ The apparatus consisted of an electrically heated
platinum tube with a coaxial cylindrical electrode. The rate
at which the hydrogen diffused out of the platinum was con-
trolled by varying the pressure of the hydrogen inside the
tube. Under these conditions the quantity of hydrogen
which diffuses out has been shown "^ to be proportional to the
square root of the pressure, at constant temperature. Most
of the experiments were made at about 1 200° C. At low tem-
peratures (800° C.) the currents when the wire was positively
charged showed no sign of approaching saturation up to 960
volts. This indicates that the platinum had been insufficiently
glowed out and was behaving like a fresh wire (see p. 183).
At the higher temperatures (about 1200° C.) approximate
saturation was attained with 80 volts, but even here changes
of the current with time were observed after altering the
potential. Such changes have generally been found to be char-
acteristic of the behaviour of freshly heated wires. It may be
important to remember that the platinum was in this condi-
tion as it is possible that a well-glo wed-out tube might behave
differently.

The variation, with the pressure of the hydrogen inside the
tube, of the positive emission at 1 200° C. is shown by the fol-
lowing numbers : —

Positive Emission (i = i*8 x io~^^ amp. per cm.').

Pressure P (mm.).

Found.

Calculated.

56-3

172

65-6

780

92-4

The numbers in the last column were calculated* by as-
suming that the emission was equal to a + <^P*, a and b be-
ing constants. The agreement of the results shows that the
emission consists of two parts, one proportional to the square

^ Loc. cit., p. 57.

"Cf. Richardson, Nicol, and Parnell, " Phil. Mag.," Vol. VIII, p. i (1904).

222 EMISSION OF ELECTRICITY FROM HOT BODIES

root of the pressure of the hydrogen inside the tube and the
other independent of it. The effect of the hydrogen diffusing
out of the platinum therefore is to produce an additional
number of positive ions proportional to the quantity of hydro-
gen which diffuses out. Other considerations make it pro-
bable that the hydrogen inside the platinum is in the atomic
state, and these results indicate that part, at least, of the
dissolved atoms are ionized. The values of the currents show
that only a small fraction (about lo "^) of the escaping hydro-
gen gets away in the form of ions ; but the proportion in the
interior which is in the ionic state may be much higher.

The positive emission from the tube at different tempera-
tures was measured, both when the interior of the tube was
evacuated and when it was filled with pure hydrogen at at-
mospheric pressure. The difference gives the emission due to
the diffusing hydrogen at the different temperatures. The
values obtained for this quantity are shown in the following
table :—

Temperature, centigrade . . 973 1052 1129 1200 1262 1331
Emission due to hydrogen

(i = 1*8 X 10- " amp. per cm.'') 6 17 43 80 172 340

These numbers increase more rapidly with the temperature than
the quantities of hydrogen diffusing out. Hence the efficiency
for liberating positive ions of a given amount of hydrogen
diffusing out of platinum increases with rising temperature.

Effects Caused by Changing from One Gas to
Another.

When a wire has been heated for a long time in one gas
the positive emission on admitting small quantities of a second
gas is larger, at first, than the steady value to which it ulti-
mately settles down.^ This effect appears to occur even if the
wire is heated for a long time in a good vacuum with the pump
in continuous operation before the second test is made. Under
these conditions the initial excess of the emission over the
final value is larger than the residual emission before the new
gas is admitted. These effects have been observed in oxygen,

1 Richardson, " Phil. Trans., A.," Vol. CCVH, p. i (1906).

EFFECT OF GASES ON POSITIVE IONS 223

nitrogen, helium, and hydrogen. The decay of the positive
emission in hydrogen was accompanied by a parallel increase
in the negative emission. This effect has not been looked for
with the other gases. In hydrogen the flow of the negative
emission apparently caused a small temporary increase in the
positive emission on subsequent testing. The decay of the
positive emission after admitting a new gas, and its temporary
revival by allowing the negative emission to flow, are similar
to the effects observed when fresh wires are heated ; but the
currents in these experiments are enormously smaller than
those given by fresh wires at the same temperature.

Nature of the Ions.

So far no direct evidence as to the nature of the ions which
carry the positive emission from hot metals caused by gases
has been adduced ; although all the results described appear
to harmonize with the view that the carriers are charged atoms
or molecules of the surrounding gas liberated, perhaps some-
what indirectly, by its interaction with the metal. In discuss-
ing the experiments in oxygen we assumed quite explicitly
that the ions were charged oxygen atoms liberated by the gas
present in the surface layers of the platinum. This assump-
tion was seen to give a fairly straightforward quantitative ex-
planation of the phenomena. It is questionable whether they
could be accounted for by any other equally simple hypothesis.

As we have already seen, the measurement of the electric
atomic weight M of the ions is the only completely satisfactory
way of settling their nature. The measurement of M for these
ions presents some difficulty on account of the smallness of
the currents when the pressure of the gas causing them is not
too large seriously to interfere with the motion of the ions.
The only measurements oielm or M which can have any claim
to apply to the positive emission caused by a gaseous atmos-
phere are those of Thomson, referred to on p. 204, since they
are the only ones which have been made with wires sufficiently
well glowed out to get rid of the initial emission. With plati-
num in an air vacuum Thomson found, using the cycloid
method, ions for which M was near 14. This agrees with the

224 EMISSION OF ELECTRICITY FROM HOT BODIES

view that the ions are atoms of oxygen or nitrogen or both.
In the later experiments the more accurate positive-ray method
of measuring M was used With platinum in a carbon mon-
oxide vacuum ions for which M = 27 were found. For
molecules of CO with a single charge M would be 28. After
saturating the platinum with hydrogen the average value of
M found subsequently fell to 9. These results clearly afford
strong support to the view that the ions which constitute this
emission at low pressures are charged atoms or molecules of
the gases concerned. At the same time only a limited number
of experiments have been made under the conditions utilized
by Thomson, and the reasons here adduced for regarding the
emissions as of the same character as those described in the
present chapter are perhaps not altogether conclusive ; so that
there appears to be room for further investigation in this direc-
tion.

There is definite evidence that the ions which carry the
positive emission in air at atmospheric pressure are of atomic
magnitude, when the platinum has not been glowed out in a
vacuum so as entirely to get rid of the initial emission. H. A.
Wilson^ has shown that the main features of the current-
E.M.F. curves obtained by him, and referred to at the begin-
ning of this chapter, can be accounted for on the hypothesis,
that the only conditions which prevent the attainment of satu-
ration are the mutual repulsion of the ions, which alters the
distribution of the field between the electrodes, and the, back-
ward diffusion of the ions into the emitting electrode. When
the potential difference is neither too high nor too low, the
disturbance of the electric field is small but not negligible.
In this part of the curve the potential difference V satisfies the
equation

V = ^ . '°g "- - '°g '•■ + x(2.,= log^ - r- + rAi,, . (4)
27r \ ^1 /

where i is the current, k the mobility of the ions, ^gthe volume
density at the electrode whose radius is r^, and r^ the radius at
the other electrode. Thus, this part of the /, V curve is a

1 " Electrical Properties of Flames and Incandescent Solids," p. 38.

EFFECT OF GASES ON POSITIVE IONS 225

straight line whose intercept on the voltage axis is proportional
to tj. By measuring the intercept and the slope of the line,
together with a knowledge of the radii of the cylinders, both
f^ and k may be determined. The value of k for the positive
ions found by this method in air at atmospheric pressure at
1000° C. is 43 cm. sec ~^ per volt cm. ~\ This agrees with the
value to be expected for a positively charged atom of potas-
sium from kinetic theory considerations, so far as the data for
the calculation of this quantity can be relied on. Whether
this interpretation is accepted or not, the experimental value
of k leaves little room for doubting that the ions are charged
atoms or molecules.

This conclusion only applies, generally speaking, to the
ions as they are found close to the hot metal. In the colder
gas at some distance away the ions grow in size, and the
value of k diminishes. This is shown by the experiments
of McClelland described on p. 6, in which the mobility of
the ions in the gas drawn away from incandescent metals was
measured directly by a blowing method. It is also shown by
some experiments made by Rutherford,^ who measured the
current from a hot platinum plate to a parallel electrode when
the currents were very small, compared with the saturation
value. Under these conditions the relation between the voltage
V and the current density / is expressed by the equation

where k is the mobility of the ions, and / the perpendicular
distance between the electrodes. It is clear that k may be
deduced by measuring V, /, and /. Rutherford found that k
increased with increasing distance between the plates. In
addition, very small values of k were found at high tempera-
tures. These were attributed to the loading of the ions by
the platinum dust which is sputtered under these conditions.

We have seen that the emission of positive ions from
platinum in various gases satisfies the equation i = AT*^"'''^.
The values of the constants in a number of cases are collected

» " Phys. Rev.," Vol. XIII, p. 321 (1901).
15

Gas.

Pressure

(mm.).

Oxygen

7 X 10^'

1*52 X 10*

4X 10'

Air

760

7 X iqI*

2-46 X 10*

lo^i

Nitrogen

. 2-8

4 X 10^^

3-56 X 10*

3x10

Hydrogen

1-9

ioi«

179 X 10*

I023

Hydrogen

226

I020

2-85 X 10*

3 X 10^

226 EMISSION OF ELECTRICITY FROM NOT BODIES

in the following table. The values for the negative emission
under similar conditions are added for comparison : —

678 X 10*
4*49 X 10*
5*6 X 10*
474 X 10*
278 X 10*

It is a remarkable fact that the constants for the positive
emission, in the table above, exhibit a linear relation between
log A and d similar to that shown by the constants for the nega-
tive emissions from platinum and tungsten, which was con-
sidered in Chapter IV. Moreover, the constant a/c, or c, con-
sidered on p. 122, has a very similar value, being equal to
I "43 X 10' for the positive emission from platinum in various
gases, as compared with the values 3-29 x 10^ for the nega-
tive emission from platinum and 2 56 x 10^ for the negative
emission from tungsten. We have seen that, in the case of the
negative emissions, the linear relation in question is closely
connected with the contact difference of potential between the
metal contaminated by gases and the pure metal. A relation
between the constants A and d for the positive emission, such
as is contained in the data above, would be expected to arise,
in the same way as for the negative, if the positive ions were
present in the metal and if their internal concentration were
independent of the nature and pressure of the gas and of other
external factors. The theory of the emission of these posi-
tive ions would then be similar to that of the emission of the
negative electrons. The main differences would result from
the atomic dimensions of the positive ions and their much
smaller concentration in the metal. The effect of gases on the
positive emission would then be closely connected with the
corresponding contact potentials, although the effects might
not show an exact correspondence with those given by the
negative emission on account of the atomic character of the
positive ions. With the positive ions there may be a material,
as well as an electrical, factor to consider. Several years ago
the writer ^ pointed out that the phenomena which character-

1 " Phil. Trans., A.," Vol. CCVH, p. 6i (1906).

EFFECT OF GASES ON POSITIVE IONS 227

ize the positive emission from " old " platinum wires in various
gases could be united into a coherent whole from this point
of view. At that time, however, such a theory was considered
improbable from the fact that gases like oxygen appeared to
exert an effect on the positive emission out of all proportion
to that exerted on the negative. It may be, however, that the
issue is not so simple as was supposed, and that the hypothesis
under consideration has been dismissed too lightly. On the
other hand, if the hypothesis is accepted some other explana-
tion will have to be sought for the values of e/w found by
Thomson which, as we have seen, make the emitted ions atoms
of the surrounding gas. Moreover, the linear relation between
the constants A and b for the positive ions rests only on five
pairs of values, and the agreement may prove to be accidental.
It is clear that this subject is one which afi"ords scope for
further experimental investigation.

The Emission from Fresh Wires in Gases.

When platinum is freshly heated in air at pressures up
to atmospheric the emission, particularly at rather low tem-
peratures, exhibits interesting peculiarities, which show a close
resemblance to some of the effects observed with freshly heated
wires in a vacuum. The phenomena to be described refer to
platinum heated in air at atmospheric pressure unless the
conditions are definitely stated to be otherwise. H. A.
Wilson ^ observed that the positive emission decayed with the
time of heating, rapidly at first and then more slowly. The
writer 2 found that at moderate temperatures this decay in-
creased rapidly with the positive potential applied to the hot
metal and was inappreciable when the latter was earthed, or
at a relatively low potential. Thus a new wire at 925° C. was
found when charged with + 40 volts to give a current of 100
divisions which remained constant for 100 minutes. On rais-
ing the potential to + 760 volts the current had the following
values at the times stated : —

» *• Phil. Trai:§., A.," Vol. CXCVII, p, ^15 (1901).
»/«</., Vol. CCVII, p. 30 (1906),
15 *

2 28 EMISSION OF ELECTRICITY FROM HOT BODIES

Time (minutes) . . o 36 9 14 20 25 36 47 54 60 66
Current (divisions) . 3570 1930 950 760 570 485 475 190 115 112 103 103

On returning to + 40 volts the currents at successive intervals
of 6 minutes were 80, 84, 90, and 94 divisions. This experi-
ment was made with a thin wire of about 001 cm. diameter
surrounded by a coaxial cylindrical electrode of 3*2 cm. di-
ameter provided with guard rings. Similar results were ob-
tained when the thin wire was replaced by a heated platinum
tube of 0"2 cm, outside diameter. It was also noticed that
the positive emission increased m. magnitude if the hot electrode
was left negatively charged.

The diminution of the rate of decay of the emission caused
by reducing the applied positive potential has been confirmed
by the observations of W. Wilson ^ and of Sheard.^ The latter
also observed that the emission from a positively charged wire
at a low temperature could be increased by heating the wire
to a higher temperature for some time in a negatively charged
or uncharged condition. At 628° C. he found that a wire
under test gave an emission of 14 divisions under + 200 volts
which showed no appreciable decay with time. The wire
was then connected to earth and heated during intervals of
10 minutes at various temperatures up to 840° C. Subsequent
to each of these heatings the emission under + 200 volts was
tested at the original temperature of 628° C. It was found
to be greatly increased by the treatment. The increased
emission was a definite function of the temperature at which
the wire had been heated under zero voltage, with sharp
maxima at 650° C. and 760° C. respectively and a minimum
between. The current at 628° C, after heating to 760° C,
was about 40 times as great as that observed prior to this
treatment. Similar, but smaller, effects with maxima at the
same points were observed with a wire which had been re-
vived by heating in a bunsen flame.

The fact that the emission decays most rapidly when a
large positive potential is applied to the hot metal shows that
the removal of charged ionizable matter by the electric field

1 " Phil. Mag.," Vol. XXI, p. 634 (1911).

»7ifrf., Vol. XXVIII, p. 170 (1914). _

EFFECT OF GASES ON POSITIVE IONS iig

is an essential feature of the decay phenomenon. If this
material is not removed by the field it diffuses back to the hot
metal and helps to emit more positive ions. It seems fairly
clear that part, at any rate, of the active material is not avail-
able at relatively low temperatures but is only formed at
somewhat higher temperatures ; so that the effect of heating
alone may be, in certain cases, to increase and not to diminish
the current at a standard temperature. The point has not
been investigated very carefully, but the writer's impression is
that the current decays rapidly under heating alone at very
high temperatures. It is probable that under these conditions
the heating destroys the active substance formed at inter-
mediate temperatures. A current which does not vary with
time may exceptionally be obtained owing to the fact that
the active material is being formed by the heating at the same
rate as the electric field removes it.

These conclusions are strengthened when the decay curves
at intermediate temperatures are considered. These have been
investigated by Sheard^ who found that they contained
humps similar to those observed by the writer in a good
vacuum (p. 182). At temperatures below 628° C. Sheard
found that the decay was inappreciable with the platinum used
by him. The results at temperatures between this and 774° C.
are shown in Fig. 27. Similar curves which showed more pro-
nounced maxima were obtained when the revived emission
due to heating in a bunsen flame was examined at about the
same temperatures. These curves can be accounted for if we
suppose that three substances are concerned in the emission.
One of these A decays continuously with pronounced emission of
ions. The second B is formed by the heating and is inactive
or comparatively so. B then decays into C with a further
positive emission. It will be seen that the curves bear some
resemblance to those shown by the decay of the radio-active
deposit from radium emanation, where the successive changes
have been explained in a somewhat similar manner. The in-
set represents the radio-active case in which an active product

' •• Phil. Mag.," Vol. XXVIII, p. 170 (1914) ; cf. also Sheard and Woodbury,
" Phys Rev.," Vol. II, p. 288 (1913).

230 BMISSION OP ELECTRIClfY EROM HOT SODlES

A changes into an inactive product B, from which the active
body C is subsequently formed. In the case now under dis-
cussion it is not necessary to suppose that B is formed from
A, and the phenomena are complicated by the fact that all the
rates of change are functions of the temperature ; so that a
slight change of temperature may make a considerable differ-
ence in the appearance of the curves.

(4 (b 18 ^Zo"
Time - MinuteB.

Fig. 27.

The curves connecting current and electromotive-force for
the positive currents from freshly heated platinum wires in air
exhibit complications similar to those shown by the positive
emission from new wires in a high vacuum. At low tempera-
tures the currents may show no indication of approach to
saturation, even when the positive currents are quite small,
when the negative emission is negligible, and when the time
rate of decay of the positive currents also is inappreciable.

EFFECT OF GASES ON POSITIVE IONS 231

Thus with a platinum tube 02 cm. in diameter heated to
809° C. and surrounded, in air at atmospheric pressure, by a
cold tube 32 cm. in diameter, the writer^ found the relation
between the positive currents and the potential difference to
be given by the following numbers : —

Volts on hot tube + o 4 10 20 40 80 400 960

Current (i = 1*8 y 10-" amp. per cm.*) .0 2*6 10 22 32 64 225 390

Using the same arrangement with the hot tube at
1200° C. an increase of the potential difference from 80 to
400 volts increased the current only in the ratio 64 to 75.
Thus the difficulty in reaching an approximation to saturation
with fresh wires appears to occur only at low temperatures. If
it is due to the same cause as the similar effect observed in a
vacuum (p. 183) this is important, since it would show that
neither effect can be attributed to secondary actions arising from
the bombardment of the cold cathode by the positive ions. The
kinetic energy of the positive ions at the cathode is negligible
at atmospheric pressure. As these peculiar effects have, so far,
not been explored very fully, it is perhaps undesirable to lay
too much emphasis on the precise interpretation of the ob-
served phenomena, but it is difficult to avoid the conclusion
that with fresh wires at low temperatures some, at least, of
the positive ions are in some way liberated at the surface of
the wire by the direct intervention of the electric field.

There are distinct indications that under other conditions
the electric field may tend to inhibit the formation of the
positive ions. Thus at 706° C. in oxygen at 528 mm.
pressure the writer^ found the relation between the positive
current and the mean voltage on the filament to be that given
by the numbers in the next table. The experiments were
made with a thin platinum wire and the readings were taken
in the order of the successive columns from left to right : —

Mean volts + : —

o 175 38 175 37 175 5-8 18 175 38 o

Current (1 = 6 x 10-^* amp.) : —

4 20 14*8 i8'5 I5-8 19*5 15*5 15 30 I4'8 4*8

» •• Phil. Trans., A.," Vol. CCVII, p. 58 (1906).
' Loc. cit., p. 7 ; cf. also p. 11.

232 EMISSION OF ELECTRICITY EROM HOT BODIES

The current with 38 volts is only about 75 per cent of that
with 175 volts. Similar results were obtained at 0*4 mm.
and 826° C. and at 0*0015 mm.; so that the gas does not
appear to have much to do with this effect. The currents in
the table were not those obtained when the changed potential
was first applied, but the steady values reached after a few
minutes. On raising the potential the currents were larger,
and on lowering it smaller, at first. So far as the writer's
experience goes this type of behaviour is shown neither by an
absolutely fresh wire nor by a well-aged wire but only in the
intermediate stages. The results indicate the presence of a
substance removable by the electric field which is capable of
giving rise to more ions if left in the neighbourhood of the
hot metal for some time. Such a state of things might
conceivably arise in the stage where the emission increases
with lapse of time under otherwise constant conditions.

The maxima sometimes observed in the time decay curves,
as well as Sheard's experiments on the revival of the emis-
sion at a low temperature by heating in the absence of electric
field to various higher temperatures, show that there are at
least two distinct substances or actions concerned in the emis-
sion of positive ions from freshly heated platinum wires.
This conclusion has been confirmed in a different way by
Sheard and Woodbury.^ They heated a fresh wire in air at
atmospheric pressure at various temperatures under conditions
such that the decay of the emission was inappreciable. The
emission was then found to follow the equation i = AT^e''''^
with a constant value of d over the range tested (845° K. to
1040° K.). The emission was then allowed to decay until a
considerable amount of it had been driven off, when the
measurements at different increasing temperatures were re-
peated. On plotting the value of log i - -^ log T against T"^
the new curve was found to consist, not of one straight line as
at first, but of two straight lines inclined at an angle. This
indicates that under the condition of greater aging of the wire
the emission at the lower temperatures has one value of d and
that at the higher temperatures another. The value of d for
1 " Phys. Rev.," Vol. II, p. 288 (1913).

EFFECT OF GASES ON POSITIVE IONS 235

the higher temperatures was the same as that which covered
the whole range of temperature in the original test.

The three lines of investigation referred to show that the
positive emission from fresh platinum wires involves, as a rule,
the occurrence of at least two distinct substances or processes.
The ions emitted by these substances, or during these processes,
are not necessarily different. In order to condense the discus-
sion let us suppose that the observed differences are due to
different substances. This hypothesis is most strongly sup-
ported by the phenomena described in Chapter VI. The two
substances might be derived one from the other by decomposi-
tion or they might be different compounds of the same basic
element ; in either of these events the positive ions emitted
from them would be expected to be the same. It is true that
there is definite evidence of the emission from the purest avail-
able platinum of two well-marked types of ion having values
of M about 40 and 24 ; but it cannot be considered certain
that these ions correspond, respectively, to the quick initial
decay and to the slower decay after passing the maximum, or
to the corresponding phenomena discovered by Sheard. As
the matter has not been accurately investigated from this point
of view it is impossible to be quite certain, but an examination
of the evidence at present available indicates that all the
various phenomena now under consideration should have been
present in the early stages when the platinum wires examined
by the writer (p. 201) gave no indications of the presence of
any ions except those having a value of M in the neighbour-
hood of 40. It is probable that similar effects would be
observable at the stage at which the lighter ions are emitted,
but, so far, there does not appear to be any convincing evi-
dence that they have been examined.

Other interesting properties peculiar to freshly heated
platinum wires, many of them closely related to those just
considered, will be found described in Chapter IV, pp. 103 et
seq., and Chapter VI, passim.

CHAPTER VIII.

THE EMISSION OF IONS BY HEATED SALTS.

The first experiments to indicate that heated salts possessed re-
markable electrical properties were made by Sir J. J. Thom-
son,^ who showed that the conductivity between platinum
electrodes in a hot crucible containing air at atmospheric pres-
sure was much increased by the presence of potassium iodide,
potassium chloride, ammonium chloride or sodium chloride.
At about the same time Arrhenius ^ found that the conduc-
tivity of the bunsen flame was greatly increased by the injec-
tion of various salts. The injection of similar salts of the
alkali metals in the proportion of their equivalent weights
causes a greater increase in the conductivity the more electro-
positive the basic element and the higher its atomic weight.
This is shown by the following numbers for the conductivities
caused by equivalent quantities of salt under a potential dif-
ference of 56 volts : Cs = 123, Rb = 41-1, K = 2i-o, Na =
3"49, Li = I '29, H = 075. These numbers are taken from
a paper by Smithells, Dawson, and Wilson.^ As the electrical
phenomena in flames are probably affected by the chemical
actions which occur we shall not consider them further in this
book. The reader who desires more information on the sub-
ject may be referred to " The Electrical Properties of Flames
and Incandescent Solids," by H. A. Wilson (University of
London Press: 191 2), where it is considered at length.

In 1 90 1 H. A. Wilson * examined the electrical conduc-
tivity caused by spraying salt solutions into the space between

» " Phil. Mag.," Vol. XXIX, pp. 358, 441 (1890).

2 «' Ann. der Physik," Vol. XLIII, p. 18 (1891).

3 " Phil. Trans., A.," Vol. CXCIII, p. 108 (1899).
* Ihid., Vol. CXCVII, p. 415 (1901).

234

The emission of iojvs by heated salts 235

two hot coaxial platinum cylinders. The arrangement in fact
was that already described on p. 209. The currents were
found to be very difficult to saturate, but in most cases satura-
tion was attained by the application of about 1000 volts. The
relation between the currents and the temperature was very
complicated, doubtless owing to the occurrence of chemical
reactions between the salts and the water vapour present. At
low temperatures the largest currents were given by potassium
iodide and were measurable on a galvanometer at 300° C. At
temperatures approaching 1400° C. Wilson found that the satu-
ration currents, with all the salts of the alkali metals tested,
became independent of the temperature. Under these circum-
stances the quantity of electricity transported in unit time was
the same as that which, according to Faraday's law, would be
associated with the electrolysis of the salt sprayed into the
space between the electrodes in the same interval. This result
was verified for the following salts : CsCl, CsjCOj, Rbl, RbCl,
RbjCOs, KI, KBr, KF, K2CO3, Nal, NaBr, NaCl, Na2C03, Lil,
LiBr, LiCl and LigCOj. The salts behave as though each metal
atom present were capable of once giving rise to a single ion
and then played no further part in the electrical phenomena.
Why this happens is not altogether obvious. It may be that the
positive ions, which there is reason to believe are atoms of the
metal that have lost an electron, are absorbed into the interior
of the negative electrode, or they may end their career by
forming an inactive chemical compound. The available data
are insufficient to decide between the relative merits of these
and alternative hypotheses which might suggest themselves.

The effect of the presence of various inorganic substances on
the leakage of electricity across a parallel plate air condenser
at temperatures in the neighbourhood of 300° C. was examined
by Beattie.^ A large number of substances were found to in-
crease the currents, the most marked effects being obtained
with the halogen compounds of zinc, and various mixtures
which might be expected to give rise to these bodies. These
phenomena have since been investigated by Garrett and

1 •• Phil. Mag.," V. Vol. XLVIII, p. 97 (1899) ; vi. Vol. I, p. 442 (1901.)

236 EMISSION OF ELECTRICITY FROM HOT BODIES

Willows/ Garrett,^ and Schmidt and Hechler,^ among others.
An idea of the nature of the phenomena may be obtained by
considering the following experiment which may be regarded
as typical of a number of those made by these authors. Two
parallel metal plates are arranged in an oven so that their
temperatures may be maintained at various values up to 400°
C. The lower plate can be maintained at various positive and
. negative potentials whilst the upper, which is insulated, can be
connected to an electrometer. The small currents with no
salt between the plates are first measured, so as to enable them
to be allowed for, and then the currents are determined after
the salt under test has been sprinkled on the lower plate.
With some salts the current flows only when the plate is
positively charged, whereas others cause a leakage of electricity
of both signs but usually to different extents. The following
list, compiled from papers by Garrett * and Schmidt,^ embraces
the substances which have been found to give rise to a con-
siderable amount of ionization at temperatures of about
400° C. :—

Fe.Clg : A\C\ : NH.Cl : MgCl^ : SnClj + 2H2O : MnClg :
CdClat : ZnCla : CaF^ : Al^Fgt : NH.Br : ZnBr^ : CdBrg : NH J :
Cdia: Znl^: NH4NO3: CdCNOg)^! : Co(N03)2t : Quinine sul-
phate. The substances marked thus | only caused a leakage
when the plate was charged positively. With all the others
some effect was obtained with charges of either sign.

The following substances have been found to give little or
no ionization at these low temperatures : —

Sn : Pb : Bi : As : Hg : I, : CuClg : SrCl.^ : BaCl^ : LiCl : KCl
SbCla : SnCl^ : HgCl^ : HggCl^ : KBr : HgBr^ : KI : Agl : Fbl,
Hgig : NaF : CuO : ZnO : SnOa : Fefi, : CaO : MgO : ZnSO,
FeSO, : CuSO^ : MgSO^ : MgCO, : ZnCOg : K2CO3 : Na^COg
NaHCOa : Pb(N03)2 : BaCNOa)^ : CH3OH : C2H5OH : (CH3)2CO
(C2H5)20 :,CHCl3 : CeHg : CgHi, : CSg : CH3COOH : lactic acid
quinone : hydroquinone : naphthalene : phenanthrene : fluorene

1 " Phil. Mag.," Vol. VIII, p. 437 (1904).

^Ibid., Vol. XIII, p. 728 (1907).

» " Verb, der Deutsch. Physik. Ges.," Vol. IX, p. 39 (1907).

* " Phil. Mag.," Vol. XIII, p. 729 (1907).

6 " Ann. der Phys.," Vol. XXXV, p. 404 (1911).

THE EMISSION OF IONS BY HEATED SALTS 237

Many of the salts enumerated in this table give a very
large ionization at higher temperatures. The behaviour of KI
and that of iodine call for special comment. These are given
as inactive in the table, whereas Wilson (p. 235) obtained
large currents when potassium iodide was sprayed into hot
air at about 300° C, and Campetti ^ and Sheard ^ have obtained
very considerable currents from iodine vapour at about 400° C.
There seems to be little doubt that the currents obtained by
Wilson were conditioned by an action between the potassium
iodide and the water vapour present. Kalandyk ^ has recently
found that the conductivity of KI vapour at 308° C. is
negligible, but that it becomes appreciable when water
vapour is also present. Why the results of these observations
with iodine do not agree with those of Campetti and of Sheard
is uncertain.

With the type of apparatus just described the measured
electrical leakage may arise in a good many ways. It may be
caused by an emission of ions of either sign from the heated
salt directly, it may be due to the volume ionization of the
salt vapour, or it may arise from the emission of ions by the
action of the salt vapours on the electrodes. When the salted
electrode discharges electricity of both signs all of these actions
may be occurring. If only one sign is discharged then there can
be no volume ionization, but the current may be due either to
the emission of ions of the same sign from the hot salt or of
the opposite sign from the opposite electrode by the action of
the salt vapours. Thus it is impossible to give a very precise
interpretation to the effects obtained with the type of apparatus
now under discussion.

Sheard * who has examined the emission from cadmium
iodide in some detail has succeeded in unravelling the various
factors to a considerable extent. By using an air-cooled elec-
trode for collecting the ions, he was able to eliminate the pos-
sibility of the emission of ions by the action of the salt vapour

* " Sci. Torino Atti," 40, i, p. 55 (1904).

»" Phil. Mag.," Vol. XXV, p. 381 (1913).

» " Roy. Soc. Proc., A.," Vol. XC, p. 638 (1914).

«" Phil. Mag.," Vol. XXV, p. 370 (1913).

238 EMISSION OF ELECTRICITY FROM HOT BODIES

on the opposite electrode ; and by allowing the vapours from
the salt to pass through the plates of a condenser, charged to
a difference of potential sufficient to remove all the ions in-
stantaneously present, and then into a second testing vessel,
he was able to examine the processes occurring in the vapour
without having to deal with complications due to the ions
emitted by the salt. In this way he succeeded in showing
that there was an emission of ions directly from the hot salt,
and an ionization process in the vapour independent of this.
Whether the formation of ions from the vapour is entirely a
direct volume ionization, or is in part due to interaction be-
tween the vapour and the electrodes, is not absolutely certain.
Kalandyk ^ found that the currents through the vapour were
not altered much when one of the platinum electrodes was
covered with spongy platinum, indicating that the surface of
the electrodes was not of much importance. Sheard,'' on the
other hand, found that the currents in the vapour, although
apparently saturated, varied very much with the direction of
the applied potential difference, a result which points to the
contrary conclusion.

Sir J. J. Thomson ^ has tested the leakage of electricity
from a number of inorganic substances, in air at atmospheric
pressure, and at temperatures for the most part considerably
higher than those used in the investigations just referred to.
He found that the oxides discharged only negative electricity,
the chlorides and phosphates only positive. The nitrates
tested discharged only positive electricity until they were con-
verted into the oxides, after which only negative electricity
was discharged. In every case, except that of lead peroxide,
the sign of the charge which leaked away was opposite to that
acquired by the salt when rubbed with a pestle in a mortar.

In Thomson's experiments the salts under test were placed
on an electrically heated porcelain tube. He found that the
phosphates gave larger currents, when charged positively, than
the other groups of salts examined, aluminium phosphate be-
ing particularly efficient.

^ Loc. cit., p. 644. "^ Ibid., p. 380.

» " Camb. Phil. Proc," Vol. XIV, p. 105 (1906).

THE EMISSION OF IONS B V HE A TED SAL TS 239

In most of the recent work on the emission of ions from
hot salts, the salts have been placed on an electrically heated
strip, or wire, of platinum, which formed one electrode. The
other electrode has been cold, and arranged so as to surround
the first as far as possible. In a large number of cases, there
is no current with this arrangement except when the hot salt
is positively charged. Under these circumstances we know
that there is no volume ionization, and that positive ions only
are emitted, either from the salt directly or by the interaction
of the salt vapour on the hot electrode. Similar considerations
apply if negative electricity alone is discharged. Under these
conditions, the observed currents can be assigned definitely to
the emission of ions either directly from the hot salt or from
the hot electrode under the influence of the salt vapour. The
number of possible alternative interpretations of the observed
effects is, therefore, considerably reduced. These remarks
apply also to the experiments of Thomson, whose apparatus
was of this general type. We shall now consider the pheno-
mena in greater detail, keeping for the most part to cases in
which the effects are due to an emission of ions in the sense
just indicated.

Relation Between Current and Potential
Difference.

Naturally this depends a good deal on the shape and re-
lative position of the electrodes, the pressure of the surround-
ing gaseous atmosphere, whether ions of only one sign or ions
of both signs are emitted, the presence or absence of volume
ionization, and the magnitude of the emission. In H. A.
Wilson's experiments with concentric tubes at atmospheric
pressure, where volume ionization and large currents were dealt
with, large potential differences of the order of 1 000 volts were
necessary to attain approximate saturation. At low pressures,
and where there is only an emission of ions of one sign from
one electrode, the current-E.M.F. curves are similar to
those given by the ions emitted from hot metals under
parallel conditions. Saturation is usually attained the more
readily the lower the temperature and the smaller the current.

240 EMISSION OF ELECTRICITY FROM HOT BODIES

As a rule, it is rather more difficult to attain saturation with
salted than with unsalted electrodes, although sometimes the
reverse is the case. Thus in some experiments in which the
writer^ heated a number of salts in a closed platinum tube
2 cm. in diameter, and measured the currents passing to a
central cold electrode i cm. in diameter, the currents at a
number of potential differences and pressures of air before ad-
mitting the salts had the values given in the following table : —

Pressure

(nun.)

Volts . -» 40 80

120

160

200

240

280

320

360

0*0075

Current . -» i 1*28

I '45

1-57

1-68

177

1*90

2-13

2-31

o*5 (approx.]

Current . _^ i 1*25

1-44

1-54

i-6i

1*90

2-45

3-47

5-0

5*5

Current . -^ i 1*29

1-53

171

I -80

1-83

2-5

(i = io-

-''amp. approx.).

The substantial increases with the higher voltages at 0*5
and 5*5 mm. pressure are undoubtedly due to impact ioniza-
tion in the gas. The observations with sodium sulphate in
the tube gave practically the same variation of current with
voltage at similar pressures as that indicated by the numbers
in the preceding table for the empty tube. With aluminium
phosphate and beryllium sulphate also the curves were similar
except that the current increased somewhat more rapidly with
rising potential differences between 40 and 200 volts. It is
possible but not certain that this increase is due to impact
ionization of the salt vapour close to the hot electrode. In
that case it should be more marked with the more vola-
tile salts. Roughly speaking, this requirement appears to be
satisfied. The numbers found with barite, the mineral form
of barium sulphate, after heating for ten hours are shown in
the next table : —

Pressure
(mm.)

Volts
o"ooi5 Current
0-8 (i = 10-'' amp,

approx.)
9*4 (i = 10-'' amp

approx.).

o 40 80 120 160 200 240 320 400

o I 1*025 ^'06 i'o6 i*io 1*12 i*i4 1*19

) I 1-03 I'll 1-13 i*2i 1*24 1-42 i-6o

J I i*i2 i*i8 i'25 1*31 i*35 1*46

These numbers show a much better approach to satura-
tion even than the empty tube. However, it is to be remem-

1 " Phil. Mag.," Vol. XXII, p. 66g (191 1). —

THE EMISSION OF IONS BY HEATED SALTS 241

bcred that the values for the empty tube were observed in the
earlier stages of the experiment, and the positive ionization
from platinum which has got into the condition of an " old"
wire is much more easily saturated than that from freshly heated
platinum. The ease of attaining saturation with barite in
comparison with the other salts may be due to the possibly
smaller volatility of the source of ionization with this
material.

The foregoing data for the relation between current and
potential difference are only to be taken as representative
samples. As we have stated already the results obtained
vary considerably with changes in the conditions enumerated
at the beginning of this section. Current-E.M.F. curves for
a number of salts in different gases at various pressures with
different types of electrodes may be found in the following
papers: H. A. Wilson, "Phil. Trans., A.," Vol. CXCVII, p.
424 (1901) ; Garrett and Willows, " Phil. Mag.," Vol, VIII, p.
446 (1904); Garrett, "Phil. Mag.," Vol. XX, p. 588 (1910);
G. C. Schmidt, "Ann. der Physik," Vol. XXXV, p. 440
(191 1); Horton, "Roy. Soc. Proc, A.," Vol. LXXXVIII, p.
127 (1913); C. Sheard, "Phil. Mag,," Vol. XXV, p. 370

(1913).

For many experiments it is sufficient to know that satura-
tion or approximate saturation can be attained, and to make
sure that this object has been accomplished. The time lag
effects which are often observed when the applied potential
difference is suddenly changed are considered on p. 249 below.

Changes with Time.

In general when salts are heated in a vacuum or in a
gaseous atmosphere at constant pressure the saturation currents
vary in an interesting way with the time, even when the tem-
perature and the applied potential are kept constant. This
effect was first noticed by Garrett and Willows ^ in making
experiments with zinc iodide. They found that the positive
emission from this substance under conditions apparently
constant first increased to a maximum and then diminished.

1 " Phil. Mag.," Vol. VIII, p. 450 (1904).
16

242 EMISSION OF ELECTRICITY FROM HOT BODIES

The currents i after passing the maximum could be expressed
as a function of the time / by means of the equation

/= Ae-^ .... (I)
where A and X are constants. This formula is the same as
that which often governs the decay of the initial emission from
hot metals (p. i8o), and can be accounted for in a similar way
by assuming that the emission is due to the decomposition of
some substance at a rate proportional to the amount of it in-
stantaneously present. Zinc bromide gave similar results, but
the rate of decay of the emission was greater than with zinc
iodide. In a later paper Garrett ^ returned to the emission
from zinc iodide. He found that the emission did not diminish
indefinitely, but that a final steady value was approached
asymptotically. The part of the emission which varied with
time could be represented throughout the whole range, includ-
ing the initial rise, by the formula

where A, \ and X^ are constants. This formula implies the
initial formation of an inactive product which subsequently
decays with the emission of ions (cf. Rutherford's "Radio-
activity," Chapter IX).

The phenomena exhibited by ordinary laboratory speci-
mens of pure aluminium phosphate have been examined in
detail by Garrett.^ Fig. 28 shows the variation of saturation
current with time when this substance is heated at about
1200° C. in an atmosphere of carbon dioxide at 0*5 mm.
pressure. The upper curve gives the same data as the lower
one on an enlarged vertical scale. This curve shows that the
quick initial rise and decay is followed by a slower increase
from a minimum to a final steady value. The whole curve is
represented very accurately by the formula

i = A{e -^1' - e-^^') + B(i - e-^^% . (3)

with A, B, Xj, Xg, and X3 constants. This formula implies
the inactive formation (A, Xj) of an active product which
quickly decays (A, Xi) together with the independent inactive

1 " Phil. Mag.," Vol. XIII, p. 745 (1907).
^Ibid., Vol. XX, p. 577 (1910).

THE EMISSION' OF IONS BY HEATED SALTS 243

formation of a product (B, X,) which decays at an infinitely
slow rate (B, \ = o) with emission of ions. The values of
the constants vary with the temperature ; so that the general
appearance of the cur\'es changes considerably according to
the temperature. When the salt was heated in air or hydrogen
the initial rise was preceded by a quick decay from a large

'W 80 120 t60

Time in minutes

Fig. 28.

200 2W 280 320

initial value. This part of the curve did not appear if the
salt was previously heated at a lower temperature sufficiently
high to drive off observed water vapour; so that, on these
and other grounds, it is attributed by Garrett to the action of
water vapour.

Time changes of the character under discussion are a
general feature of the emission when ordinarily prepared
samples of salts are first heated. In addition to those already
mentioned a number of cases have been investigated by G. C.

16 ♦

244 EMISSION OF ELECTRICITY FROM HOT BODIES

Schmidt.^ They include Znig in nitrogen, Al CI3 in nitrogen,
Cd CI2 in air, Cd Brj in air and Cdlg in nitrogen. A number
of these were examined at different pressures and tempera-
tures. Under the conditions of Schmidt's experiments the
emission from the cadmium salts fell away from the beginning
and did not show an initial rise to a maximum. Similar ob-
servations with NajSO^ in a good vacuum at 1005° C. have
been recorded by the writer,^ and on sodium pyrophosphate
and the phosphates of sodium and aluminium by Horton.^

400

45 60 /5

T/ME /// Minuted

Fig. 29.

Effects of a like character are observed also when negative
ions, whether heavy ions or electrons, are emitted by salts (see
p. 93). Thus with calcium iodide the writer* observed an
initial rise to a maximum in about 1 5 minutes followed by a
slower decay, at temperatures between 523° C. and 654° C. At
the higher temperatures the maximum was attained by the
electrons sooner than by the heavy ions ; at the lower tempera-
tures there was no noticeable difference in this respect. The
variation of these currents with time at 654° C. is shown in
Fig. 29.

The phenomena exhibited by cadmium iodide have been
examined in some detail by Sheard,^ who tested both the con-

1 " Ann. der Physik," Vol. XXXV, p. 401 (1911).

2 " Phil. Mag.," Vol. XXII, p. 676 (1911).

2 "Roy. Soc. Proc, A.," Vol. LXXXVIII, p. 134 {1913).

4 "Phil. Mag.," Vol. XXVI, p. 464 (1913).

* lUd., Vol. XXV, p. 370 (1913). —

THE EMISSION OF IONS B V HE A TED SALTS 245

ductivity of the vapour and the emission of ions from the salt.
At temperatures below the melting-point of the salt (400° C.)
the saturation currents in the vapour decayed continuously
from a maximum initial value, in agreement with Schmidt's re-
sults. At higher temperatures there was a rise to a maxi-
mum in about 15 minutes followed by a slower decay. The
currents due to the emission of ions from the heated salt
showed a different behaviour from those in the vapour. At
470° C, for example, there was an enormous negative emission
which decayed very rapidly with time. The positive emission
was at first too small to measure, but it gradually increased to
a maximum value in 90 minutes and then fell away. At
this stage the positive emission was greater than the negative,
but the greatest positive emission was less than one two-
hundredth part of the large negative emission observed on first
heating. A similar but less marked contrast between the
positive and negative emissions was observed when iodine was
similarly tested. Sheard also examined the behaviour of the
salt which distilled out of the experimental tube in successive
experiments. He found that the first distillate gave a small
negative and a large positive emission whereas the second
showed the contrary behaviour. In all the distillates there
was a great disparity in the magnitudes of the positive and
negative emissions ; and in almost every case the distillate
from a preparation which gave a large negative and a small
positive emission, or vice versa, showed the contrary behaviour.
The currents from all the distillates were much smaller than
the large initial emission from the fresh salt. The distilled
salt showed no appreciable change in appearance, but chemical
analysis showed that successive distillation reduced the per-
centage of iodine.

There can be little doubt that these interesting time
changes in the emission of ions from salts and in the conduc-
tivity of salt vapours are symptomatic of the occurrence of
chemical changes ; but it is very difficult to form a definite
opinion as to what the precise nature of the change is, in any
particular case. When the currents are increasing with time
it seems fairly clear that a substance possessing greater ther-

246 EMISSION OF ELECTRICITY FROM HOT BODIES

mionic activity is being formed and when the currents are
diminishing the resulting products are less active in this re-
spect. One difficulty in forming a judgment as to the nature
of the chemical changes arises from the delicacy of the elec-
trical test. This is so sensitive that the amount of matter con-
cerned might often be incapable of detection by chemical
methods. It is also possible that many of the effects are due
to the occurrence of unstable forms which are not persistent
enough to be recognized by chemical methods. This is es-
pecially likely since the time changes show that the bodies
concerned have only a transitory existence. In many cases
these time changes are attributable to the presence of conta-
minants. Thus ordinary laboratory specimens of " pure " alu-
minium phosphate give an initial emission which is large
compared with that from the pure salt and which after a time
falls to a small value. Horton ^ has shown by spectroscopic
examination that this decay in the emission is accompanied
by the disappearance of sodium salts.

The complicated phenomena in the case of cadmium iodide
have been studied more fully, perhaps, than those shown by any
other salt, and here it does seem possible to form, at any rate,
a limited judgment as to the nature of the phenomenon from
the chemical side. Schmidt^ has ventured the opinion that
the time changes in the vapour arise from the decomposition of
the molecules of Cdig into Cd^+ and Ij,. with a subsequent
interchange resulting in Cd + - and I2 + - , that is to say,
two neutral molecules. It does not seem to the writer,^ how-
ever, that any theory of this type will account for the ob-
served time changes in the vapour in presence of an excess of
salt. So long as there is any excess of salt the vapour will
be supplied at a steady rate and the phenomena observed in
it should be independent of time until the salt disappears. It
is necessary to suppose that the actions in the vapour are not
conditioned solely by the amount of Cdl2 vapour present but

^ Loc. cit.

' " Ann. der Physik," Vol. XXXV, p. 428 (1911). These views are modified
somewhat in a later paper (ibid., Vol. XLI, p. 673 (1913)) without, however,
overcoming the difficulty referred to (cf, p. 248).

3 0. W. Richardson, " Phys. Rev.," Vol. XXXIV, p. 387 (1912).

THE EMISSION OF IONS BY HEATED SALTS 247

rather by some other substance coming from the salt. The
time changes must in fact be conditioned by something the
amount of which is determined by actions occurring at the
salt and not simply by a decomposition of cadmium iodide
vapour. In one aspect this question has been definitely
settled by Kalandyk ^ who has shown that the currents in
cadmium iodide vapour under the conditions of these experi-
ments are independent of the time, provided every trace of
water is removed from the salt and from the apparatus. The
way in which water brings about the time changes usually ob-
served is unknown. Kalandyk's experiments only tell us that
there are no time changes when water is absent, they do not
offer an explanation of the changes which occur in the presence
of water or water vapour. Sheard's results point to the con-
clusion that the large negative initial emission, when it is
present, is connected with the liberation of iodine. On this
view the smaller negative emission from the distillates would
be related to the reduced iodine content of the salt, which
after distillation probably consists of a solution of an unrecog-
nized subiodide of cadmium in Cdl2. The presence of the
subiodide would reduce the equilibrium pressure of iodine in
presence of cadmium iodide vapour. The probable existence
of a subiodide of cadmium is distinctly indicated by the work
of Morse and Jones ^ who succeeded in isolating a body having
the composition Cd^Ias. probably a solution of the subiodide
in Cdlj.

It is likely that the effect of water vapour is not confined
to this particular instance and that many of the time changes
observed with other salts would not occur if all traces of water
were eliminated. Such a result, at any rate, would not be
surprising if the time changes are indicative of the occurrence
of chemical reactions. For it is well known that many chemi-
cal actions which proceed very energetically in presence of a
trace of water vapour are completely inhibited in its absence.
The importance of water vapour generally for these effects is
supported by the behaviour of potassium iodide, whose vapour

' Loc. cit.

•" Amer, Chem. Jour.," Vol. XII, p. 488 (1890).

248 EMISSION OF ELECTRICITY FROM HOT BODIES

exhibits little or no ionization at low temperatures if water
vapour is completely absent. Again, as we shall see later,
there is a close correspondence between the emission of posi-
tive ions from salts and from fresh platinum wires, and W.
Wilson ^ has found that the positive emission from the latter
is, under certain conditions, very sensitive to the presence of
small quantities of water.

In a recent paper Schmidt^ has come to the conclusion
that the time changes previously observed by himself and
others are to be attributed entirely either to removal of ions
by the electric field or to diminution of the salt surface, in the
case of a decrease of ionization with time, or to a time lag in
the temperature or pressure of the vapour reaching the elec-
trodes, in the case of an increase with time. The main
grounds for this conclusion are (i) that the currents are greater
when the same amount of the salt is tested in the powdered
form as compared with a pastille, indicating that the amount
of surface is a factor, and (2) when conditions are arranged
so that the superficial area of the salt does not change during
an experiment, the time variations disappear. Although the
first of these grounds is probably correct it does not seem to
the writer that either of them is established by the experi-
ments described by Schmidt. In these experiments all the
currents are measured under a potential difference of only 2
volts, and they must have been very far from saturation. It
is well known that under such conditions the magnitudes of
the currents may be almost independent of the number of ions
available for carrying them, the main factor in determining
their values being the mobilities of the ions. Schmidt's con-
clusions are also in direct contradiction to the experimental
results of Sheard, who undoubtedly observed in the same tube
a simultaneous decrease in the negative and increase in the
positive saturation currents, both effects changing at different
and characteristic rates.

The time changes we have had under consideration so far
are such as arise when a T:onstant potential difference is main-
tained between the electrodes. In many cases this decay
1 " Ann. der Physik," Vol. XLI, p. 673 (1913).

THE EMISSION OF IONS BY HEATED SALTS 249

appears to be due merely to heating and to be independent
of the magnitude or sign of the electric field. This is not,
however, a universal rule. With aluminium phosphate the
writer has observed that the general decay of the positive
emission with time is much more marked when the salt is
positively charged than when it is uncharged or negatively
charged. The phenomenon has, however, not received much
attention. We have already remarked upon similar effects
exhibited by the positive emission from fresh wires (pp. 183
and 227).

Apart from this it has generally been found that im-
mediately after changing the sign of the applied potential
difference the currents of either sign are larger than the re-
latively steady values to which they shortly settle down.
Effects of this kind have been recorded by H. A. Wilson ^
with salts of the alkali metals heated in air at atmospheric
pressure, by Schmidt^ with zinc and cadmium iodides in
various gases at low pressures, and by Garrett ^ and by the
writer * with aluminium phosphate in a vacuum.^ As a rule
these changes are soon over and are independent of the general
decay or increase with time already considered. This is well
shown in the case of zinc and cadmium iodides by the curves
given by Schmidt. In the case of the specially prepared pure
aluminium phosphate referred to below, the writer found that
the effect of changing the electric field was smallest at low
and high temperatures and most marked at intermediate
temperatures. These effects thus appear to depend to some
extent on the temperature of the salt.

With some salts when the temperature is suddenly changed
the emission assumes an abnormal value for a short time. Thus
when sodium phosphate had been overheated Horton ^ ob-
served that the currents at a given lower temperature were
abnormally high at first. A similar effect has been noticed

»•• Phil. Trans., A.," Vol. CXCVII, p. 415 (1901).

'"Ann. der Physik," Vol. XXXV, p. 428 (igii).

» " Phil. Mag.," Vol. XX, p. 577 (1910).

«/6id., Vol. XXII, p. 7CO (iQu).

"Cf. also Horton, " Roy. Soc. Proc, A.," Vol. LXXXVIII, p. 117 (1913).

» " Camb. Phil. Proc.," Vol. XVI, p. 92 (1910).

250 EMISSION OF ELECTRICITY FROM HOT BODIES

by the writer ^ with sodium sulphate. In the case of salts
like calcium iodide which emit a mixture of electrons and heavy
ions the writer ^ has observed a time lag in the current caused
by changing an external magnetic field. In fact a sudden
change in any physical condition controlling the magnitude of
the thermionic current appears temporarily to upset the internal
conditions which determine the value of the saturation current
under given external conditions.

In the case of aluminium phosphate Horton ' has observed
a decay in the steady emission when the salt is left in air at a
low pressure in the cold. The writer is inclined to suspect
that this effect is connected with the gradual dehydration of
the salt, but there is not enough evidence to form a certain
judgnient on the point. Similar effects have been observed by
the writer in the case of the negative emission from calcium
iodide (p. 94).

Variation with Temperature.

The ionization currents from salts or in salt vapours as
ordinarily measured may exhibit very complicated changes
when the temperature is varied. Thus H. A. Wilson in the
experiments already described, in which salts were sprayed
into the hot air between two coaxial platinum cylinders, found
that the curves expressing the relation between current and
temperature possessed maxima and minima at certain tem-
peratures. These complications are undoubtedly due to the
occurrence of chemical reactions in such a way that the ioniza-
tion is caused by different substances at different temperatures.
The particular effects observed by Wilson were probably caused
by the formation of hydrates owing to the action of the salts on
the water vapour present. The chemical actions, whose precise
nature is less obvious, which give rise to the time changes
considered in the preceding section probably cause the
complications which are frequently observed in the relation be-
tween emission and temperature in other cases when salts are
heated. It is clear that the frequent occurrence of chemical
action greatly increases^ the difficulty of interpreting experi-

1 «• Phil. Mag.," Vol, XXII, p. 680 (1911). ^Ibid., Vol, XXVI, p, 465 (1913).

3" Roy, Soc. Proc, A.," Vol. LXXXVIII, p. 126 (1913).

THE EMISSION OF IONS B V HE A TED SAL TS 251

ments designed to discover the relation between emission and
temperature when a given salt is heated.

In spite of these difficulties there is a very considerable
amount of experimental evidence which goes to show that
when a salt is heated under conditions such that the emission
of ions is always caused by the same substance the currents
increase rapidly and continuously with rising temperature, and
the relation between the total emission (or the saturation
current) and the temperature is that expressed by the formula

/ = AT* e-^^
which has been found to govern the temperature relations of
other thermionic currents. Thus Garrett ^ showed that this
relation held when a number of salts were heated on a brass
plate at temperatures ranging around 300° C. Data which
lead to a similar conclusion have been furnished by Garrett *
for the positive emission from aluminium phosphate in COj
and Hj at 0*05 mm. pressure at about 1100° C, by Schmidt^
for cadmium iodide, by the writer * for the negative emission
consisting of a mixture of electrons and heavy ions which
is given off by calcium iodide, strontium iodide, and calcium
fluoride, and by Kalandyk ' for the currents through the
vapours of cadmium iodide, zinc iodide, and zinc bromide.
The values of the constant b deduced from some of these ex-
periments are shown in the following table : —

Nature of
Emission.

Pressure.

Substance.

Positive

Negative

Post live

Atmospheric CaFj
AlFj
NH^NOj
Znl,
FcClj
NH^Cl
CaF,
NH^NO,
MgCl,

0*05 mm. of COj Aluminium
Phosphate
»• I) "a t>

Approximate ^ , ,
Authority. Mean fcor

Temperature.

Garrett

297° c.

1-3 X lO*

330° c.

1*45 X 10*

312° c.

I '65 X 10*

241° c.

I "45 X 10*

355° C.

3*05 X 10*

352° c.

2*5 X 10*

346° c.

3-0 X 10*

342° c.

2*15 X 10*

326° C.

I '2 X 10*

[ioo° C.

3 '55 X 10*

1200° C. 2*65 X 10*

» " Phil. Mag.," Vol. XIII, p. 732 (1907).

«/6irf., Vol. XX, p. 581 (1910).

»" Ann. der Physik," Vol. XXXV, p. 401 (1911).

* " Phil. Mag.," Vol. XXVI, p. 452 (1913).

» •• Roy. Soc. Proc, A.," Vol. XC, p. 642 (1914).

252 EMISSION OF ELECTRICITY FROM HOT BODIES

Nature of
Emission.

Pressure.

Substance.

Authority.

^"^M^n™*** Value of
.viean to p

Temperature. " *"•

Negative

o-ooi mm.

Cal2

Richardson

500° C.

276 X 10^

»»

Sri,

540° c.

576 X IO<

»j

CaFj

600° C.

3*64 X 10*

Current through

Constant

Cdlj

Kalandyk

250° C.

2*35 X 10*

vapour

«>

400° C.

i'i4X 10*

»i

ZnBr,

400° c.

174 X 10*

«»

Znlj

380° c.

1-57 X 10*

With the positive emission from zinc iodide in air at 2*5
mm. pressure Garrett found that there was a break in the
curve obtained by plotting log iY~^ against T"^ at 250° C. ;
this was attributed to a fresh source of ions coming into play
at this temperature.

The values of b given in the table above are all of the
same order as those given by the emission of ions from hot
metals. For the most part they tend to run lower than the
values characteristic of the negative emission from most
metals and are more comparable with the values for the posi-
tive emissions. The writer found that there was no certain
difference, at any rate over considerable ranges of tempera-
ture, in the values of b for the heavy ions and for the electrons,
in the case of the three salts Calj, Srl2, and CaFj which
give off a mixture of these bodies. Kalandyk's experiments
were made in such a way as to vary the temperature of the
salt vapour without changing that of the salt. Thus the
pressure of the salt vapour in these experiments was presum-
ably constant and equal to the vapour pressure of the salt at
the temperature at which the latter was maintained. It does
not seem likely that the difference between the two values of
b for Cdig given by Kalandyk is due to the difference of mean
temperature merely ; but the matter has not been sufficiently
investigated to enable the precise cause of this difference to be
ascertained. In considering his results Kalandyk uses the
formula A^"*/^ instead of AT*^"*'"^. This of course alters the
values of the constants somewhat ; except for this, there is no
detectable difference between the behaviour of the two func-
tions over the range of T covered by the experiments ; so
that for the purpose of expressing the numerical values there
is nothing to choose between these formulae.

THE EMISSION OF IONS BY HEATED SALTS 253

It is to be remembered that the values of b given in the
table can only be relied upon as being approximately correct,
as in many cases the conditions other than temperature which
affect the formation of the ions have been insufficiently investi-
gated.

The Influence of the Nature and Pressure of the
Surrounding Gas on the Thermionic Currents
FROM Salts.

Garrett ^ observed that the currents from aluminium phos-
phate, when positively charged and heated on a strip of plati-
num at a constant temperature, varied in a regular manner
with the pressure of the surrounding gas. This effect occurs
when the currents are approximately saturated ; so that it
must be caused by a change in the actual number of ions
emitted, and cannot be due merely to a change in the mobility
of the ions. The effect of varying the pressure and keeping
the other conditions constant was found to be as follows : —

At the lowest pressures the emission of ions was quite
small, but it increased steadily with rising pressure until a
certain pressure was reached at which the emission had a
maximum value. After this the emission diminished at a rate
which was smaller than that of the previous rise, and which
fell off continuously as the pressure was increased. Although
the diminution of the currents with rising pressure fell off as
the pressure increased, it was still quite noticeable at about
50 mm. pressure in the neighbourhood of 1 100° C. Results of
much the same character were obtained in both air and carbon
dioxide. The pressure at which the current attained a maxi-
mum value was found to diminish very considerably as the
temperature of the salt was raised.

This passing of the current through a maximum value as
the pressure is raised, is similar to the behaviour of an ionized
gas subject to a constant potential difference, in the range of
pressure in which a large part of the current is due to impact
ionization. It does not appear, however, that impact ioniza-
tion can be the cause of the phenomena now under considera-

» " Phil. Mag.," Vol. XX, p. 579 (1910).

2 54 EMISSION OF ELECTRICITY FROM HOT BODIES

tion. In the first place, they occur under conditions such that
the currents vary very little with moderate changes in the
applied voltage. In the second place, they occur with voltages
which are not large enough to give rise to any appreciable
amount of impact ionization. Finally, the change with tem-
perature, of the pressure for maximum current, is in the wrong
direction, and also the rate of change is too great, to be in
agreement with this explanation.

The phenomenon in question is not confined to aluminium
phosphate. Similar observations have been made by Horton ^
on sodium and lithium phosphates, and by the writer'* on
NagPO^ and NajSO^. Horton's experiments with sodium
phosphate were made at 800° C. , and the effect of the different
gases, carbon monoxide, hydrogen, and oxygen was examined.
The largest emission was observed in hydrogen, but it decayed
more rapidly with time than that in the other gases. The
emission in carbon monoxide was about ten times as large as
that in oxygen, although the curves connecting emission and
pressure were similar. The maximum in hydrogen was not
detected, as the currents increased continuously up to the
highest pressure (20 mm.) at which experiments were made.
In a later paper Horton ^ showed that the behaviour of lithium
phosphate was similar to that of sodium phosphate in these
respects. The writer's observations on NagPO^ and NagSO^
in air showed that under comparable conditions these sub-
stances behaved in much the same way as sodium phosphate
in oxygen, as recorded by Horton. With NagSO^, which was
examined over the range of temperature from 730° C. to
1160° C, the following additional points were noted, among
others. The maximum emission at a certain pressure which
was observed at the lower temperatures (about 800° C.) with
relatively fresh salt, was found to disappear if the salt had
been heated for a long time at a high temperature (about
1150° C.) before testing. The maximum at the higher tem-
peratures was not observed to disappear under this treatment.

1 " Camb. Phil. Proc.," Vol. XVI, p. 89 (1910).

« » Phil. Mag.," Vol. XXII, p. 676 (1911).

»" Camb. Phil. Proc," Vol. XVI, p. 318 (1911).

THE EMISSION OF IONS BY HEATED SALTS 255

The effect of water vapour, instead of air, was also tried.
The emission in water vapour was about six times as great as
in air, and the pressure of maximum emission was found to be
raised from 0-2 mm. to 0*5 ram. at 1 160° C. The emission in
air was subsequently found to have been permanently dimin-
ished by the treatment with water vapour. The variation of
the emission in air with pressure at the lowest pressures was
carefully tested. The effect of the gas was found to be very
irregular. Sometimes the magnitude of the emission would
be very sensitive to the admission of a small amount of air and
at other times very insensitive under conditions apparently
identical. In all cases the relation between current and pres-
sure was of the form a + bp^ where a and b are constants,
provided / was sufficiently small.

Horton^ has since extended his observations to 1080° C.
and 1190° C. and has examined sodium pyro-phosphate and
several specimens of aluminium phosphate as well as sodium
ortho-phosphate, with results for the most part similar to
those already described. Two specially pure specimens of
aluminium phosphate prepared by the method indicated on
p. 277 failed to exhibit the pressure of maximum emission.
The emission from these preparations is very small and may
possibly be due to the underlying platinum. Similar results
were obtained with the small emission from the impure alu-
minium phosphates which had been heated for a long time.
With this salt the maximum, as well as most of the emission,
is clearly due to some impurity which disappears with con-
tinued heating. The magnitudes of some of the positive
emissions at various pressures of air, which were obtained
after continued heating, are shown in the accompanying
table :—

Positive Thermionic Currents (i = io-» Amp.) in Air at Various
Pressures at 1190° C.

Material. 0005 mm.

Platinum 5'2

Pure aluminium phosphate . 07

Impure aluminium phosphate . 2*9
Sodium phosphate . . . 1080

» "Roy. Soc. Proc., A.," Vol. LXXXVIII, p. 117 (1913).

I mm.

2 mm.

S mm.

10 mm.

ao mm,

1-65

2-2

2-9

1-2

2"0

1-5

2-0

3-1

4"l

1500

1630

1750

1810

1740

256 EMISSION OF ELECTRICITY FROM HOT BODIES

The initial emission from the impure aluminium phosphate
is larger than that for the sodium phosphates at these tempera-
tures, and like them it shows the pressure maximum. It also
decays at an enormously more rapid rate. In these experi-
ments an increase of current with diminishing pressures was
observed at very low pressures, in most cases. This is attri-
buted by Horton to an action between the heated anode and
the mercury vapour, but it seems possible that the alterations
of pressure in this region may have caused a difference of
temperature between the thermocouple and the emitting sur-
face ; so that with a constant thermocouple reading the tem-
perature of the hot surface may vary with the pressure of the
gas.

In all these experiments small quantities of salt were used
and the salts were heated electrically on a strip of platinum.
In order to vary the conditions as much as possible the writer ^
made experiments in which a number of salts were heated at
the bottom of a long platinum test tube. To prevent the
platinum tube from collapsing it was placed in an exhausted
steel crucible heated in an electric furnace. The currents
from the platinum tube to an air-cooled central electrode were
measured. They were approximately saturated. The salts
tested were: Na2S04, BeSO^, AIPO4, and BaSO^. In the
last case both the chemically prepared salt and the mineral
barite were used. With this apparatus the relation between
the saturation currents and the pressure of the air in the tube
was found to be quite different both for the different salts as
compared with each other and also as compared with the
same salt when tested by the strip method. The nature of
these differences is illustrated by Figs. 30 and 31, Curve i
in Fig. 30 shows the variation of positive emission with
pressure of oxygen for sodium phosphate as observed by
Horton by the strip method at 800° C. Curve 2, Fig. 30,
shows the behaviour of Na3P04 by the tube method in air at
775° C. The effect of changing the pressure in the one case
is almost the exact opposite of what it is in the other. Sepa-
rate experiments have shown that this difference cannot be

^Loc. cit.

THE EMISSION OF IONS B Y HE A TED SALTS 257

attributed to the difference of temperature or of the gases
used in the two experiments. In Fig. 31 similar observations

0 2 4^

/'/tESSURC fM/LLIMCTefts)

Fig. 30.

with aluminium phosphate are exhibited. Curves i and 2
show the results obtained when ordinary "chemically pure"
aluminium phosphate is tested in air by the tube method at

100

10 15

Fig. 31.

780° C. Curve i gives the observations for rising and curve 2
for diminishing pressures. Most of the difference between
these curves is due to a time lag in the effect of changing the

258 EMISSION OF ELECTRICITY FROM HOT BODIES

pressure, but part of it is due to a drift in the temperature of
the tube. The mean of the two curves can be taken to re-
present the actual effect of pressure at the mean temperature
(780° C). Curve 3 shows the quite different results obtained
with aluminium phosphate in carbon dioxide by Garrett at
1005° C. by the strip method. According to Garrett's experi-
ments the only effect of reducing the temperature from 1005°
C. to 780° C. would have been to shift the maximum towards
higher pressures, apart, of course, from the inevitable reduc-
tion of the value of the current at any pressure with reduced
temperature. Thus, as similar results were obtained by Gar-
rett in air, in this case also the difference between the curves
cannot be attributed to the difference in the gases and tem-
peratures used. Curve 4 shows some observations with
specially prepared pure aluminium phosphate in the tube.
As the current from this substance was only of the same order
as that given by the empty tube it is perhaps questionable
whether the observed effects were really caused by the salt.
The pressure-emission curves with barite were quite different
from those given by the chemically prepared BaSOi. In fact,
as tested by the tube method, the salts NagSO^, NagPO^,
BeSO^, BaSO^, barite, and the two specimens of aluminium
phosphate all gave rise to curves which were quite different
one from another. For a fuller account of these differences
the original paper must be consulted.

The behaviour of barite, which was examined in some de-
tail, exhibited a number of points of interest. In contrast
with most other salts the emission from this substance appeared
to increase with continued heating in a vacuum. The original
small value could be restored by heating the salt in air at
atmospheric pressure. This points to the conclusion that the
increased emission with continued heating is due to the forma-
tion of reduction products. This conclusion is strengthened
by the fact that the tubes usually smelt of sulphurated hydro-
gen after carrying out a test at low pressures, and by the fact
that the emission from the salt was found to be increased after
it had been heated in hydrogen. Still larger currents, how-
ever, were obtained during the heating in hydrogen, when the

THE EMISSION OF IONS BY HEATED SALTS 259

process of reduction was in active operation. There is thus
distinct evidence here of an emission of ions caused by chemi-
cal action. When the salt had been heated in air at atmos-
pheric pressure, and the pressure was changed so rapidly that
there was little chance of any alteration in the composition of
the salt taking place, the emission was practically independent
of the pressure of the air from 760 to 0'002 mm. Small
changes in the emission were actually observed in carrying
out such an experiment; but there are a number of subsidiary
causes which might fully account for them, and, in any event,
the changes which were observed were negligible compared
with those which occur when salts heated on a platinum strip
are treated similarly.

It is clear from these results that the emission of ions from
salts cannot be regarded as a function of the pressure of the
surrounding gas merely, at any rate without further specifica-
tion. The most striking differences between the results of the
experiments with the tube as compared with the strips are :
(l) The very varied individual behaviour of the salts when
tested by the tube method. With the strip method these dif-
ferences disappear and are replaced by a definite type of curve
with one maximum. This behaviour is shown by all the salts
and all the gases which have been tested. On account of the
very varied chemical characteristics of the gases used, this uni-
formity points to a physical and not to a chemical pheno-
menon, so far as the action between the gas and the salt
influences the emission. This physical effect of the gas must
be one which is present when the salt is heated by the strip
method but not when the tube method is used. (2) With
the strips the emission is very sensitive to a small increase
of gas pressure at low pressures. In the tube experiments
this sensitiveness is not observed. With some salts the emis-
sion increases a little with rising pressure, with others it
diminishes.

A large number of the facts can be brought into agreement
if one assumes that the emission is conditioned partly or en-
tirely by an interaction between the hot electrode and a vapour
given off by the salt. At a low pressure, in the strip experi-

17*

2 6o EMISSION OF ELECTRICITY FROM HOT BODIES

ments, such a vapour would easily diffuse away from the hot
electrode. There would be no corresponding opportunity with
the heated tube. If gas were admitted in the strip experi-
ments this diffusion would be prevented and the vapour would
be thrown back on to the strip ; so that up to a certain point
there would be observed a rapid increase of emission with ris-
ing pressure. The cause of the falling off in the emission at
higher pressures is less clearly indicated. It seems most likely
to arise from the cooling of the salt surface by the gas ; so
that the temperature of the surface of the salt diminishes with
rising pressure when the temperature of the underlying strip
is kept constant. In this way the amount of vapour available
for the process which causes the emission of ions would fall off
as the pressure rises. There are a number of other causes
which might give rise to a similar effect, so that it is, perhaps,
undesirable to lay too much stress on this particular explana-
tion.

The foregoing explanation of the increase of current with
gas pressure observed in the strip experiments is confirmed by
the occurrence of a phenomenon which was frequently noticed
in the tube experiments at low pressures. On letting in more
gas the immediate response of the emission was always in the
direction of lower values followed by a gradual adjustment to
the steady value characterizing the new pressure. On dimin-
ishing the pressure a similar, but less marked, set of changes
in the contrary direction was observed. On the explanation re-
ferred to, the immediate effect of letting in more gas would be
to compress the vapours into the bottom of the tube, reduce
the amount of vapour in contact with the hot platinum, and
so diminish the current. The subsequent recovery would be
due to the diffusion of the vapours into the fresh, gas. The
contrary effect on reducing the pressure may be accounted for
on similar lines.

There is one very important point which has not, so far,
been mentioned in discussing these effects. We shall see in
the next section that the positive ions emitted from heated
salts, even in an atmosphere of gas, appear to consist of charged
atoms of some metal present in the salts. There is no indica-

THE EMtSSlOht OP' IONS B V HE A TED SALTS 2 6 1

tion of the occurrence of positive ions whose electric atomic
weights have values corresponding to those of the atoms or
molecules of the surrounding gases, at any rate as a general
feature of the phenomena. Thus the effect of gases on the
emission of ions from salts must be an indirect one. It is not
a process involving ionization of the gas.

As regards the very varied curves given by the different
salts when tested by the tube method, all that it seems desir-
able to say at present is that they are probably symptomatic
of the chemical changes occurring. The emission at any pres-
sure must depend on the chemical composition of the salts and
salt vapours present. This is changed by altering the pres-
sure of the gas and the emission follows the pressure changes
in a corresponding way. The complexity of the curves is to
be expected, as the reactions are known to be very involved.

Some peculiar phenomena displayed by the negative emis-
sion from calcium iodide (cf Chap. Ill, p. 92) which were ob-
served by the writer ^ after this salt had been allowed to stand
in the cold in air and in a vacuum may possibly be related to
those just discussed.

Specific Charge {elm) and Electric Atomic Weight
(M) OF the Ions.

The first experiments to measure ejin for the positive ions
from salts were made by Garrett 2 with aluminium phosphate,
using the method due to Thomson which is described on
p. 8. From these experiments Garrett concluded that about
10 per cent of the ions emitted had an electric atomic weight
equal to or less than that of hydrogen. This conclusion has
not been confirmed by experiments with aluminium phosphate
made by Davisson ' by another method (see below, p. 268).
In examining other salts also, the writer has frequently looked
for evidence of the presence of ions having values of M of this
order of magnitude without finding any. Although such ions
may for some reason at present unknown have carried part of
the current under the particular conditions of Garrett's experi-

> " Phil. Mag.," Vol. XXVI, p. 452 (1913).

» Ibid., Vol. XX, p. 582 (1910). »/Wd., p. 139 (1910).

262 EMISSION Op- ELECTRICITY FROM HOT BODIES

ment, it seems quite certain that they do not play an important
role, as a rule, in the emission of positive ions either from
aluminium phosphate in particular or from salts in general.

Measurements of the electric atomic weights of the positive
ions from the salts of the alkali metals have been made by the
writer ^ using the slit method described on p. 195. In the first
instance the sulphates of all the alkali metals, lithium, sodium,
potassium, rubidium, and caesium were examined. We have
seen that the values of ejm and M are determined by the hori-
zontal displacements, between the maximum points in the curves,
due to a reversal of the deflecting magnetic field. These
curves represent the proportion of the total number of emitted
ions which pass through the slit for different horizontal dis-
placements of the latter. In general, with specimens of salt
which are ordinarily regarded as " chemically" pure, it is found
that the nature of the displaced curves and the distance be-
tween the maxima depends on the time during which the salt
has been heated. This is well illustrated by the observed
behaviour of lithium sulphate. On first heating, the magneti-
cally displaced curves had a single maximum at the position
corresponding to M = 35-9. After heating for 12 hours
each displaced curve possessed two maxima although there
was only one in the undisplaced curve. This shows that two
kinds of ions were present which were deflected to different
extents by the magnetic field. The value of M for the least
deflected was found to be 41-8 whilst the outside maxima
gave M = 5-5. As the heating was continued the positions
of these maxima remained practically unchanged, but the
inner maxima became smaller and smaller with continued
heating. After 44 hours the inside maxima were inap-
preciable and the outer maxima gave M = 5-57. After 52
hours the conditions were much the same and a measurement
of M yielded the value 7*43. With further heating the outer
maxima disappeared gradually as the salt volatilized and a
new inner maximum appeared. After 70 hours' heating this
maximum was at the position corresponding to M = 20'6.
At this stage the currents are small and the emission has a
1" Phil. Mag.," Vol. XX, pp. 981, 999 (1910).

THE EMISSION OF IONS BY HEATED SALTS 263

value of M very near to that from a platinum strip which has
been heated for a long time (cf. p. 201).

In this experiment, although the ions which were first
emitted had a value of M near 40, the greater part of the
whole number of ions emitted during the whole experiment
had a value of M within the range 5*5 to 7*5. The values are
immediately explicable on the assumption that the ions given
off by Lij SO^ are atoms of the metal which have lost an elec-
tron and that the heavier ions are due to some adventitious
impurity. The atomic weights of lithium and potassium are
700 and 39* 10 respectively so that it is natural to attribute
the heavier ions to salts of potassium. The fact/ that the po-
tassium ions come off first is in agreement with the results of
experiments on flames, which show that the conductivities pro-
duced by equivalent weights of salts of different alkali metals
increase rapidly with the atomic weight of the metal. Thus
while potassium salts are present one would expect the emis-
sion due to them to mask that due to the lithium salt, even
though this might form the greater proportion of the salt dealt
with.

These experiments and innumerable others, some of which
will shortly be described, establish quite definitely the con-
clusion that the positive ions emitted by heated salts are charged
atoms of some metal. This metal is not necessarily a con-
stituent of the salt which appears to be under investigation,
but may arise from the presence of some impurity which has a
greater power of emitting positive ions.

The sulphates of the remaining alkali metals gave less evi-
dence of the presence of impurities than did that of lithium.
Thus the extreme variation of M for potassium sulphate was
found to be from 3 5*5 to 37-0 during 60 hours of heating. None
of the salts except lithium sulphate showed a double maximum
in the magnetic field, although sodium sulphate and caesium
sulphate both gave somewhat exceptional values on first heat-
ing. This may be due to the presence of foreign ions in in-
sufficient amount to give rise to a distinct maximum. The
initial values for sodium were rather high, indicating the
presence of potassium. The exceptional value for caesium rests

264 EMISSION- OP ELnCTRlClTV FROM HOT BODIES

only on one observation, and it is also uncertain owing to the
small deflexions given by the relatively heavy ions from this
substance. The completeness of the separation of the maxima
in the case of lithium is, of course, favoured by the large dis-
parity of atomic weights when compared with the other pairs
of metals, as well as by the relative amount of impurity already
alluded to.

The final values of efnt and of M which were deduced from
the positions of the maxima characteristic of the basic metal of
the salt under investigation are collected in the following
table :—

LL^SO^

NajSO^

K2SO4

RbjSO^
CSaS04

Substance.

Time Heated
(hours).

elm
(E.M. Units).

Actual
M,

Average

Value of

• . .

1760

5-5 ^

1735

5-57^

6-2

1300

7*43 J

413

23*4 1

430

22-51

22-5

439

22'0 j

439

22"oJ

261

37*0^

261

37'o

261

37-0

36-5

272

35*5

266

36-3

266

36*3^

—

lOI

IOI-8

95]

59-1

163 V

140

59-1

163J

Atomic
Weight.

7'00
23-0

39*0

85-5
132-8

All the corresponding numbers in the last two columns differ
by less than the possible experimental error, thus proving
that the ions are atoms of the basic metal which have lost one
electron. To be quite precise what is proved strictly is that
the ions are made up of n atoms which have lost n electrons ;
but it is extremely unlikely that n is different from unity. To
extend the proof tests were made with sodium fluoride and
sodium iodide as well as sodium sulphate. In each case the
value ofM agreed with the atomic weight of sodium to within
5 per cent, which is about the accuracy claimed for the method
used. Thus the acid constituent of the salt has no influence on
the nature of the ions emitted by the salts of the alkali metals.
Some salts of the alkaline earth metals have been examined
by the writer ^ and an exhaustive investigation of this group

1 •' Phil. Mag.," Vol. XXII, p. 669 (1911) ; Vol. XXVI, p. 452 (1913).

THE EMISSION OF IONS BY HEATED SALTS 265

has been made by Davisson,^ The measurements in each case
were made by the slit method. One of the most interesting
results of these experiments is that they afford no evidence of
the existence of positive ions consisting of atoms of the basic
metal which have lost two electrons; although since these
metals are divalent the possible occurrence of such ions is in-
dicated by electrolytic phenomena. For the sake of brevity
we shall denote an ion consisting of an atom which has lost
one electron by the symbol M^ where M is the chemical sym-
bol of the element. A divalent positive ion may be denoted
in a similar manner by M^^. The measured values of the
electric atomic weights demonstrate that positive ions having
the constitution Ba^ are given off when the following barium
salts are heated : BaSO^, BaCl2 and BaFj. Ions having the
constitution Sr^ have been shown to be emitted by the follow-
ing salts of strontium : SrS04, SrClg, SrFg, and Srig. In
some of these cases there was evidence of the presence of ions
having a value of M close to that for K+. These were prob-
ably due to contamination of the preparations by salts of
potassium. There is no mistaking the presence of the ions
Sr^ and Ba^, as the values of M for them are very different
from the values for K^ and Na^ which are the commonest
adventitious impurities.

The case of calcium is not so clear as the experiments are
not accurate enough to distinguish between the values of M
for Ca^ (4O'0 and K^. (39"i). The same uncertainty arises
in regard to magnesium where sodium may be an impurity.
The respective values here are Mg^ = 243 and Na = 23-0.
A careful consideration of the conditions which govern the
emission of the ions points to the conclusion that a consider-
able number of calcium salts emit Ca^ and that some mag-
nesium salts emit Mg^. No evidence of the existence of Ca^^
or Mg^^ has been found. The salts of beryllium which have
been examined have been found only to give ions with values
of M corresponding to K^ or Na^ or to a mixture of these
bodies.

The haloid salts of the metals of the zinc group furnish
1" Phil. Mag.," Vol. XXIII, pp. 121, 139 (1912).

S66 EMISSION OF ELBCTRIClTV FROM HOT BODIES

the only examples, which have so far come to light, of the
existence of polyvalent positive ions. The theoretical value
of M for Zn+ is 65-4 and for Zn^^ 327. Values of M close
to 65 have been obtained for the ions emitted from ZnSO^
and ZnClo, indicating that the ions from these salts are singly
charged atoms as in the cases already considered. The mean
value of M for the ions from ZnBrg on the other hand has
been found to be 50, and for Zx\\ when first heated, four de-
terminations by the quicker balance method gave values be-
tween 28*8 and 34-2. These results point to the conclusion

T/Me IN MINUTIS.

Fig. 32.

that the ions from the zinc haloids in general consist of a
mixture of Zn+ and Zn^^, the proportion of Zn^^ increasing
with the atomic weight of the haloid constituent. The
changes with the time which were noticed when a specimen of
cadmium iodide was heated and tested by the balance method
are shown in Fig. 32. The values of M are indicated on the
vertical scale and the duration of heating on the horizontal
scale. As the experiment progressed the emission at a con-
stant temperature diminished ; so that the temperature had
to be raised from time to time in order to obtain a convenient
current. The corresponding temperatures are also indicated

THE EMIS^IOtJ Ofi IONS BY HEATED SALTS 267

in the figure. The straight lines AB, CD, and EF indicate the
theoretical values of M for Cd^^, K and Na+. It will be
seen that the experimental values, which are denoted thus
X, jump successively from one of these lines to another. The
demarcation between the ions characteristic of the salt and
those due to impurities is not always so sharp as in this
particular example.

Very little has yet been done with salts of metals of
the other chemical groups. A test made with manganous
chloride (MnClg) by the balance method -gave an initial value
M = 33*9. The value of M rose to a maximum of about 80
in 65 minutes and then fell to 39 at the end of 90 minutes.
In this case it seems probable that a number of different kinds
of positive ions are emitted in succession and that the numbers
found are the average values of M for a mixture. The emission
has not been found to be persistent enough to enable measure-
ments to be made by the slit method so as to test the question
of homogeneity as well as to determine the value of M.

A considerable number of salts have been tested and
found to give evidence of the emission only of K^ or Na^ or
a mixture of these ions, arising presumably from contamina-
tion with alkaline salts as impurities. Among these may be
mentioned : ferric chloride (K^), aluminium phosphate (Na^
and K^), barium phosphate (K+), beryllium sulphate (K^)
and beryllium nitrate (Na^ and K^). The symbol in brackets
indicates the nature of the ions as deduced from the experi-
mental value of M.

The heavy negative ions emitted by certain haloid salts
have been described in Chapter III, p. 92. The value of
M indicates that these are atoms of the halogen constituent in
combination with a single negative electron.

The experiments under consideration have afforded no evid-
ence of the existence, in the positive emission from salts, of
any ions which are not charged metallic atoms, either of the
basic element of the salt or of one of the alkali metals present
as an impurity. We have seen in the previous section that
the emission of positive ions from hot salts may be greatly
increased at a constant temperature by the presence of a small

268 EMISSION OF ELECTRICITY EROM MOT BODIES

quantity of various gases under certain conditions. The
question arises as to whether the ions emitted in a dilute
gaseous atmosphere under such conditions are still metallic
atoms or whether atoms or molecules of the surrounding gas
do not now carry part of the current. This question has
been answered definitely in favour of the former alternative
by some important experiments made by Davisson.^ Using
the slit method the value of M was measured for the ions
given off by aluminium phosphate in hydrogen, air, and carbon
dioxide, and by calcium sulphate in air. In each case ex-
periments were made in a good vacuum and in the gases at
various low pressures. The values of M were found to be
independent of the nature and pressure of the gas until the
pressures became so high that the collisions of the ions with
the gas molecules caused serious deviations from the condi-
tions required by the theory of the method of measurement.
The limiting pressures were roughly : 005 mm. for CO2,
o*i2 mm. for air, and 1-4 mm. for hydrogen, in the case of
the Na^ ions given off by aluminium phosphate. The interfer-
ence of the gas increased with its density, as was to be ex-
pected, and there was no evidence of the existence of any other
effect of the gas on the value of M except that due to its
mechanical interference with the motion of the ions. In ac-
cordance with these principles also the effect of air in the case
of the Ca^ ions from CaSO^ was less than that observed with
the Na^ ions from aluminium phosphate, on account of the
greater mass of the calcium ions.

The curves obtained with aluminium phosphate in hydro-
gen at a pressure of about i millimetre are shown in Fig. 33.
The regularity and symmetry of these curves is strong evid-
ence as to the homogeneity of the ions. The arrows indicate
the positions where maxima should appear for ions having
values of M = I and M = 2 corresponding to H^ and (Hg)^
respectively. The absence of these maxima does not support
the conclusion drawn by Garrett which was referred to at the
beginning of this section. When salts are heated in a vacuum
there is usually an appreciable emission of gas. The spectrum

^ Loc. cit., p. 145.

THE EMISSION OF IONS BY HEATED SALTS 269

of this gas when an electrodeless discharge is passed through
it has been examined by Horton ^ in the case of aluminium
phosphate. All the lines except a few faint ones which were
unidentified were found to be attributable to either Hg, H, C,
or O. A spectroscopic examination of the gases evolved
by strontium chloride and strontium sulphate has been made
by Davisson.'^ In each case only mercury and carbon mon-
oxide lines were found. Davisson measured the value of M
for the carriers of the positive emission simultaneously with
the spectroscopic examination of the evolved gas. On first
heating SrSO^ the value of M was found to correspond to

1
1

jT /

___[

[__

Fig. 33.

K^. In all the other experiments the ions were found to
be Sr+. There was no indication of the existence of CO^
in any of the experiments. In another set of experiments
Davisson measured the positive thermionic emission and the
emission of gas from strontium chloride simultaneously. Both
emissions varied in a fairly regular way with the time, but in
an entirely independent manner, indicating that there was no
direct connexion between them.

The measurements of ejin and of M which have been de-
scribed in this section all refer to ions which are emitted from
salts by the action of heat alone, and regarding whose emission

» " Roy. Soc. Proc., A.," Vol. LXXXIV, p. 433 (igio).
•Loc. cit., p. 142.

2 70 EMISSION OF ELECTRICITY FROM HOT BODIES

the electric fields employed play only a secondary role. In addi-
tion it is necessary to mention that Gehrcke and Reichenheim ^
have measured the corresponding quantities for the anode rays
from various salted anodes, whilst Knipp ^ has examined the
nature of the ions in the canal rays from a Wehnelt cathode.
In both these cases it seems likely that the ions are liberated
as a result of the complicated electrical actions occurring and
that the effects are of a character somewhat different from that
of the phenomena contemplated in the rest of this book.

The Mobilities of Ions from Hot Salts.

Measurements of the mobilities of the ions, in air at at-
mospheric pressure, drawn away from the haloid salts of zinc
heated to a temperature of about 360° C. have been made by
Garrett and Willows.^ The method used was one originally
devised by McClelland.* The following values of the
mobility in cms. per sec. per volt cm. "^ were obtained for the
positive ions: — from ZnClg, 0*0062; from ZnBrg, 00059;
from Znig, O"0057. Somewhat variable values were obtained
with the negative ions, the average for ZnClg being about 0'02.
The values for the positive ions are about 1/200 of the mo-
bilities for X-ray ions in air at atmospheric pressure. This
indicates that the ions from salts are more complicated struc-
tures. Since the measurements of e/w and of M have shown
that the positive ions when originally emitted consist of atoms
which have lost either one or two electrons, it follows that the
ions tested in these experiments must have become loaded up
with uncharged matter. In all probability this consists for
the most part of condensed salt vapours. It is to be re-
membered that when the gas is in the tube in which the mo-
bilities are measured its temperature is much lower than when
it was in contact with the hot salt. The values for the mo-
bilities given above are similar to those found by McClelland ^
for the ions in gases drawn away from flames and incandescent
metals.

^ " Phys. Zeits.," Jahrg. 8, p. 724 {1907).

"^ " Phil. Mag.," Vol. XXII, p. ,^26 (1911).

s Ibid., Vol. VIII, p. 452 (1904).

* " Camb. Phil. Proc," Vol. X, p. 241 (1899). » Loc. cit.

THE EMISSION OF IONS B Y HE A TED SAL TS 271

A more complete investigation along similar lines has been
made by Moreau,^ using a large number of salts of the alkali
metals. The supply of salt was obtained by bubbling air
through solutions of various strengths. The air was then
allowed to pass through a red-hot porcelain tube in which the
salt became ionized. It then traversed the space between two
coaxial cylindrical electrodes between which varying potential
differences were maintained. When the stream of air flows at
a known uniform rate a knowledge of the dimensions of the
cylindrical electrodes and of the potential difference required
to drive all the ions of given sign to the central electrode is
sufficient to determine the mobility. The measurements of
the mobility were made after the air had travelled various dis-
tances from the hot porcelain tube ; so that the temperature
of the ionized air had dropped to various values between 1 5° C.
and l7o''C. The temperature of the tube in which the salt
was ionized was comparable with 1000° C. The concentrations
of the salt vapours were taken to be proportional to the
strengths of the solutions through which the air was made
to bubble. In these experiments there is, of course, a great
difference between the temperature at which the ions are
formed and that at which the various measurements are
made.

Under conditions similar to those indicated, Moreau ex-
amined several questions in addition to that of the dependence
of the mobility of the ions upon various factors. These ques-
tions include the relation between the quantity of ionization
and the concentration and temperature of the salt vapour, and
the rate of recombination of the ions at various low tempera-
tures. Several of the most important conclusions drawn by
Moreau from these experiments are enumerated in the follow-
ing list : —

I . The number of positive ions formed is equal to the
number of negative. [This conclusion involves the assumption
that the charges of the ions of opposite sign are equal ; strictly
speaking, the equality demonstrated by the experiments is be-

> " Ann. de Chimie et Phys.," June, 1906 ; " Bull, dc la Soc. Sci. tt M<d.
de rOuest," 15, No. 2 (1906) ; 15, No. 4 (1906).

2 72 EMISSION OF ELECTRICITY FROM HOT BODIES

tween the total quantities of electricity of either sign liberated
in the form of ions,]

2. Assuming that the concentration of the salt vapour is
proportional to that of the solution through which the air
bubbles, the experiments show that the number of positive
or negative ions formed varies as the square root of the con-
centration of the salt vapour for a given salt at a given tem-
perature.

3. The mobilities are different for the ions from different
salts, but with the same salt the mobility of the negative ions
is equal to that of the positive ions. The mobilities diminish
rapidly as the temperature of the stream of air is reduced.
With the salts of the alkali metals the mobility of the ions
varies inversely as the cube root of the concentration of the
salt vapour, for a given salt at a given temperature. These
statements are illustrated by the values of the mobilities in
cm. sec.~^ per volt cm."^ given in the following table: —

Potassium Bromide.

Temperature °C. 170 no 100 70 30 15

N 0*42 o"2o 0*15 o'og 0*046 o*oi2

N/4 0*72 o'35 0*27 o*i6 0*046 0*026

N/16 0*95 o*57 o*35 0*28 0*083 0*026

Potassium Nitrate.

Temperature °C. 170 no 100 70 30 15

N 0*28 0*14 o*o8 0*09 0*033 o*oi2

N/4 0*51 0*26 0*17 0*15 0*033 0*026

N/16 o*8o 0*40 0*33 o*2i 0*068 0*040

Rubidium Chloride.
Temperature °C. 170 — 100 70 30 15

N o*73 — 0*30 o*ig 0*084 0*021

The temperatures given are those of the air in the tube in
which the measurements were made. The row of figures op-
posite the letter N gives the mobilities for the ions from solu-
tions containing i gram molecule of the salt per litre, when
the temperature of the ionized vapour has fallen to the tem-
perature immediately above. The numbers opposite N/4 are
for a solution of 1/4 of this strength, and so on.

All the values of the mobilities are much smaller than
those for the ions in salted flames at a high temperature. The

THE EMISSION OF IONS B Y HE A TED SALTS 273

largest values are somewhat smaller than those for X-ray ions
at atmospheric pressure, and the smallest are larger than those
for the ions liberated during the oxidization of phosphorus.
The structure of the ions is thus intermediate between those
of these two classes. The variation of mobility with salt con-
centration is accounted for if one supposes that the ions are
loaded by the condensation of salt vapour on primitive ions
similar to those observed at very low pressures. We have
seen already that the properties of the ions from the haloid
salts of zinc agree with this hypothesis,

4. The coefficient a of recombination of the ions in the rela-
tively cold tube at some distance from the source of ionization
varies with temperature and salt concentration in the same way
as the mobility of the ions. Its value in fact is in agreement
with Langevin's formula

a = 47r(/^i + k^^ . . . (4)

when k-^ and k^ are the respective mobilities of the positive and
negative ions, here equal, and 6 is a proper fraction which
approaches unity at low temperatures.

5. The proportion of the salts which becomes ionized in-
creases rapidly with the temperature of the hot tube. From
the variation with temperature the energy required to ionize
one gram molecule of the salts KCl, KBr, KI, and KNOj ap-
pears to be about 60,000 calories. This value is of the same
order as that for the energy required to liberate the corres-
ponding number of ions in other cases of thermionic emission.

J. J. Thomson ^ has shown that when ionization takes place
in a thin layer close to one of two parallel plates, and the cur-
rents are small compared with the saturation value, the mo-
bility k of the ions may be obtained from the equation

k-'§J^ . , . . (5)

where V is the potential difference and / the distance between
the plates, and i is the current. This method has been used
by Garrett * to measure the mobilities of both positive and

^ " Conduction of Electricity through Gases," and ed., p. loi. Cambridge
(1906).

« " Phil. Mag.," Vol. XIII, p. 739 (1907).

:J74 EMISSION OF ELECTRICITY FROM HOT BODIES

negative ions from a number of salts at comparatively low
pressures. Some of the values of k thus obtained are given
in the following tables : —

Positive Ions in Air at 215° C.

Pressure P
(mms. of mercury).

15
20

25
30
35
40

45
50
55
60
70
90

Znh.
0-055

0*044

0-035

0-031

0*024

0-022

0-06
0-055

0-041

0-032
0-03
0-027
0-023

0-014
0-009

Pbla.

0-061
0-054

0-036

0-032

e-025

0-021

Cdls.
0-I2

0-087
0-073

0-06

0-05

ft xP
for Bils.

o-6o
0-S25

1-025

1-120
1-20
1-215
I-I5

0-980
0-810

Negative Ions in Air at 215° C.

Pressure P ^ni

(mms. of mercury). *'

1-05
0*56

10
20
30
35
40
50
60
80

0-42
0-35

Cal].
I'lo

0-56
0-33

0-22
0-2

Balj.

I-II
0-74

0-45

0-29

P xft
for Znli.

105

16-80

16-80
17-50

16-80

In these experiments the air in which the mobilities were
measured was at the same temperature as the salt which caused
the ionization. Unless the structure of the ions changes
with the pressure of the gas the product of the mobility by
the pressure should be independent of the pressure.^ The
last column in each table shows that this is approximately
satisfied except at the lowest pressures. The value of the
product is also of the same order of magnitude as that given
by the results of Garrett and Willow's experiments at atmos-
pheric pressure in corresponding cases. This shows that the
structure of the ions does not change much from atmospheric
pressure down to the pressures used in these experiments.
Garrett also found that the mobilities of the ions from Cdlj,
Znig, Pbig, and Bil^, at pressures between 10 and 25 mm.,

' Cf. Langevin, " Annales de Chim. et de Phys.," Vol. XXVII, p. 28 (1903) ;
O. W. Richardson, " Phil, Mag.," Vol. X, p. 177 (1905),

THE EMISSION OF IONS BY HEATED SALTS 275

increased rapidly as the temperature was increased from 185
to 215° C.

Experiments on the positive ions from aluminium phos-
phate in H2, CH^, air, CO2, and SO2 have been carried down
to much lower pressures by Todd,^ who measured the mobilities
by a modification of Langevin's'^ method. The values of the
product mobility x pressure given by these experiments are

^ ■

•

-CH^ ,

-Atr •

-C(W •

-Sfld

.^<,r,

•

^=^,^

•*--*

■ *~

t *

mm.

( 1

}

"s, ,

—

^^~-

» >

FlQ. 34.

exhibited by the curves in Fig. 34. The value of the product
is much larger than in the cases hitherto dealt with, probably
owing to the high temperature of the salt. With each gas
the product is practically constant at the higher pressures until
a certain critical pressure is reached, beyond which any further
reduction in the pressure causes an enormous increase in the
product. At these pressures the complex structures present

»•• Phil. Mag.." Vol. XXII. p. 791 (1911).
« " Annales de Chim. et de Phys.." Vol. XXVIII, p. 289 (1903).
18 ♦

276 EMISSION OF ELECTRICITY FROM HOT BODIES

at higher pressures evidently begin to dissociate. The values
of the product for the higher pressures were much the same
as those for X-ray ions in the corresponding gases at atmos-
pheric pressure. This agreement is probably fortuitous as the
values of the product, at any rate in other similar cases, de-
pend very much on the temperature of the gas and of the hot
salt. In the case of hydrogen there is an indication of ap-
proach to a new constant value of >^ x P at the lowest pres-
sures. Something of this sort is to be expected in all gases,
since the experiments described in the last section have shown
that the ions at these lower pressures are charged metallic
atoms ; so that there can be no further simplification in struc-
ture after this stage is reached. When water vapour was
present the values of the mobilities at low pressures were
found by Todd to be abnormal.

General Considerations.

The measurements of the electric atomic weights of the
positive ions emitted by heated salts abundantly prove that
the chief process concerned in the liberation of the ions con-
sists of a decomposition accompanied by the emission of
positively charged metallic atoms. This decomposition may
in different cases be that of the salt which forms the bulk of
the specimen under examination or that of some intermediate
body whose formation is accompanied by little or no emission,
or it may be that of some other salt, or of an intermediate
product arising from such salt, which is present as an impurity
in the specimen. The fact that complex changes of the emis-
sion with time have usually been observed when salts are
heated indicates that the intervention of an intermediate body
is a very general feature of the phenomena. The only case
in which there is no clear evidence of the existence of a time
factor is that of cadmium iodide in the absence of water vapour
which was studied by Kalandyk (p. 247). Even here it is not
absolutely certain that the whole of the initial rise was due to
the time necessary for the vapours to acquire a steady condition
in the space between the electrodes by diffusion ; but if this
is admitted it would appear that this case affords the only

THE EMISSION OF IONS B Y HE A TED SAL TS 277

example of the primary decomposition of the principal salt
merely which has so far been observed.

The important, and often predominant, part played by
impurities in the case of many salts has frequently been de-
monstrated. Among the most convincing cases that of
lithium sulphate discussed on p. 262 and that of aluminium
phosphate may be mentioned. Ordinary laboratory specimens
of " pure " aluminium phosphate have been found to vary
greatly in their emissive power. Thus Sir J. J, Thomson ^
found a specimen of this salt to be much more active than any
of a large number of other salts which he tried, whilst a speci-
men examined by the writer* did not appear to be remarkable
in this respect. In the belief that the activity of this sub-
stance is mainly attributable to the presence of alkaline im-
purities the writer ' prepared a specimen of aluminium
phosphate which one would expect to be comparatively free
from such contamination by using only the materials alu-
minium chloride, phosphorus pentoxide, ammonia, and water,
all of which had previously undergone distillation. As was
expected this preparation gave a very small positive emission.
After heating for a few minutes the emission was only about
Y^^th part of that from Kahlbaum's "pure" aluminium
phosphate under similar conditions. This result has been
confirmed by Horton.^ By measurements of the electric
atomic weights Davisson * has shown that the positive ions
given off by the commercial " pure " aluminium phosphate
consisted at first of K^. These were followed later by Na^.
which formed the bulk of the emission. The presence of
sodium was also detected by the spectroscope whilst its dis-
appearance when the emission has decayed to a small value
has been demonstrated in the same way by Horton.*^ The
emission from the specially pure aluminium phosphate after
heating for a short time is so small that it is perhaps question-
able whether it is not attributable to the underlying platinum,
although Davisson * obtained indications of A1+ by measur-

>" Camb. Phil. Proc.," Vol. XIV, p. 105 (1907).
»" Phil. Mag.," Vol. XXII, p. 698 (1911). » Loc. cit.

<"Roy. Soc. Proc., A.," Vol. LXXXVIII, p. 117 (1913).
»" Phil. Mag.," Vol. XXIII, p. 144 (1912).

Positive Emission

(i-io"*

Ampere).

I Min. 2 Mins,

10 Mins

. 50 Mins.

100 Mins.

i8*o 6*9

2-5

174

1-24

20I 87

5-6

3-6

3350 4430

5650

3750

1600

5220 5600

5270

2400

940

278 EMISSION OF ELECTRICITY FROM HOT BODIES

ing the atomic weight of the carriers. Another case which il-
lustrates the importance of looking out for the presence of
alkaline contaminants is that of cadmium iodide considered
on p, 266. Emissions which are conditioned mainly by the
presence of impurities are apt to decay much more rapidly
than those from substances like the involatile alkaline salts,
where the r61e played by impurities is of a subordinate char-
acter. This is well shown by the following table of the
currents from various substances, after heating for different
times at 1190° C, given by Horton : — ^

Substance. At Start.
Platinum .... 183
Pure aluminium phosphate 2040
Sodium phosphate . . 2550
Sodium pyrophosphate . 3380
Impure aluminium phos-
phate . . , 7560 3220 1450 250 59 32

In the foregoing treatment the increase of positive emission
with rising gas pressure which is observed when a number of
salts are heated on strips of metal has been attributed to a
mechanical action of the gas in interfering with the escape of
a volatile ionizable product from the neighbourhood of the hot
anode. In view of the complexity of the phenomena observed
in gaseous atmospheres, and since this suggestion offers only
a partial explanation of the observed facts, it seems desirable
very briefly to consider some of the other views which have
been put forward to account for this effect. Garrett ^ suggested
that the increased currents might be due to the action of neutral
doublets shot out from the salts in ionizing the gas through
which they passed. This view is subject, among other dis-
advantages, to one which is quite fatal. It fails to account
for the fact that the increased current observed when the salt
is positively charged is entirely absent when the salt is charged
negatively. At one time Horton ^ held the view, based on
the older values of the electric atomic weights for the positive
ions from hot metals, on the identity of the kinetic energy of
these ions with that of those emitted by aluminium phosphate,

1 Loc. cit. « " Phil. Mag.," Vol. XX, p. 573 (1910).

3 •' Roy. Soc. Proc, A„ " Vol. LXXXIV, p. 433 (1910).

THE EMISSION OF IONS BY HEATED SALTS 279

and on the detection of carbon and oxygen lines in the spectrum
of the gas evolved by heated aluminium phosphate, that the
ionization by salts consisted in the emission of carbon mon-
oxide molecules in the positively charged condition. Such
a position is, of course, untenable as a general account of the
emission of these ions, in view of the various determinations
of their electric atomic weights which have recently been re-
corded. Horton^ has since modified it so as to make the
gaseous ions carry only the additional current obtained on
increasing the pressure, and has concluded that the effect
is not a peculiar property of carbon monoxide but one which
is common to the various gases, hydrogen, air, carbon mon-
oxide, and carbon dioxide, which have been tested for it The
weak point of this position is that it does not account either
for the absence of the effect when the salts are heated in a
closed tube instead of on a strip, or for the experimental re-
sults obtained by Davisson which were described on p, 268.
These results have been criticized by Horton "^ on the grounds
that the experiments were made at temperatures so low that
the number of gaseous ions would be expected to be inap-
preciable, and that, in any event, when the pressure is raised
sufficiently for gaseous ionization to become effective the
method of measurement fails owing to the interference of the
gas molecules with the motion of the ions. The temperatures
of the experiments are not stated at all clearly in Davisson's
paper, but in many of them they were sufficiently high to
ensure, particularly in the case of hydrogen, the presence of
a sufficiently large additional emission due to the gas at
pressures so low that the method of measurement worked
satisfactorily. Moreover, the deviations at high pressures in
the apparent values of efm are exactly such as would be ex-
pected from the mechanical interference of the gas molecules,
and there is no indication of a specific influence of the gas on
the nature of the emitted ions. No doubt the point is an
extremely difficult one to decide with certainty, but it seems
to the writer that the balance of evidence is definitely against
the view that any considerable proportion even of the increased
1 " Roy. Soc. Proc, A.," Vol. LXXXVIII, p. 117 (1913). *Ibid.

28o EMISSION OF ELECTRICITY FROM HOT BODIES

emission observed when salts are heated on strips of metal in
a gaseous atmosphere at a low pressure is carried by charged
atoms or molecules of gas. There is no doubt that the positive
ions emitted by salts heated in a vacuum are not of this
character. It is quite possible, and indeed rather likely, that
when salts are heated in a gaseous atmosphere such ions are
liberated at the hot electrode to some extent, but the experi-
ments seem to show that if they exist they form an insignifi-
cant proportion of the total electrical emission. This part of
the current would be expected to be most important at high
pressures. Unfortunately it is only at low pressures that the
nature of the original ions is discoverable by direct experi-
ment.

The only experiments which have been made on the
kinetic energy of the ions emitted by hot salts are some by
F. C. Brown ^ who used ordinary " pure " aluminium phos-
phate. These show that the kinetic energy has the same
value and mode of distribution as that of the ions emitted by
other hot bodies.

A comparison of the results of this chapter with those de-
scribed in the two chapters preceding shows that there is an
exceedingly close parallelism between the emission of ions
from salts and from freshly heated metal wires. This paral-
lelism is not merely one which affects the more general pheno-
mena which characterize the two emissions, such as the typical
relations between current and potential difference or current
and temperature, and the charges and kinetic energies of the
ions, but it is one which often extends in a very surprising
way into the minute details of the two groups of phenomena-
Thus the peculiar time changes when salts are first heated and
the changes in the currents from salts due to a sudden alteration
in the applied potential difference are very similar to effects
which have often been observed with newly heated metals.
In both cases, in the majority of instances, the ions emitted
possess electric atomic weights corresponding to potassium or
sodium. One might be tempted to infer from this that the

» " Phil. Mag.," Vol. XVIII, p. 663 (1909). ~

THE EMISSION OF IONS BY HEATED SALTS 281

effects exhibited by metals arise from alkaline saline impurities ;
but such a conclusion cannot be considered to rest on a sub-
stantial foundation since the alkaline elements if dissolved or
alloyed with the metals might give rise to effects similar to
those caused by their salts. The positive emission from fresh
wires is certainly not attributable to superficial saline impurities
merely, since the most drastic treatment of the surface with
acids, including hydrofluoric acid, fails to remove it. Perhaps
the most noticeable difference between the emission from salts
and that from fresh metals is the absence in the latter case of the
response of current to change of pressure observed when salts
are heated on metal strips. This would be expected if the
alkaline atoms are completely ionized when emitted from metals,
and, of course, the difference could be accounted for in a
number of other ways. A surprising feature which the two
groups of phenomena have in common is the way in which ions
whose electric atomic weights correspond to K^ and Na+ turn
up when the treatment would have led one to anticipate ions
derived from one of the commoner gases.

So far as the relative efficiency of different salts in emitting
ions when they are heated is concerned, it is clear that the de-
gree of electropositiveness of the metallic constituent is a most
important factor. The writer's experience is that the salts of
the alkali metals are the leaders in this kind of activity, the
comparative efficiency of the metals within this group increas-
ing with increasing atomic weight. Superficially, at any rate,
it would appear that volatility in salts is a factor conducive to
ionization ; at any rate, a number of volatile salts, including
the haloid compounds of zinc and cadmium, are notable in
this respect. There does not appear to be any very close
connexion between the emission of positive ions from heated
salts and the ionization of these salts in aqueous solution, as
the solutions of the haloid salts of cadmium are distinguished
for their relatively low electrical conductivity. Salts like
aluminium phosphate which, though inactive if pure, generally
emit ions owing to the presence of some impurity often seem
to give rise to effects larger than would be expected from the
nature and amount of the impurity present. It may be that

282 EMISSION OF ELECTRICITY FROM HOT BODIES

the activity of a given salt is increased, if equal quantities are
compared, when a given amount of it is disseminated through-
out a relatively large quantity of an inactive diluent. Such
an effect would be similar to the effect of mixtures of salts in
facilitating phosphorescence.

CHAPTER IX.

IONIZATION AND CHEMICAL ACTION.

The difficulty, already alluded to, which frequently occurs
when we attempt to discriminate between chemical and ther-
mal action as the cause of ionization, suggests the propriety of
closing this volume with a brief account of a number of inter-
esting cases of gaseous ionization whose origin has generally,
or at least frequently, been assigned to chemical action. Such
phenomena have been known for over a century. Pouillet,^
for example, observed that the air in the neighbourhood of a
burning carbon rod acquired a positive charge whilst the rod
itself became negatively charged. A jet of burning hydrogen
was also found to be negatively charged, the surrounding air
being positively charged. Similar effects with burning coal
were recorded by Lavoisier and Laplace.'^ It seems likely that
these effects are due to the high temperature of the materials
rather than to the chemical actions taking place, although it is
perhaps rash to hazard such an opinion in default of a more
accurate investigation, such as the phenomena seem to merit.

Lavoisier and Laplace' also discovered that when iron is
dissolved in sulphuric acid the hydrogen evolved contains a
large excess of positive electrification. It has since been found
that the gases liberated by chemical or electrolytic action from
solutions almost invariably exhibit electrical conductivity.
These effects have been investigated by Enwright,* Towns-

^" Pogg. Ann.," Vol. II, pp. 422, 426.
•••Phil. Trans.," 1782.

••' Mdmoires de 1' Academic des Sciences," 782.
«•• Phil. Mag.," (5), Vol. XXIX, p. 56 (1890).
283

284 EMISSION OF ELECTRICITY FROM HOT BODIES

end,^ Kosters,'' H. A. Wilson,^ Meissner,* Bloch,^ Reboul,® and
de Broglie and BrizardJ The ions present in these gases are
bodies of considerable size. Thus Townsend found that their
mobilities in an electric field were only about io~* of those of
Roentgen ray ions in air under similar conditions as to pres-
sure and temperature. When the gases liberated by elec-
trolysis were passed into a vessel containing water vapour, a
dense cloud was formed whose weight was proportional to the
charge in the gas. By measuring the rate of fall of such a
cloud under gravity, together with a knowledge of the weight
of the cloud and of the magnitude of the electric charge
present in it, Townsend was able to determine the charge e
of these ions. The value found was 5*1 x lo"^'' E.S.U. in
excellent agreement with the value found subsequently for the
corresponding quantity for gaseous ions from other sources.

In all these cases of the presence of ions in the gases liber-
ated by the electrolysis of liquids and by chemical actions in
the wet way, the effects are undoubtedly complicated by the
occurrence of ionization due to bubbling and splashing. In
fact, the recent experiments of Bloch * and of de Broglie and
Brizard " seem to show that the ions arise entirely from the
action of the bubbles of gas in bursting through the surface of
the liquid. Thus Bloch found that if the surface of the liquid
were covered with a layer of benzene or of a number of other
liquids, the conductivity of the liberated gas disappeared com-
pletely. Further information about the experiments which
have been made on the electrification caused by bubbling and
splashing may be found in J. J. Thomson's " Conduction of
Electricity through Gases," second edition, page 427, and in the
following papers : —

1 " Camb. Phil. Proc," Vol. IX, p. 345 (1897) ; " Phil. Mag.," (5), Vol. XLV,
p. 125 (1898) ; •' Camb. Phil. Proc," Vol. X, p. 52 (1899).

2«'Wied. Ann.," Vol. LXIX, p. 12 {1899).

8" Phil. Mag.," (5), Vol. XLV, p. 454 (1898).

*"Jahresber. fUr Chemie," 1863, p. 126.

6 " Ann. de Chimie et de P^ys.," (8), Vol. IV, p. 25 (1905) ; " C. R.," Vol.
CXLIX, p. 278 (1909) ; " C. R.," Vol. CL, pp. 694 and 969 (1910).

8 Ihid., Vol. CXLIX, p. no (1909) ; Vol. CLII, p. 1660 (19").

''Ihid., Vol, CXLIX, p. 924 (1909); Vol. CL, p. 916 (1910) ; Vol. CLII,
p. 136 (igii).

8/Jtd,, Vol. CL, p. 694 (1910). ^Ihid., p. 969 (1910).

IONIZATION AND CHEMICAL ACTION 285

Lenard, "Wied. Ann.," Vol. XLVI, p. 584 (1892); Lord
Kelvin, "Roy. Soc. Proc," Vol. LVII, p. 335 (1894); J. J.
Thomson, "Phil. Mag." (5), Vol. XXXVII, p. 341 (1894);
Lord Kelvin, Maclean and Gait, "Phil. Trans., A." (1898);
Kosters, "Wied. Ann.," Vol. XLIX, p. 12 (1899) ; Kaehler,
"Ann. der Phys.," Vol. XII, p. 11 19 (1903); Aselmann,
"Ann. der Phys.," Vol. XIX, p. 960 (1906).

Air which has been drawn over phosphorus is capable of
discharging both positively and negatively electrified con-
ductors. This was first noticed by Mattenci.^ The pheno-
menon has since been investigated by Naccari,^ Elster and
Geitel,' Shelford Bidwell,* Barus,*^ Schmidt,' Harms,^ Goekel «
and Bloch.* Barus noticed that the phosphorized air very
readily formed clouds in a moist atmosphere. Both Bloch and
Harms found that the currents through phosphorized air could
be saturated if sufficiently large electromotive forces were ap-
plied. Bloch determined the mobility and the coefficient of
recombination of the ions and found that both these quantities
were only about one-thousandth part of the corresponding
quantities for X-ray ions. The ions in phosphorized air are
thus comparatively large structures and are probably loaded up
with the compounds of phosphorus formed during the reaction.
Both Bloch and Harms found that the number of ions formed
was small compared with the number of molecules of oxygen
which combined with the phosphorus. Barus showed that no
ions are formed when chemically inactive gases such as hy-
drogen are passed over phosphorus, and Elster and Geitel
showed that the ionization which occurs when air is passed
over heated sulphur is small compared with that which arises
during the slow oxidation of phosphorus. These experiments
show that the ionization of phosphorized air is intimately con-

1 " Encyclopaedia Britt.," Vol. VIII, p. 622 (1855 edition).

«•' Atti della Scienzi de Torino," Vol. XXV, p. 252 (1890).

»" Wied. Ann.," Vol. XXXIX, p. 321 (1890).

"•" Nature," Vol. XLIX, p. ai2 (1893).

'" Experiments with Ionized Air," by C. Barus. Washington, 1901.

•" Ann. der Phys.," Vol. X, p. 704 (1903).

■"' Physik. Zeits.," 3 Jahrg., p. iii (1902).

'Ibid., 4 Jahrg. (1903).

» " Ann. de Chimie et de Physique," (8), Vol. IV, p. 25 (1905).

286 EMISSION OF ELECTRICITY FROM HOT BODIES

nected with the chemical action and is probably directly
caused by it. However, the slow oxidation of phosphorus is
exceptional when compared with most chemical reactions at
low temperatures, inasmuch as it is accompanied by the emis-
sion of light. It seems probable that both the ionization and
the emission of light are direct and simultaneous consequences
of the chemical reaction, but the possibility that the ionization
is an indirect photoelectric effect due to the action of the light
emitted does not seem to be altogether excluded.

Another case of ionization, apparently caused by chemical
action, in which phosphorus takes part has been observed by
the writer.^ At about 600° C. platinum reacts energetically
with phosphorus vapour. During the occurrence of the re-
action the platinum emits positive but not negative ions.
After platinum has been left cold in contact with phosphorus
vapour, a vigorous emission of positive ions takes place when
the metal is heated subsequently. This decays at constant
temperature like the positive emission from new wires. Over-
heating the wire was found to reduce the emission at the pre-
vious temperature temporarily. There was some recovery at
constant temperature from the reduction due to overheating
which was subsequently followed by the general decay at
constant temperature already referred to. These phenomena
suggest that the emission involves two distinct processes
whose rates are altered to different extents when the tempera-
ture is changed. Increasing the temperature appears to re-
duce the quantity of the substance which immediately gives
rise to the emission of the ions without destroying the parent
substance to an equal extent. Similar changes due to sudden
disturbances of the temperature have been found to character-
ize the emission of ions from heated salts (see p. 249). In
some cases, although not invariably, the effect shown by salts
is in the opposite sense to that just referred to. Thus when
sodium phosphate or sodium sulphate was overheated, the
emission at the original lower temperature was found tem-
porarily to be increased.

iQ. W. Richardson, " Phil, Mag,," (6), Vol. IX, p. 407 (1905).

IONIZATION AND CHEMICAL ACTION 287

The ionization, discovered by Le Bon,^ which accompanies
the hydration and dehydration of certain crystals has fre-
quently been attributed to chemical action. The case which
has attracted most attention is that of quinine sulphate. This
substance, when allowed to cool after heating to a certain
high temperature, phosphoresces and causes the surrounding
gas to become conducting. Miss Gates'' showed that the
ionization was not caused by rays capable of penetrating the
thinnest aluminium foil. She also found that the current from
the salt was greater when it was positively than when it was
negatively charged and that the hydration of a given amount
of salt caused a greater conductivity than the dehydration.
These results were confirmed by Kalaehne,^ who concluded, in
addition, that the hydration of a given amount of the salt at a
fixed temperature liberated a constant quantity of electricity
independently of the rate of hydration, although the actual
instantaneous currents depend very considerably on the rate
of hydration. Recent experiments by de Broglie and Brizard *
suggest that in all these cases the ionization is only an indirect
effect of the absorption or liberation of water vapour. Both
the ionization and the luminosity observed with the sulphates
of quinine and cinchonine seem to be due to minute sparks
arising from the triboluminescence of the crystals of these
substances which takes place during hydration and dehydra-
tion. Although it is almost impossible to saturate the currents
from these substances the ions have a high coefficient of re-
combination. Both the ionization and the scintillations in-
crease as the pressure is reduced from atmospheric

We have seen (p. 202) that the evidence is quite con-
clusive that the large emission of positive ions from freshly
heated wires is not directly caused by chemical action between
the hot wires and surrounding gases. This is clear since the
effects are shown as well in a good vacuum as in a gaseous
atmosphere and by platinum when surrounded by gases to

1 " C. R.," Vol. CXXX, p. 891 (1900).

«" Phys. Rev.," Vol. XVIII, p. 135 (1904).

»" Ann. der Phys.," Vol. XVIII, p. 450 (1905).

«"C. R.," Vol. CLII, p. 136 (1911).

288 EMISSION OF ELECTRICITY FROM HOT BODIES

which it is beh'eved to be chemically indifferent as by other
metals when heated in various gases with which they react
energetically. Indeed Strutt's experiments (p. i88) led him
to the conclusion that oxidation and reduction by gases were
unfavourable to the emission rather than otherwise. These
facts do not preclude the hypothesis that this emission is a
direct consequence of chemical reactions affecting alkaline
contaminants present in the metals. In fact the changes in
the emission with time at constant temperature and after
sudden changes in such factors as the temperature and volt-
age which govern the equilibrium conditions definitely suggest
that this emission is affected, directly or indirectly, by chem-
ical changes. On the other hand, everything points to such
changes being of an obscure character and nothing is de-
finitely known either as to what the chemical changes are or
as to the way in which they affect the emission.

The results referred to do not prove that an emission of
ions may not occur as a consequence of chemical action be-
tween metals and surrounding gases. They only show that
effects of this kind, such as have so far been looked for, are
small in comparison with the large positive emission from new
wires. There is in fact quite definite experimental evidence
which, on a superficial examination at any rate, suggests that
the emission of ions can occur as a direct result of chemical
action between metals and surrounding gases. Thus Cam-
petti ^ found an emission of positive ions when copper com-
bines with oxygen or chlorine. The emission during the
oxidation of copper has been confirmed by Klemensiewicz,^
who showed that it was small compared with the initial effect.
He also found a similar effect when oxidized copper was re-
duced in hydrogen. The oxidation and subsequent reduction
of both tungsten and iron wires were also examined. Tung-
sten gave larger and iron much smaller effects than copper.
Klemensiewicz also investigated the reversible oxidation and
deoxidation of palladium and iridium, but was unable to detect
the emission of either positive or negative ions. It is neces-

1 " Atti Torino," Vol. XLII ; " N. Cim.," (5), Vol. XIII, p. 183 (1907).
""Ann. der Physik," (4), Vol. XXXVI, p. 805 (1911).

IONIZATION AND CHEMICAL ACTION 289

sary to be rather cautious in the interpretation of the results
of these experiments. In the writer's opinion it is not certain
that the obvious conclusion that the emission is a direct con-
sequence of the chemical action is the correct one. We have
seen that it is often quite difficult to get rid of the last traces
of the " initial emission," and even when this appears to have
been accomplished what seem to be quite trivial changes in the
conditions of the experiment will frequently revive the emit-
ting substance to a considerable extent (see p. 185). Thus to
make sure that the effects under discussion are really direct
chemical effects it is at least necessary to make sure that the
emission can be repeatedly obtained from the same material
without diminution, under given conditions. So far this test
does not seem to have been made.

We have seen (p. 222) that the steady positive emission
from platinum in an atmosphere of various gases undergoes
a temporary increase when the composition of the gas is
changed. If this increase were confined to cases in which the
gases interchanged had considerable chemical affinity for each
other, like oxygen and hydrogen, one would be tempted to
attribute it to a reaction between the gases in the surface
layers of the metal. Such a view seems impossible, however,
when we recollect that this effect has been observed when the
chemically inert gas helium is introduced.^ It would be in-
teresting to see if the increase occurred if pure helium were
replaced by pure argon or vice versa.

The part played by chemical action in connexion with the
ionization from hot salts has already been considered at some
length in chapter viii. , and there does not seem to be any-
thing to add to the discussion there given. In fact it is diffi-
cult to advance beyond the generalities already discussed,
since there is no definite information either as to what the
chemical reactions in question are, or as to how they affect
the ionization. The action of hydrogen on BaS04 considered
on p. 259 appears to a certain extent to furnish an exception
to this statement.

1 Richardson, " Phil. Trans., A.," Vol. CCVII, p. i (1906).
19

290 EMISSION OF ELECTRICITY FROM HOT BODIES

Emission of Electrons under the Influence of
Chemical Action.

The effects considered so far are noteworthy in two re-
spects. In the first place, the emitted ions are of atomic or
greater magnitude. There is no evidence of the emission of
electrons as a result of any of these actions. In fact, in nearly
every case in which the chemical origin of the ionization is
not extremely doubtful, only positive ions are emitted. In
the second place, we have seen that it is very questionable
whether many of these effects can be considered a direct re-
sult of chemical action at all. The cases in which the con-
nexion between ionization and chemical action appears to be
most intimate are furnished by the oxidation of phosphorus,
the action of phosphorus on platinum and the emission of ions
from heated salts. Certain types of chemical action resulting
in the liberation of electrons were first examined by Reboul ^
who investigated the following reactions : the oxidation of
amalgamated aluminium and of sodium and potassium by
moist air, the action of HgS on silver and on the alkali metals,
the action of CO2 on the alkalies and that of nitrous fumes on
copper. In all these cases ionization was observed when the
various reagents were attacked at the ordinary laboratory tem-
perature by the gases referred to, and in most cases more nega-
tive than positive ions were apparently emitted. In some of
these cases it is doubtful whether ionization occurs unless the
reaction is allowed to proceed with sufficient vigour to raise
the temperature considerably, or until it has gone on long
enough to form a layer of the products of the reaction over
the surface of the liquid or solid reagent. Thus some of the
effects observed are probably to be attributed to thermal emis-
sion or to electrical effects arising from bubbling in, or fracture
of, the layer in question.

Experiments which are not open to these objections, or at
least not obviously open to them, have been made by Haber
and Just.^ These authors investigated the action of one or

1 " C. R.," Vol. CXLIX, p. no (1909) ; Vol. CLII, p. 1660 (1911).
""Ann. der Phys.," Vol. XXX, p. 411 (1909); ihid., Vol. XXXVI. p. 308
(1911); "Zeits. f. Elektrochemie," Vol. XVI, p. 275 (1910).

IONIZATION AND CHEMICAL ACTION 291

more of the following gases or vapours, viz. : HjO, COClj,
CSClj, HCl, O3, Clj, Brj and Ij on various dilute amalgams
of the alkali metals, on caesium and on the liquid alloy of
sodium and potassium. The experiments were made by al-
lowing a fine stream or jet of the liquid reagent to flow into
a dilute atmosphere of the gas. The current was then
measured which passed from the jet to a surrounding cylindri-
cal electrode under various conditions. Many of the experi-
ments were made with the atmosphere of gas or vapour at a
very low pressure and the jet or stream of drops was made to
flow so fast that no observable tarnishing of the metal surface
could be detected. The thickness of the layer of salt formed
on one of the drops in an atmosphere of bromine in which an
energetic electrical emission occurred is estimated by the
authors as 3 x io~^ cm. It was thus not more than a few
molecules thick.

All the reactions referred to caused an emission of nega-
tive electricity from the metal but there was no positive
emission when the reactions occurred at room temperatures.
Experiments with the alloy of sodium and potassium at low
pressures showed that the current was stopped by a magnetic
field ; thus proving that the carriers of the discharge when
first liberated from the reacting metal are electrons. This ef-
fect of a magnetic field disappears at higher pressures, prob-
ably owing to the electrons combining with the molecules of
the gas. No emission from a jet of sodium potassium alloy
could be detected in an atmosphere of hydrogen or of nitrogen.
This result is not in agreement with a previous observation by
J. J. Thomson ^ who found an emission of electrons when hy-
drogen was admitted to the alloy of sodium and potassium.
The discrepancy could be reconciled if the hydrogen used by
Thomson were not entirely free from moisture. In many of
these cases the number of electrons emitted is very consider-
able in proportion to the amount of chemical action occurring.
In a particular case in which the alloy of sodium and potassium
was attacked by carbonyl chloride Haber and Just estimate
that one electron was emitted for every 1600 molecules of salt

1 " Phil. Mag." (6), Vol. X, p. 584 (1905).
19*

2 92 EMISSION OF ELECTRICITY FROM HOT BODIES

formed, approximately. The negative ions given off by the
amalgams of the alkali metals are apparently not electrons, as
the currents from these bodies were unaffected by a magnetic
field. In some of the reactions the electrons were found to be
emitted with sufficient kinetic energy to charge up the neigh-
bouring silver electrode even when they had to travel against
a small opposing electric field. Thus with COCI2 and NaK
alloy, the silver plate was found to charge up by amounts
varying from 07 to i*2 volts negative to the alloy. When
iodine reacted with the alloy, however, at least i -3 volts ac-
celerating potential difference was necessary to obtain an ap-
preciable current. In the case of caesium the corresponding
energies were somewhat greater in every case. Thus with
COCI2 the electrode charged up to - i 6 volts, with Brj to
- I 'O volt, and with iodine an accelerating potential differ-
ence of only 0"4 volt was necessary to detect the emission.

The maximum potentials obtained in the way just indi-
cated do not, unfortunately, enable us to deduce the maximum
kinetic energies with which the electrons are liberated by the
chemical action, as no attempt has been made in the experi-
ments referred to to correct for the effect of the contact dif-
ference of potential between the emitting metal and the
receiving electrode. This contact difference of potential causes
an electric field which affects the motion of the electrons in the
space between the electrodes, but it does not affect the instru-
ments used to measure the potential difference between the
electrodes during the experiments. The allowance to be made
for this is uncertain. Sodium potassium alloy is several volts
electropositive to clean silver, and if this full potential differ-
ence were operative possibly as much as 3 volts would have
to be added to the numbers given above. On this assumption
the maximum emission energies in equivalent volts would be
as follows : For Na K alloy and COClg from 37 to 4*2, Na K
alloy and Brg about 3*0, Na K alloy and \ 17, Cs and COClg
46, Cs and Brj 4*0, and Cs and Ij 26. On the other hand if
the silver had been splashed with the alloy, a not impossible
contingency in experiments of this character, the effective con-
tact potential difference might lie anywhere between the full

IONIZATION AND CHEMICAL ACTION 293

value and zero. Thus all it seems legitimate to assume from
these numbers is that the maximum kinetic energy of the
electrons liberated by the action of COClj on sodium potassium
alloy lies between the limits 07 and 4*2 equivalent volts, with
a similar possible range of uncertainty in the values for the
other reactions.

An attempt to remedy this deficiency has recently been
made by the writer. Whilst the experiments are not yet
completed the results obtained are of interest from several
points of view and throw considerable light on the phenomena
under discussion. In these experiments the sodium potassium
alloy was forced out of a narrow orifice at the centre of a
copper sphere of about 7 cms. diameter. The drops fell once
every five seconds, approximately, and their maximum dia-
meter was about 4 mms. Measurements of the electron
currents from the drops to the copper sphere were made
under various accelerating and retarding potential differences
in atmospheres of air, water vapour and carbonyl chloride at
various pressures from 02 mm. to O'ooi mm. or less. No
emission of electrons was observed in dry air. The carbonyl
chloride was admitted to the apparatus from a small tube
maintained at about - 120° C. The curve AFHG in Fig. 35
represents the currents to the copper cylinder under different
potentials in this vapour. In the particular experiment which
gave this curve the carbon monoxide formed was allowed to
accumulate in the apparatus and at the end the pressure had
risen from o*002 to 0-22 mm. as shown by the McLeod gauge.
The presence of this indifferent gas does not, however, appear
to affect the current-RM.F. curves much, as practically the
same curve was obtained when a much smaller quantity of
vapour was used and the pressure shown on the McLeod
gauge was 0'002 mm. both at the beginning and at the end
of the experiment. In both cases there was no appreciable
current until an accelerating potential difference of 1*5 volts
was applied as measured by the voltmeter. The variation of
current with accelerating potential is seen to be nearly linear
from about 2 to about 5*5 volts, after which the rate of increase
falls off. Raising the potential from 8 to 20 volts only in-

294 EMISSION OF ELECTRICITY FROM HOT BODIES

creased the current about 15 per cent. Immediately before
the curve AFHG was taken and just after a similar curve had
been obtained at a total gas pressure as indicated on the
McLeod gauge of less than 0*002 mm., whilst there was still
some active gas in the apparatus but not enough to generate
a large current by chemical action, the photoelectric currents
due to the violet mercury line X = 4358*3 were investigated.
These gave the current-electromotive force curve AKHL.

-2 101234567

Accelerating Potential (Volts).

Fig. 35.

These data were obtained with a little carbonyl chloride in the
apparatus and under conditions which gave a curve for the
chemical effect practically identical with AFHG. It is thus to
be presumed that the surfaces were in substantially the same
condition in the two cases and that there would be no change
in the contact electromotive force in the interval.

Now the photoelectric curve AKHL is quite different from
the photoelectric curve for a clean surface of an alkali metal
in an inactive gas at a very low pressure such as was used in
the experiments. The latter curve would be given by AKO MN
and can be constructed from the principles established by the

IONIZATION AND CHEMICAL ACTION 295

writer and Dr. K. T. Compton.^ The point M is determined by
the fact that the alloy (under the conditions which led to the
curve KHL) gave no photoelectric emission with the orange
mercury lines whereas a small emission was observed with the
green line. The horizontal distance 6V between K and M
is thus given by the relation eSV = /^(z/k - i^m) where h is
Planck's constant, vk the frequency of the violet line, and vm
that of the green line. This makes 8V equal to 0'8 volt

It is at once seen that the actual photoelectric curve KHL
resembles the chemical action curve FHG much more than it
does the normal photoelectric curve KOM. It is almost cer-
tain that the difference between the photoelectric curves KHL
and KOM is caused by the electrons becoming entangled in
the layer of reaction products at the surface of the alloy in
the former case and not in the latter. On this view the
similarity between KHL and FHG is to be attributed to a
similar action of the layer of products in the case of chemical
emission also. On account of this layer many of the electrons
will only be able to escape if they are helped out by an ex-
ternal accelerating field, thus accounting for the slow rise of
KHL and FHG as compared with KOM. If these supposi-
tions are correct FHG cannot be regarded as giving a true re-
presentation of the distribution of energy among the electrons
as they are actually emitted by the chemical action, the main
features of the curve being attributable rather to the deflect-
ing and retarding influence of the molecules in the layer of
products at the surface.

On the other hand it is probable that some of the elec-
trons will be able to get through such thin layers without any
appreciable loss of velocity ; so that it is to be expected that
the point F will truly correspond to the electrons which are
emitted with the greatest energy. The point M corresponds
to an emission with zero velocity since it corresponds to the
least frequency which is capable of exciting the photoelectric
emission. Thus the kinetic energy of the electrons emitted by
the action of COCI, on the alloy will be measured, in equiv-

»0. W. Richardson and K. T. Compton, «' Phil. Mag.," Vol. XXIV, p. 575
(191a).

296 EMISSION OF ELECTRICITY FROM HOT BODIES

alent volts, by the horizontal distance between F and M,
This leads to the value 2-4 volts. If there is any loss of
maximum velocity due to absorption of kinetic energy in the
layer the true value would be greater than this. On the other
hand there does not appear to be any cause which would
make it less; so that 2-4 equivalent volts can probably be re-
lied upon as an inferior limit to the value of this energy.
Preliminary experiments with water vapour point to a con-
siderably lower value for the kinetic energy of the electrons
emitted when the alloy is attacked by this reagent.

The curve ABDE represents the relation between current
and potential difference for the electrons emitted from a small
loop of hot platinum wire placed at the centre of the same
evacuated copper sphere. The curve ABCN represents the
theoretical relation between current and electromotive force
calculated by the principles laid down in chapter v., on
the assumption that the emitted electrons have the distribution
of energy given by Maxwell's law for the molecules of a gas
»t the temperature of the metal. Below B the agreement
between the theoretical and experimental values is accurate,
above B the difference can be adequately accounted for by the
mutual repulsion of the electrons, the effect of the magnetic
field of the heating current, interference by gas molecules and
other causes. If there were no change in the surface of the
copper sphere between the two experiments, the distance CM
should measure the contact difference of potential between
platinum and sodium potassium alloy, which should therefore
be about 3*4 volts. A calculation, according to the photo-
electric method already utilized, based on the minimum fre-
quency of the light necessary to excite an emission of electrons
from platinum on the one hand, and from the alloy (corre-
sponding to the point M) on the other, gives for this contact
potential difference the value 2*5 volts. The difference between
these two estimates may, however, be due to a difference in
the contact potential of the copper in the different atmospheres
of gas present in the two experiments,

A comparison of ABDE with AFHG is instructive. In
these cases at any rate it is clear that the current electromotive

IONIZATION AND CHEMICAL ACTION 297

force curves for electrons emitted by thermionic and by chemical
action are quite different. If this difference is general we are
furnished with a simple criterion for distinguishing between
thermionic and chemical emission. It is hardly necessary to
point out that the experiments which have so far been made
are inadequate to establish the generality of the difference re-
ferred to.

If the foregoing minimum estimate, 2-4 equivalent volts, for
the minimum value of the maximum kinetic energy of the elec-
trons is reliable, the experiments afford very strong support for
the view that the emission is a direct consequence of the chemi-
cal action, and is not an indirect result depending, for example,
on thermionic emission due to local rise of temperature caused
by the heat generated at the surface of the metal by the re-
action. In the latter case the distribution of energy among
the emitted electrons is determined by the consequences of
Maxwell's law for the temperature in question. The distribu-
tion given by this law is given, at 1500° absolute, by shifting
the curve ABC 0*32 volts to the left, so as to make the point
C lie over the zero on the voltage axis. It is at once seen
from the curve that the proportion of the electrons whose
energy exceeds two volts at this temperature is quite insigni-
ficant and negligible compared with the proportion — about
0*013 — indicated by the chemical curve FHG. The propor-
tion of the electrons which reach the sphere against a given
voltage after starting from a small region near the centre of
the sphere does, however, increase rapidly with rising tempera-
ture, being given at any absolute temperature T by the ex-
pression

(. + '^>-«, ...(■)

where k is Boltzmann's constant. According to this formula
the value o'oi3 would be reached at about 3800° K. This
temperature estimate would be raised very considerably if any
allowance were made for the resistance to the escape of the
electrons offered by the layer of reaction products such as we
have seen to be necessary to explain the general course of the
curve FHG. In any event it does not seem possible that so

298 EMISSION OF ELECTRICITY FROM HOT BODIES

high a temperature as 3800° K. can be attained locally at the
surface of a drop having the high thermal conductivity of the
alloy used. Haber and Just ^ have shown in a similar case
that the heat generated by the reaction is insufficient to raise
the temperature of the whole drop by as much as 2° C. The
curve FHG also appears to approach the voltage axis at a
finite angle indicating that there is a true maximum energy of
emission as in the case of photoelectric excitation by mono-
chromatic radiation and not an asymptotic approach to infinite
values such as is required by the expression (i). One cannot,
however, be quite certain of this point without more experi-
mental evidence than has so far been obtained.

Ionization of Gases by Heat.

There is no satisfactory a priori reason for expecting the
emission of ions at a high temperature to be confined to
matter in the solid and liquid states. It is, however, to be
anticipated that the thermal ionization of gases will only be
appreciable at the very highest temperatures, on account of the
large value of the ionization energy of gases. This quantity,
which has been measured by experiments on impact ionization
and on photoelectric action, has in all cases been found to
be much greater than the energy changes governing the
liberation of an ion in the phenomena which have been con-
sidered in this book. Up to the present there is no evidence
that purely thermal ionization has been observed in any of the
commoner gases. It seems likely that the ions present in
flames are to be attributed to the chemical actions occurring
rather than to the direct effect on the gases of the high tem-
perature which prevails. In the case of gases which have
been heated in the presence of metal electrodes there is no
certain evidence of the formation of ions except by interaction
between the gases and the electrodes or by emission from the
electrodes themselves.

A possible exception to these statements is furnished by
some experiments made by J. J. Thomson ^ on sodium vapour.

1 " Ann. der Phys.," Vol. XXXVI, p. 308 (1911).
« " Phil. Mag.," Vol. X, p. 584 (1905).

IONIZATION AND CHEMICAL ACTION 299

He found that when a current was made to pass between two
electrodes immersed in this vapour at about 300° C. metallic
sodium collected on the negative but not on the positive
electrode, indicating that sodium atoms in the vapour had
dissociated into an electron and a positive sodium ion. The
phenomenon could also be accounted for if the bombardment of
the positive electrode by electrons present made it hotter than
the negative electrode. The optical properties of sodium
vapour make it probable that it will dissociate, in the manner
indicated, below 1000° C. It is necessary to add that Thom-
son's experiments have been repeated by Fredenhagen *
without success ; so that it does not seem absolutely certain
that this phenomenon has yet been discovered.

It is necessary also to make an exception in favour of salt
vapours. In the case of cadmium iodide the evidence of the
occurrence of ionization of the vapour is quite definite (p. 238) ;
but, even in this case, the possibility that it arises by inter-
action with the electrodes is not absolutely excluded. In any
event the phenomena in salt vapours are probably complicated
by secondary chemical actions.

1 " Phys. Zeits.," Vol. XII, p. 398 (1911).

INDEX OF NAMES.

Armstrong, Pfce.
Arrhenius, 234.
Aselmann, 285.
Avogadro, 37, 152.

Baeyer, von, 49, 155.

Babr, Eva von, 24.

Barus, 285.

Beattie, 235.

Becquerel, 2, 5.

Bestelmeyer, 11, 91.

Bidwell, 285.

Bloch, 284-85.

Blondlot, 2.

Bohr, 32.

Boltzmann, 45, 96, 297.

Le Bon, 287.

Branly, 4.

Brizard, 284, 287.

de Broglie, 284, 287.

Brown, F. C, 141, 146, 157, 190-91,

280.
Brown, S. L., 42,

Campetti, 237, 288.

Canton, 2.

Cavallo, 2.

Child, 90.

Compton, K. T., 44, 295.

Cooke, 58, 166-68, 170-72.

Coolidge, Pfce.

Davisson, 195, 261, 265, 268-69, 277,

279.
Dawson, 234.
De Broglie, 284, 287.
Debye, 35.
De Forest, Pfce.
Deininger, 18-19, 54. 57. 60, 69, 73.

81-82, 131.
Drude, 25, 99.
Du Fay, 2.
Dushman, 11.
Du Tour, 2.

Edison, 4.

Elster, 2, 3, 4, 6, 179, 285.

Enwright, 283.

Faraday, 235.
Du Fay, 2.

Ferguson, Pfce.
Fleming, Pfce., 4.
De Forest, Pfce.
Franck, 24.

Fredenhagen, 12, 54, 76-77, 85-86, 89,
129-30, 132, 135, 299.

Gaede, 134.

Gait, 285,

Garrett, 186, 204, 206, 235-36, 241-43,

249, 251-53, 258, 261, .i68, 270, 273-

74. 278.
Gates, Miss, 287.
Gehrcke, 270.
Gehrts, 49,86
Geitel, 2, 3, 4, 6, 179, 285.
Germershausen, 87, 130.
Goekel, 285,
Guthrie, 2, 179.

Haber, 52, 77, 128-29, 132, 290-91,

298.
Hallwachs, 99.
Halsall, 9.
Marker, 17, 126.
Harms, 285.
Hechler, 236.
Hennings, 44.
Higgins, 127.
Van't Hoff, 50, 211.
Hopwood, 20.
Horton, 54, 69, 76, 81-82, 85-89, 130,

135, 204, 241, 244, 246, 249-50, 254-

56, 269, 277-79.
Hughes, 44.
Hulbirt, 198.
Hull, Pfce.

Jentzsch, 54, 80-84, 165-67, 170.

Jones, 247.

Joule, 173.

Just, 52, 77, 128-29, 132, 290-91, 298.

Kaehler, 285.
Kahlbaum, 277.
Kalaehne, 287.

Kalandyk, 237-38, 247, 251-52, 276.
Kaye, 126-27.

Keesom, 36. _

Kelvin, 285.

Klemensiewicz, 1S6, 203, 288.
300

INDEX OF NAMES

301

Knjpp, 270.
Kosters, 284-85.

Ladbnburo, 99.

Langevin, 273-75.

Langmuir, Pfcc, 11, 54-55i ^i. ^4. 69>

71, 74, 76, 100, 107, 117, 119. 125-

26, 130-31, 136-37. 170.
Laplace, 283.
Lavoisier, 283.
Le Bon, 287.
Lenard, 10, 285.
LeettT, 171, 184.
Liebreich, 86, 170-71.
Lilienfeld, 91-92.

McClelland, 5, 6, 20-22, 25, 71, 225,

270.
MacKay, Pfce.
Maclean, 285.

McLcod, 135, 183, 212, 293-94.
Martyn, 54, 87-88, 113-14.
Matteuci, 285.

140-164, 189-90, 192,

Maxwell, 34

296-97.
Meissner, 284,
Millikan, 44.
Moreau, 271.
Morse, 247.

Naccari, 285.

Nernst, 10, 54, 82, 85, 189.

Newall, Pfce.

NiCOl, 221.

Ohm, 2.

Owen, 9-10, 54, 82, 189.

Page, 44.
Parker, 54, 130-31.
Parnell, 221.
Partzsch, 99.
Pawlow, 24.
Peltier, 42, 109, 115.
Planck, 35, 98, 295.
Poisson, 61, 64.
Pouillet, 283.
Preece, 4.

237-38,

Priestley, 2.

Pring, 54. 95. 130-32-

Rbboul, 284, 290.
Reichenheim, 270.
Reisz, Pfce.
Riecke, 25.
Roentgen, 5, 6, 284.
Rogers, 97, 99-100.
Rubens, 99.
Rutherford, 225.

SCHLICHTER, 55, 68-69, 75-76.

Schmidt, 236, 241, 244-46, 248-51, 285.
Schneider, 167.

Schottky, 68, 155-56, 164, 192.
Sheard, 183, 228-29, 232-33,

241, 244-48.
Shclford Bidwell, 285.
Smith, K. K., 55, 59-60, 69, 71.
Smithells, 234.
Souder, 44.
Strutt, 188-89, 288.

Thomson, 5, 7-11, 22, 25-26, 32, 89-90,
95. 107. 194-95. 204, 206-7, 223-
24, 227, 234, 238-39, 261, 273,
277, 284-85, 291, 298-99.

Todd, 275-76.

Tour, Du, 2.

Townsend, 22, 193, 283-84.

Van't Hoff, 50, 211.
von Baeyer, 49, 155.
von Bahr, Eva, 24.

Watson, 2.

Wehnelt, lo-ii, 54, 80-81, 85-87, 90-

91, 130, 165-67, 170-71, 189, 270.
Wheatstone, 165, 172-73.
Wiechert, 10.

Willows, 236, 241, 270, 274.
Wilsmore, 78.
Wilson, H. A., i, 22, 24, 33, 54, 69,

72-73, 100, 102-5, 107-8, 1 1 1-16,

209, 211, 220, 224, 227, 234-37,

239, 241, 249-50, 284.
Wilson, W., 96, 228, 248.
Winkelmann, 78.
Woodbury, 229, 232.

SUBJECT INDEX.

Absorption of electrons, heating effect,
172-78, _

Air, conductivity of, between hot plati
num electrodes, 209-11.

Air, positive emission from hot plati-
num in, 218-19.

Charge of positive ions from metals,

192-93.
Chemical action and ionization, 50-53,

85, 128-38, 283-99.
Constants of electron emission, values

of, 69, 81, 83, 104, n8, 169, 171,

177, 218, 220.
Constants of positive emission, values

of, 189, 214, 2i8, 2 20, 251, 252.
Contact potential difference, 39, 88,

109, 121.
Contact potential difference and heat-
ing effect, 174-77.
Contact potential difference, theory of

effect of gases on, 88, 108-17, 122.
Cooling effect, 164-71.
Crystals, ionization caused by hydration

of, 287.
Current and electromotive force, 20,

59-68, 80, 90, 106, 182-84, 239-41,

294-97.

Electric atomic weights of ions from

salts, 261-70.
Electric atomic weights of positive ions

from metals, 193-203.
Electromotive force and current, 20,

59-68, 80, 90, 106, 182-84, 239-41,

294-97.
Electron absorption, heating effect,

172-78.
Electron emission, cooling effect, 164-

71-
Electron emission, energetics of, 27-53,

95, 139-78, 296-97.
Electron emission, in high vacua, 133-

37- . .

Electron emission, temperature varia-
tion of, 54-101.

Electron theory, 25, 27-53; 61-68, 95-
loi, 108-14, 140-66, 168, 194.

Electrons, distribution of, in tempera-
ture equilibrium, 45-48.

Electrons, distribution of velocity

among emitted, 139-64, 296-97.
Electrons, emission of, from compound

substances, 79-95.
Electrons, latent heat of, 28-44, 57, 69-

79, 81, 83, 116, 164-78.
Electrons, liberation of, by chemical

action, 49, 52, 85, 128-38, 290-98.
Electrons, reflection of, from solids, 48,

52, 154-
Electrons, specific charge of, 7.
Electrons, steady motion of, in electric

field, 45, 63, 65, 143, 148, 153, 155,

157-64-
ffm, 7, 193-203, 261-70.
Emission, complete photoelectric, 95-

lOI.

Emission constants, conditions influenc-
ing values of electron, 70-79, 83,

103-26, 132, 218, 220.
Emission constants, values of electron,

69, 81, 83, 104, 118, 169, 171, 177,

218, 220.
Emission constants, values of, for

negative ions from salts, 252.
Emission constants, values of positive,

189, 214, 218, 220, 251, 252.
Emission, energetics of electron, 27-53,

95, 139-78, 296-97.
Emission of electrons, and chemical

action, 49, 52, 85, 128-38, 290-98.
Emission of electrons, and temperature

variation, 54-101.
Emission of electrons, cooling effect

164-71.
Emission of electrons, effect of gases

on, 70-79, 87-91, 102-38.
Emission of electrons from compound

substances, 79-95.
Emission of electrons in high vacua,

133-37-
Emission of ions from salts and from

metals, comparison of, 280-81.
Emission of negative ions, 92-95, 244.
Emission of positive ions by hot metals,

II, 22, 24, 179-208.
Energetics of electron emission, 27-53,

95, 139-78, 296-97.
Energy, kinetic, of electrons liberated

by chemical action, 292-98.

302

SUBJECT INDEX

303

Energy, kinetic, of positive ions from

metals, 189-92.
Energy, kinetic, of positive ions from

salts, 280.
Energy, kinetic, of thermionically

emitted electrons, 139-64, 297.
Experimental methods, 12, 91,133, 142.

147, 165, 195. 221,224-39. 273. 291,

293-

Fresh wires, effect of hydrogen on
emission of electrons from, 102-17.

Fresh wires, positive emission from,
179-208, 211.

Fresh wires, positive emission £rom, in
gases, 227-33.

Gases drawn away from neighbour-
hood of hot bodies, properties of,
5. 270-73.

Gases, effect of, on currents from salts,
253-61, 278-80.

Gases, effect of, on electron emission,
70-79,87-91, 102-38.

Gases, effect of, on liberation of positive
ions from hot metals, 209-33.

Gases, ionization of, by heat, 298-99.

Gases, theory of effect of, on electron
emission, 88, 108-17, 120-22, 125.

Hkating effect, 172-78.

Helium, positive emission from hot
platinum in, 219.

Hot metals, positive ions from, 1 1, 22,
24, 179-208.

Hot metals, quantity of positive electri-
city emitted by, 208.

Hydrogen diffusing into air, effect of,
on emission from platinum, 221-22.

Hydrogen, effect of, on electron emis-
sion, 87, 102-7.

Hydrogen, positive emission from hot
platinum in, 220.

Hydrogen, theory of effect of, on emis-
sion, 88, 108-17.

Impact ionization, 21.

Impurities, influence of, 14, 71-77, 87,

102-38, 177, 179-208, 222-23, 237-

33, 262-69, 277-80.
Ionization and chemical action, 50-53,

85, 128-38, 283-99-
Ionization, by collision, 21.
Ionization of gases by heat, 298-99.
Ionization, positive, from hot metals,

magnitude of, 208.
Ions, emission of, by heated salts, 92-95,

234-82.
Ions, emission of, from metals, during

chemical action, 286, 288-89.
Ions from salts, mobilities of, 270-76.
Ions from salts, nature of, 261-70, 276-

82.

Ions, mobilities of, 6, 270-76.

Ions, specific charge of, 7, 193-203,

261-70.
Ions, theory of, 4.

Kinetic theory, 33-35.

Latent heat of electrons, 28-44, 57»
69-79, 81, 83, 116, 164-78.

Latent heat of electrons, temperature
variation, 30, 116, 168.

Law of temperature variation of emis-
sion, 27-101.

Magnetic field, effect of, on motion of

electrons or ions, 8, 65.
Measurement of temperature, 14, 17.
Mobilities of ions, 6, 270-76.
Motion of electrons in magnetic field,

8,65.

Negative emission from salts, time
variation, 244.

Negative ions, emission of, from com-
pounds, 92-95, 244.

Nitrogen, negative emission from tung-
sten in, 123-25.

Nitrogen, positive emission from pla-
tinum in, 217-18.

Oxygen, positive emission from plati-
num in, 213-17.

Oxygen, theory of positive emission
from platinum in, 215-17.

Phosphorus, emission of ions due to

action of platinum on, 2S6.
Phosphorus, ionization due to oxidation

of, 285-86,
Photoelectric emission, 95-101, 294-96.
Platinum, effect of gases on electron

emission from, 71, 102-17.
Positive emission, decay with time,

179-82, 241-50, 278.
Positive emission from fresh wires,

179-208, 211, 227-33.
Positive emission from metals, effect of

changing gas, 222-23.
Positive emission from metals in gases,

nature of the ions, 223-27.
Positive emission from metals, revival

of, 185.87.
Positive emission from metals, variation

with temperature, 188-89.
Positive emission from salts, 234-82.
Positive emission from salts, effect of

gases on, 253-61, 278-80.
Positive emission from salts, effect of

impurities on, 261-67, 277-82.
Positive emission from salts, tempera-
ture variation, 250-53.
Positive emission from salts, time

variation, 241-50, 278.

304 EMISSION OF ELECTRICITY FROM HOT BODIES

Positive emission, relative efficiency of

different salts, 281-82.
Positive ions, emission of, by hot

metals, 11, 22, 24, 179-208.
Positive ions from hot metals, effect of

gases on liberation of, 209-33.
Positive ions from metals, charge of,

192-93.
Positive ions from metals in gases,

nature of, 223-27.
Positive ions from metals, kinetic energy

of, 189-92.
Positive ions from metals, nature of,

203-7.
Positive ions from metals, specific

charge (e/wi) of, 193-203.
Positive ions from salts, 234-82.

Quantum theory, 35-39.

Reflection of electrons, 48, 52, 154.
Revival of positive emission from
metals, 185-87.

Salts, emission of ions by heated,

234-82.
Saturation, attainment of, 20, 59-68,

182-84, 239-41.
Solar electricity, 47.
Space charge, 61.
Specific charge of electrons, 7.
Specific charge of ions, 7, 193-203, 261-

70.
Splashing, ionization due to, 284-85.
Standard temperatures, 18,

Temperature of hot wires, measure-
ment of, 14, 17.

Temperature variation of electronic
emission, 54-101.

Temperature variation of positive emis-
sion from metals, 188-89.

Temperature variation of positive emis-
sion from salts, 250-53.

Temperatures, standard, 18,

Theory of electron emission, 25, 27-53,
88, 95-101, 108.

Theory of ions, 4,

Thermodynamical theory, 27-33, 49-53,
95, 108-12, 211.

Thomson effect, 32.

Tubes, preparation of, 12.

Tungsten, effect of gases on electron
emission from, 117-26.

Tungsten, emission of electrons from,
in high vacua, 133-37.

Vacuum furnace, 14.

Variation, with time, of emission from
salts, 241-50, 278.

Variation, with time, of positive emis-
sion from metals, 179-82.

Velocities of emitted electrons, 139-64,
296-97.

Velocities of emitted electrons, formulae
for, 162-63.

Velocities of emitted electrons, law of
distribution of, 141.

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