made in recent times of ultra-violet light for producing ions that it is
desirable to give some account of the electrical effects produced by
light. The discovery by Hertz (_Wied. Ann._ 31, p. 983) in 1887, that
the incidence of ultra-violet light on a spark gap facilitates the
passage of a spark, led to a series of investigations by Hallwachs,
Hoor, Righi and Stoletow, on the effect of ultra-violet light on
electrified bodies. These researches have shown that a freshly cleaned
metal surface, charged with negative electricity, rapidly loses its
charge, however small, when exposed to ultra-violet light, and that if
the surface is insulated and without charge initially, it acquires a
positive charge under the influence of the light. The magnitude of this
positive charge may be very much increased by directing a blast of air
on the plate. This, as Zeleny (_Phil. Mag._ [5], 45, p. 272) showed, has
the effect of blowing from the neighbourhood of the plate negatively
electrified gas, which has similar properties to the charged gas
obtained by the separation of ions from a gas exposed to Röntgen rays or
uranium radiation. If the metal plate is positively electrified, there
is no loss of electrification caused by ultra-violet light. This has
been questioned, but a very careful examination of the question by
Elster and Geitel (_Wied. Ann._ 57, p. 24) has shown that the apparent
exceptions are due to the accidental exposure to reflected ultra-violet
light of metal surfaces in the neighbourhood of the plate negatively
electrified by induction, so that the apparent loss of charge is due to
negative electricity coming up to the plate, and not to positive
electricity going away from it. The ultra-violet light may be obtained
from an arc-lamp, the effectiveness of which is increased if one of the
terminals is made of zinc or aluminium, the light from these substances
being very rich in ultra-violet rays; it may also be got very
conveniently by sparking with an induction coil between zinc or cadmium
terminals. Sunlight is not rich in ultra-violet light, and does not
produce anything like so great an effect as the arc light. Elster and
Geitel, who have investigated with great success the effects of light on
electrified bodies, have shown that the more electro-positive metals
lose negative charges when exposed to ordinary light, and do not need
the presence of the ultra-violet rays. Thus they found that amalgams of
sodium or potassium enclosed in a glass vessel lose a negative charge
when exposed to daylight, though the glass stops the small amount of
ultra-violet light left in sunlight after its passage through the
atmosphere. If sodium or potassium be employed, or, what is more
convenient, the mercury-like liquid obtained by mixing sodium and
potassium in the proportion of their combining weights, they found that
negative electricity was discharged by an ordinary petroleum lamp. If
the still more electro-positive metal rubidium is used, the discharge
can be produced by the light from a glass rod just heated to redness;
but there is no discharge till the glass is luminous. Elster and Geitel
arrange the metals in the following order for the facility with which
negative electrification is discharged by light: rubidium, potassium,
alloy of sodium and potassium, sodium, lithium, magnesium, thallium,
zinc. With copper, platinum, lead, iron, cadmium, carbon and mercury the
effects with ordinary light are too small to be appreciable. The order
is the same as that in Volta's electro-chemical series. With
ultra-violet light the different metals show much smaller differences in
their power of discharging negative electricity than they do with
ordinary light. Elster and Geitel found that the ratio of the
photo-electric effects of two metals exposed to approximately
monochromatic light depended upon the wave-length of the light,
different metals showing a maximum sensitiveness in different parts of
the spectrum. This is shown by the following table for the alkaline
metals. The numbers in the table are the rates of emission of negative
electricity under similar circumstances. The rate of emission under the
light from a petroleum lamp was taken as unity:--
Blue. Yellow. Orange. Red.
Rb .16 .64 .33 .039
Na .37 .36 .14 .009
K .57 .07 .04 .002
The table shows that the absorption of light by the metal has great
influence on the photo-electric effect, for while potassium is more
sensitive in blue light than sodium, the strong absorption of yellow
light by sodium makes it more than five times more sensitive to this
light than potassium. Stoletow, at an early period, called attention to
the connexion between strong absorption and photo-electric effects. He
showed that water, which does not absorb to any great extent either the
ultra-violet or visible rays, does not show any photo-electric effect,
while strongly coloured solutions, and especially solutions of
fluorescent substances such as methyl green or methyl violet, do so to a
very considerable extent; indeed, a solution of methyl green is more
sensitive than zinc. Hallwachs (_Wied. Ann._ 37, p. 666) proved that in
liquids showing photo-electric effects there is always strong
absorption; we may, however, have absorption without these effects.
Phosphorescent substances, such as calcium sulphide show this effect, as
also do various specimens of fluor-spar. As phosphorescence and
fluorescence are probably accompanied by a very intense absorption by
the surface layers, the evidence is strong that to get the
photo-electric effects we must have strong absorption of some kind of
light, either visible or ultra-violet.
[Illustration: FIG. 14.]
If a conductor A is placed near a conductor B exposed to ultra-violet
light, and if B is made the negative electrode and a difference of
potential established between A and B, a current of electricity will
flow between the conductors. The relation between the magnitude of the
current and the difference of potential when A and B are parallel plates
has been investigated by Stoletow (_Journal de physique_, 1890, 11, p.
469), von Schweidler (_Wien. Ber._, 1899, 108, p. 273) and Varley
(_Phil. Trans. A._, 1904, 202, p. 439). The results of some of Varley's
experiments are represented in the curves shown in fig. 14, in which the
ordinates are the currents and the abscissae the potentials. It will be
seen that when the pressure is exceedingly low the current is
independent of the potential difference and is equal to the negative
charge carried off in unit time by the corpuscles emitted from the
surface exposed to the light. At higher pressures the current rises far
above these values and increases rapidly with the potential difference.
This is due to the corpuscles emitted by the illuminated surface
acquiring under the electric field such high velocities that when they
strike against the molecules of the gas through which they are passing
they ionize them, producing fresh ions which can carry on additional
current. The relation between the current and the potential difference
in this case is in accordance with the results of the theory of
ionization by collision. The corpuscles emitted from a body under the
action of ultra-violet light start from the surface with a finite
velocity. The velocity is not the same for all the corpuscles, nor
indeed could we expect that it should be: for as Ladenburg has shown
(_Ann. der Phys._, 1903, 12, p. 558) the seat of their emission is not
confined to the surface layer of the illuminated metal but extends to a
layer of finite, though small, thickness. Thus the particles which start
deep down will have to force their way through a layer of metal before
they reach the surface, and in doing so will have their velocities
retarded by an amount depending on the thickness of this layer. The
variation in the velocity of the corpuscles is shown in the following
table, due to Lenard (_Ann. der Phys._, 1902, 8, p. 149).
+------------------------------------+--------+----------+-----------+
| | Carbon.| Platinum.| Aluminium.|
+------------------------------------+--------+----------+-----------+
| Corpuscles emitted with velocities | | | |
| between 12 and 8 × 10^7 cm sec. | 0.000 | 0.000 | 0.004 |
| between 8 and 4 × 10^7 cm sec. | 0.049 | 0.155 | 0.151 |
| between 4 and 0 × 10^7 cm sec. | 0.67 | 0.65 | 0.49 |
| | | | |
| Corpuscles only emitted with the | | | |
| help of an external electric | 0.28 | 0.21 | 0.35 |
| field. +--------+----------+-----------|
| | 1.00 | 1.00 | 1.00 |
+------------------------------------+--------+----------+-----------+
If the illuminated surface is completely surrounded by an envelope of
the same metal insulated from and completely shielded from the light,
the emission of the negative corpuscles from the illuminated surface
would go on until the potential difference V between this surface and
the envelope became so great that the corpuscles with the greatest
velocity lost their energy before reaching the envelope, i.e. if m is
the mass, e the charge on a corpuscle, v the greatest velocity of
projection, until Ve = ½mv². The values found for V by different
observers are not very consistent. Lenard found that V for aluminium was
about 3 volts and for platinum 2. Millikan and Winchester (_Phil. Mag._,
July 1907) found for aluminium V = .738. The apparatus used by them was
so complex that the interpretation of their results is difficult.
An extremely interesting fact discovered by Lenard is that the velocity
with which the corpuscles are emitted from the metal is independent of
the intensity of the incident light. The quantity of corpuscles
increases with the intensity, but the velocity of the individual
corpuscles does not. It is worthy of notice that in other cases when
negative corpuscles are emitted from metals, as for example when the
metals are exposed to cathode rays, Canal-strahlen, or Röntgen rays, the
velocity of the emitted corpuscles is independent of the intensity of
the primary radiation which excites them. The velocity is not, however,
independent of the nature of the primary rays. Thus when light is used
to produce the emission of corpuscles the velocity, as Ladenburg has
shown, depends on the wave length of the light, increasing as the wave
length diminishes. The velocity of corpuscles emitted under the action
of cathode rays is greater than that of those ejected by light, while
the incidence of Röntgen rays produces the emission of corpuscles moving
much more rapidly than those in the cases already mentioned, and the
harder the primary rays the greater is the velocity of the corpuscles.
The importance of the fact that the velocity and therefore the energy of
the corpuscles emitted from the metal is independent of the intensity of
the incident light can hardly be overestimated. It raises the most
fundamental questions as to the nature of light and the constitution of
the molecules. What is the source of the energy possessed by these
corpuscles? Is it the light, or in the stores of internal energy
possessed by the molecule? Let us follow the consequences of supposing
that the energy comes from the light. Then, since the energy is
independent of the intensity of the light, the electric forces which
liberate the corpuscles must also be independent of that intensity. But
this cannot be the case if, as is usually assumed in the electromagnetic
theory, the wave front consists of a uniform distribution of electric
force without structure, for in this case the magnitude of the electric
force is proportional to the square root of the intensity. On the
emission theory of light a difficulty of this kind would not arise, for
on that theory the energy in a luminiferous particle remains constant as
the particle pursues its flight through space. Thus any process which a
single particle is able to effect by virtue of its energy will be done
just as well a thousand miles away from the source of light as at the
source itself, though of course in a given space there will not be
nearly so many particles to do this process far from the source as there
are close in. Thus, if one of the particles when it struck against a
piece of metal caused the ejection of a corpuscle with a given velocity,
the velocity of emission would not depend on the intensity of the light.
There does not seem any reason for believing that the electromagnetic
theory is inconsistent with the idea that on this theory, as on the
emission theory, the energy in the light wave may instead of being
uniformly distributed through space be concentrated in bundles which
occupy only a small fraction of the volume traversed by the light, and
that as the wave travels out the bundles get farther apart, the energy
in each remaining undiminished. Some such view of the structure of light
seems to be required to account for the fact that when a plate of metal
is struck by a wave of ultra-violet light, it would take years before
the corpuscles emitted from the metal would equal in number the
molecules on the surface of the metal plate, and yet on the ordinary
theory of light each one of these is without interruption exposed to the
action of the light. The fact discovered by E. Ladenburg (_Verh. d.
deutsch. physik. Ges._ 9, p. 504) that the velocity with which the
corpuscles are emitted depends on the wave length of the light suggests
that the energy in each bundle depends upon the wave length and
increases as the wave length diminishes.
These considerations illustrate the evidence afforded by photo-electric
effects on the nature of light; these effects may also have a deep
significance with regard to the structure of matter. The fact that the
energy of the individual corpuscles is independent of the intensity of
the light might be explained by the hypothesis that the energy of the
corpuscles does not come from the light but from the energy stored up in
the molecules of the metal exposed to the light. We may suppose that
under the action of the light some of the molecules are thrown into an
unstable state and explode, ejecting corpuscles; the light in this case
acts only as a trigger to liberate the energy in the atom, and it is
this energy and not that of the light which goes into the corpuscles. In
this way the velocity of the corpuscles would be independent of the
intensity of the light. But it may be asked, is this view consistent
with the result obtained by Ladenburg that the velocity of the
corpuscles depends upon the nature of the light? If light of a definite
wave length expelled corpuscles with a definite and uniform velocity, it
would be very improbable that the emission of the corpuscles is due to
an explosion of the atoms. The experimental facts as far as they are
known at present do not allow us to say that the connexion between the
velocity of the corpuscles and the wave length of the light is of this
definite character, and a connexion such as a gradual increase of
average velocity as the wave length of the light diminishes, would be
quite consistent with the view that the corpuscles are ejected by the
explosion of the atom. For in a complex thing like an atom there may be
more than one system which becomes unstable when exposed to light. Let
us suppose that there are two such systems, A and B, of which B ejects
the corpuscles with the greater velocity. If B is more sensitive to the
short waves, and A to the long ones, then as the wave length of the
light diminishes the proportion of the corpuscles which come from B will
increase, and as these are the faster, the average velocity of the
corpuscles emitted will also increase. And although the potential
acquired by a perfectly insulated piece of metal when exposed to
ultra-violet light would depend only on the velocity of the fastest
corpuscles and not upon their number, in practice perfect insulation is
unattainable, and the potential actually acquired is determined by the
condition that the gain of negative electricity by the metal through
lack of insulation, is equal to the loss by the emission of negatively
electrified corpuscles. The potential acquired will fall below that
corresponding to perfect insulation by an amount depending on the number
of the faster corpuscles emitted, and the potential will rise if the
proportion of the rapidly moving corpuscles is increased, even though
there is no increase in their velocity. It is interesting to compare
other cases in which corpuscles are emitted with the case of
ultra-violet light. When a metal or gas is bombarded by cathode rays it
emits corpuscles and the velocity of these is found to be independent of
the velocity of the cathode rays which excite them; the velocity is
greater than for corpuscles emitted under ultra-violet light. Again,
when bodies are exposed to Röntgen rays they emit corpuscles moving with
a much greater velocity than those excited by cathode rays, but again
the velocity does not depend upon the intensity of the rays although it
does to some extent on their hardness. In the case of cathode and
Röntgen rays, the velocity with which the corpuscles are emitted seems,
as far as we know at present, to vary slightly, but only slightly, with
the nature of the substance on which the rays fall. May not this
indicate that the first effect of the primary rays is to detach a
neutral doublet, consisting of a positive and negative charge, this
doublet being the same from whatever system it is detached? And that the
doublet is unstable and explodes, expelling the negative charge with a
high velocity, and the positive one, having a much larger charge, with a
much smaller velocity, the momentum of the negative charge being equal
to that of the positive.
Up to now we have been considering the effects produced when light is
incident on metals. Lenard found (and the result has been confirmed by
the experiments of J. J. Thomson and Lyman) that certain kinds of
ultra-violet light ionize a gas when they pass through. The type of
ultra-violet light which produces this effect is so easily absorbed that
it is stopped by a layer a few millimetres thick of air at atmospheric
pressure.
_Ionization by Collision._--When the ionization of the gas is produced
by external agents such as Röntgen rays or ultra-violet light, the
electric field produces a current by setting the positive ions moving in
one direction, and the negative ones in the opposite; it makes use of
ions already made and does not itself give rise to ionization. In many
cases, however, such as in electric sparks, there are no external agents
to produce ionization and the electric field has to produce the ions as
well as set them in motion. When the ionization is produced by external
means the smallest electric field is able to produce a current through
the gas; when, however, these external means are absent no current is
produced unless the strength of the electric field exceeds a certain
critical value, which depends not merely upon the nature of the gas but
also upon the pressure and the dimensions of the vessel in which it is
contained. The variation of the electric field required to produce
discharge can be completely explained if we suppose that the ionization
of the gas is produced by the impact with its molecules of corpuscles,
and in certain cases of positive ions, which under the influence of the
electric field have acquired considerable kinetic energy. We have direct
evidence that rapidly moving corpuscles are able to ionize molecules
against which they strike, for the cathode rays consist of such
corpuscles, and these when they pass through a gas produce large amounts
of ionization. Suppose then that we have in a gas exposed to an electric
field a few corpuscles. These will be set in motion by the field and
will acquire an amount of energy in proportion to the product of the
electric force, their charge, and the distance travelled in the
direction of the electric field between two collisions with the
molecules of the gas. If this energy is sufficient to give them the
ionizing property possessed by cathode rays, then when a corpuscle
strikes against a molecule it will detach another corpuscle; this under
the action of the electric field will acquire enough energy to produce
corpuscles on its own account, and so as the corpuscles move through the
gas their number will increase in geometrical progression. Thus, though
there were but few corpuscles to begin with, there may be great
ionization after these have been driven some distance through the gas by
the electric field.
The number of ions produced by collisions can be calculated by the
following method. Let the electric force be parallel to the axis of x,
and let n be the number of corpuscles per unit volume at a place fixed
by the co-ordinate x; then in unit time these corpuscles will make
nu/[lambda] collisions with the molecules, if u is the velocity of a
corpuscle and [lambda] the mean free path of a corpuscle. When the
corpuscles are moving fast enough to produce ions by collision their
velocities are very much greater than those they would possess at the
same temperature if they were not acted on by electrical force, and so
we may regard the velocities as being parallel to the axis of x and
determined by the electric force and the mean free path of the
corpuscles. We have to consider how many of the nu/[lambda] collisions
which take place per second will produce ions. We should expect that
the ionization of a molecule would require a certain amount of energy,
so that if the energy of the corpuscle fell below this amount no
ionization would take place, while if the energy of the corpuscle were
exceedingly large, every collision would result in ionization. We
shall suppose that a certain fraction of the number of collisions
result in ionization and that this fraction is a function of the
energy possessed by the corpuscle when it collides against the
molecules. This energy is proportional to Xe[lambda] when X is the
electric force, e the charge on the corpuscle, and [lambda] the mean
free path. If the fraction of collisions which produce ionization is
[int](Xe[lambda]), then the number of ions produced per cubic
centimetre per second is [int](Xe[lambda])nu/[lambda]. If the
collisions follow each other with great rapidity so that a molecule
has not had time to recover from one collision before it is struck
again, the effect of collisions might be cumulative, so that a
succession of collisions might give rise to ionization, though none of
the collisions would produce an ion by itself. In this case [int]
would involve the frequency of the collisions as well as the energy of
the corpuscle; in other words, it might depend on the current through
the gas as well as upon the intensity of the electric field. We
shall, however, to begin with, assume that the current is so small
that this cumulative effect may be neglected.
Let us now consider the rate of increase, dn/dt, in the number of
corpuscles per unit volume. In consequence of the collisions,
[int](Xe[lambda])nu/[lambda] corpuscles are produced per second; in
consequence of the motion of the corpuscles, the number which leave
unit volume per second is greater than those which enter it by
(d/dx)(nu); while in a certain number of collisions a corpuscle will
stick to the molecule and will thus cease to be a free corpuscle. Let
the fraction of the number of collisions in which this occurs be
[beta]. Thus the gain in the number of corpuscles is
[int](Xe[lambda])nu/[lambda], while the loss is (d/dx)(nu) +
[beta](nu)/[lambda]; hence
dn nu d [beta]nu
-- = [int](Xe[lambda]) -------- - --(nu) - --------.
dt [lambda] dx [lambda]
When things are in a steady state dn/dt = 0, and we have
d 1 / \
--(nu) = --------( [int](Xe[lambda]) - [beta] )nu.
dx [lambda] \ /
If the current is so small that the electrical charges in the gas are
not able to produce any appreciable variations in the field, X will be
constant and we get nu = C[epsilon]^{[alpha]x}, where [alpha] =
{[int](Xe[lambda]) - [beta]}/[lambda]. If we take the origin from
which we measure x at the cathode, C is the value of nu at the
cathode, i.e. it is the number of corpuscles emitted per unit area of
the cathode per unit time; this is equal to i0/e if i0 is the quantity
of negative electricity coming from unit area of the cathode per
second, and e the electric charge carried by a corpuscle. Hence we
have nue = i0[epsilon]^{[alpha]x}. If l is the distance between the
anode and the cathode, the value of nue, when x = l, is the current
passing through unit area of the gas, if we neglect the electricity
carried by negatively electrified carriers other than corpuscles.
Hence i = i0[epsilon]^{[alpha]l}. Thus the current between the plates
increases in geometrical progression with the distance between the
plates.
By measuring the variation of the current as the distance between the
plates is increased, Townsend, to whom we owe much of our knowledge on
this subject, determined the values of [alpha] for different values of
X and for different pressures for air, hydrogen and carbonic acid gas
(_Phil. Mag._ [6], 1, p. 198). Since [lambda] varies inversely as the
pressure, we see that [alpha] may be written in the form p[phi](X/p)
or [alpha]/X = F(X/p). The following are some of the values of [alpha]
found by Townsend for air.
+---------+----------+----------+----------+----------+----------+
| X Volts | Pressure | Pressure | Pressure | Pressure | Pressure |
| per cm. | .17 mm. | .38 mm. | 1.10 mm. | 2.1 mm. | 4.1 mm. |
+---------+----------+----------+----------+----------+----------+
| 20 | .24 | | | | |
| 40 | .65 | .34 | | | |
| 80 | 1.35 | 1.3 | .45 | .13 | |
| 120 | 1.8 | 2.0 | 1.1 | .42 | .13 |
| 160 | 2.1 | 2.8 | 2.0 | .9 | .28 |
| 200 | | 3.4 | 2.8 | 1.6 | .5 |
| 240 | 2.45 | 3.8 | 4.0 | 2.35 | .99 |
| 320 | 2.7 | 4.5 | 5.5 | 4.0 | 2.1 |
| 400 | | 5.0 | 6.8 | 6.0 | 3.6 |
| 480 | 3.15 | 5.4 | 8.0 | 7.8 | 5.3 |
| 560 | | 5.8 | 9.3 | 9.4 | 7.1 |
| 640 | 3.25 | 6.2 | 10.6 | 10.8 | 8.9 |
+---------+----------+----------+----------+----------+----------+
We see from this table that for a given value of X, [alpha] for small
pressures increases as the pressure increases; it attains a maximum at
a particular pressure, and then diminishes as the pressure increases.
The increase in the pressure increases the number of collisions, but
diminishes the energy acquired by the corpuscle in the electric field,
and thus diminishes the change of any one collision resulting in
ionization. If we suppose the field is so strong that at some
particular pressure the energy acquired by the corpuscle is well above
the value required to ionize at each collision, then it is evident
that increasing the number of collisions will increase the amount of
ionization, and therefore [alpha], and [alpha] cannot begin to
diminish until the pressure has increased to such an extent that the
mean free path of a corpuscle is so small that the energy acquired by
the corpuscle from the electric field falls below the value when each
collision results in ionization.
The value of p, when X is given, for which [alpha] is a maximum, is
proportional to X; this follows at once from the fact that [alpha] is
of the form X·F(X/p). The value of X/p for which F(X/p) is a maximum is
seen from the preceding table to be about 420, when X is expressed in
volts per centimetre and p in millimetres of mercury. The maximum value
of F(X/p) is about 1/60. Since the current passing between two planes
at a distance l apart is i0[epsilon]^{[alpha]l} or
i0[epsilon]^{XlF(X/p)}, and since the force between the plates is
supposed to be uniform, Xl is equal to V, the potential between the
plates; hence the current between the plates is i0[epsilon]^{VlF(X/p)},
and the greatest value it can have is i0[epsilon]^{V/60}. Thus the
ratio between the current between the plates when there is ionization
and when there is none cannot be greater than [epsilon]^{V/60}, when V
is measured in volts. This result is based on Townsend's experiments
with very weak currents; we must remember, however, that when the
collisions are so frequent that the effects of collisions can
accumulate, [alpha] may have much larger values than when the current
is small. In some experiments made by J. J. Thomson with intense
currents from cathodes covered with hot lime, the increase in the
current when the potential difference was 60 volts, instead of being e
times the current when there was no ionization, as the preceding theory
indicates, was several hundred times that value, thus indicating a
great increase in [alpha] with the strength of the current.
Townsend has shown that we can deduce from the values of [alpha] the
mean free path of a corpuscle. For if the ionization is due to the
collisions with the corpuscles, then unless one collision detaches
more than one corpuscle the maximum number of corpuscles produced will
be equal to the number of collisions. When each collision results in
the production of a corpuscle, [alpha] = 1/[lambda] and is independent
of the strength of the electric field. Hence we see that the value of
[alpha], when it is independent of the electric field, is equal to the
reciprocal of the free path. Thus from the table we infer that at a
pressure of 17 mm. the mean free path is 1/325 cm.; hence at 1 mm. the
mean free path of a corpuscle is 1/19 cm. Townsend has shown that this
value of the mean free path agrees well with the value 1/21 cm.
deduced from the kinetic theory of gases for a corpuscle moving
through air. By measuring the values of [alpha] for hydrogen and
carbonic acid gas Townsend and Kirby (_Phil. Mag._ [6], 1, p. 630)
showed that the mean free paths for corpuscles in these gases are
respectively 1/11.5 and 1/29 cm. at a pressure of 1 mm. These results
again agree well with the values given by the kinetic theory of gases.
If the number of positive ions per unit volume is m and v is the
velocity, we have nue+mve = i, where i is the current through unit
area of the gas. Since nue = i0[epsilon]^nx and i = i0[epsilon]^nl,
when l is the distance between the plates, we see that
nu / mv = [epsilon]^(nx) / ([epsilon]^(nl) - [epsilon]^(nx)),
n v [epsilon]^(nx)
-- = -- · -------------------------------.
m u [epsilon]^(ne) - [epsilon]^(nx)
Since v/u is a very small quantity we see that n will be less than m
except when [epsilon]^nl - [epsilon]^nx is small, i.e. except close to
the anode. Thus there will be an excess of positive electricity from
the cathode almost up to the anode, while close to the anode there
will be an excess of negative. This distribution of electricity will
make the electric force diminish from the cathode to the place where
there is as much positive as negative electricity, where it will have
its minimum value, and then increase up to the anode.
The expression i = i0[epsilon]^[alpha]l applies to the case when there
is no source of ionization in the gas other than the collisions; if in
addition to this there is a source of uniform ionization producing q
ions per cubic centimetre, we can easily show that
qe
i = i0[epsilon]^{[alpha]l} + -------(e^{[alpha]l} - 1).
[alpha]
With regard to the minimum energy which must be possessed by a
corpuscle to enable it to produce ions by collision, Townsend (loc.
cit.) came to the conclusion that to ionize air the corpuscle must
possess an amount of energy equal to that acquired by the fall of its
charge through a potential difference of about 2 volts. This is also
the value arrived at by H. A. Wilson by entirely different
considerations. Stark, however, gives 17 volts as the minimum for
ionization. The energy depends upon the nature of the gas; recent
experiments by Dawes and Gill and Pedduck (_Phil. Mag._, Aug. 1908)
have shown that it is smaller for helium than for air, hydrogen, or
carbonic acid gas.
If there is no external source of ionization and no emission of
corpuscles from the cathode, then it is evident that even if some
corpuscles happened to be present in the gas when the electric field
were applied, we could not get a permanent current by the aid of
collisions made by these corpuscles. For under the electric field, the
corpuscles would be driven from the cathode to the anode, and in a short
time all the corpuscles originally present in the gas and those produced
by them would be driven from the gas against the anode, and if there was
no source from which fresh corpuscles could be introduced into the gas
the current would cease. The current, however, could be maintained
indefinitely if the positive ions in their journey back to the cathode
also produced ions by collisions, for then we should have a kind of
regenerative process by which the supply of corpuscles could be
continually renewed. To maintain the current it is not necessary that
the ionization resulting from the positive ions should be anything like
as great as that from the negative, as the investigation given below
shows a very small amount of ionization by the positive ions will
suffice to maintain the current. The existence of ionization by
collision with positive ions has been proved by Townsend. Another method
by which the current could be and is maintained is by the anode emitting
corpuscles under the impact of the positive ions driven against it by
the electric field. J. J. Thomson has shown by direct experiment that
positively electrified particles when they strike against a metal plate
cause the metal to emit corpuscles (J. J. Thomson, _Proc. Camb. Phil.
Soc._ 13, p. 212; Austin, _Phys. Rev._ 22, p. 312). If we assume that
the number of corpuscles emitted by the plate in one second is
proportional to the energy in the positive ions which strike the plate
in that second, we can readily find an expression for the difference of
potential which will maintain without any external ionization a current
of electricity through the gas. As this investigation brings into
prominence many of the most important features of the electric
discharge, we shall consider it in some detail.
Let us suppose that the electrodes are parallel plates of metal at
right angles to the axis of x, and that at the cathode x = 0 and at the
anode x = d, d being thus the distance between the plates. Let us also
suppose that the current of electricity flowing between the plates is
so small that the electrification between the plates due to the
accumulation of ions is not sufficient to disturb appreciably the
electric field, which we regard as uniform between the plates, the
electric force being equal to V/d, where V is the potential difference
between the plates. The number of positive ions produced per second in
a layer of gas between the planes x and x+dx is [alpha]nu·dx. Here n is
the number of corpuscles per unit volume, [alpha] the coefficient of
ionization (for strong electric field [alpha] = 1/[lambda]', where
[lambda]' is the mean free path of a corpuscle), and u the velocity of
a corpuscle parallel to x. We have seen that nu = i0[epsilon]^[alpha]x,
where i0 is the number of corpuscles emitted per second by unit area of
the cathode. Thus the number of positive ions produced in the layer is
[alpha]i0[epsilon]^[alpha]x dx. If these went straight to the cathode
without a collision, each of them would have received an amount of
kinetic energy Vex/d when they struck the cathode, and the energy of
the group of ions would be Vex/d·[alpha]i0[epsilon]^dx dx. The positive
ions will, however, collide with the molecules of the gas through which
they are passing, and this will diminish the energy they possess when
they reach the cathode.
The diminution in the energy will increase in geometrical proportion
with the length of path travelled by the ion and will thus be
proportional to [epsilon]^-[beta]x, [beta] will be proportional to the
number of collisions and will thus be proportional to the pressure of
the gas. Thus the kinetic energy possessed by the ions when they reach
the cathode will be
[epsilon]^{-[beta]x} · V(ex/d) · [alpha]i0[epsilon]^{[alpha]x} dx,
and E, the total amount of energy in the positive ions which reach the
cathode in unit time, will be given by the equation
_
/d
E = | [epsilon]^{-[beta]x} · V(ex/d) · [alpha]i0[epsilon]^{[alpha]x} dx
_/0
_
Ve[alpha]i0 /d
= ----------- | [epsilon]^{-([beta]-[alpha])x}·x·dx
d _/0
Ve[alpha]i0 / 1 / 1 d \ \
= ----------- { ---------------- - [epsilon]^{-([beta]-[alpha])d} { ----------------- + ---------------- } } (1).
d \([beta]-[alpha])² \([beta]-[alpha])² ([beta]-[alpha])/ /
If the number of corpuscles emitted by the cathode in unit time is
proportional to this energy we have i0 = kE, where k is a constant;
hence by equation (1) we have
([beta]-[alpha])² d
V = ----------------- · --,
ke[alpha] I
where
I = 1 - [epsilon]^{-([beta]-[alpha])d} (1 + d([beta] - [alpha])).
Since both [beta] and [alpha] are proportional to the pressure, I and
([beta] - [alpha])²d/[alpha] are both functions of pd, the product of
the pressure and the spark length, hence we see that V is expressed by
an equation of the form
1
V = -- [int](pd) (2),
ke
where [int](pd) denotes a function of pd, and neither p nor d enter
into the expression for V except in this product. Thus the potential
difference required to produce discharge is constant as long as the
product of the pressure and spark length remains constant; in other
words, the spark potential is constant as long as the mass of the gas
between the electrodes is constant. Thus, for example, if we halve the
pressure the same potential difference will produce a spark of twice
the length. This law, which was discovered by Paschen for fairly long
sparks (_Annalen_, 37, p. 79), and has been shown by Carr (_Phil.
Trans._, 1903) to hold for short ones, is one of the most important
properties of the electric discharge.
We see from the expression for V that when ([beta] - [alpha])d is very
large
V = ([beta] - [alpha])²d/ke[alpha].
Thus V becomes infinite when d is infinite. Again when ([beta] -
[alpha])d is very small we find
V = 1/ke[alpha]d;
thus V is again infinite when d is nothing. There must therefore be
some value of d intermediate between zero and infinity for which V is
a minimum. This value is got by finding in the usual way the value of
d, which makes the expression for V given in equation (1) a minimum.
We find that d must satisfy the equation
/ \
1 = [epsilon]^{-([beta]-[alpha])d} {1 + ([beta] - [alpha])d + ([beta] - [alpha]·d)²}.
\ /
We find by a process of trial and error that ([beta]-[alpha])d = 1.8
is approximately a solution of this equation; hence the distance for
minimum potential is 1.8/([beta] - [alpha]). Since [beta] and [alpha]
are both proportional to the pressure, we see that the critical spark
length varies inversely as the pressure. If we substitute this value
in the expression for V we find that [=V], the minimum spark
potential, is given by
_ [beta] - [alpha] 2.2
V = ---------------- · ---.
[alpha] ke
Since [beta] and [alpha] are each proportional to the pressure, the
minimum potential is independent of the pressure of the gas. On this
view the minimum potential depends upon the metal of which the cathode
is made, since k measures the number of corpuscles emitted per unit
time by the cathode when struck by positive ions carrying unit energy,
and unless [beta] bears the same ratio to [alpha] for all gases the
minimum potential will also vary with the gas. The measurements which
have been made of the "cathode fall of potential," which as we shall
see is equal to the minimum potential required to produce a spark,
show that this quantity varies with the material of which the cathode
is made and also with the nature of the gas. Since a metal plate, when
bombarded by positive ions, emits corpuscles, the effect we have been
considering must play a part in the discharge; it is not, however, the
only effect which has to be considered, for as Townsend has shown,
positive ions when moving above a certain speed ionize the gas, and
cause it to emit corpuscles. It is thus necessary to take into account
the ionization of the positive ions.
Let m be the number of positive ions per unit volume, and w their
velocity, the number of collisions which occur in one second in one
cubic centimetre of the gas will be proportional to mwp, where p is
the pressure of the gas. Let the number of ions which result from
these collisions be [gamma]mw; [gamma] will be a function of p and of
the strength of the electric field. Let as before n be the number of
corpuscles per cubic centimetre, u their velocity, and [alpha]nu the
number of ions which result in one second from the collisions between
the corpuscles and the gas. The number of ions produced per second per
cubic centimetre is equal to [alpha]nu + [gamma]mw; hence when things
are in a steady state
d
--(nu) = [alpha]nu + [gamma]mw ,
dx
and
e(nu + mw) = i,
where e is the charge on the ion and i the current through the gas.
The solution of these equations when the field is uniform between the
plates, is
enu = C[epsilon]^{([alpha]-[gamma])x} - [gamma]i/([alpha] - [gamma]),
emw = -C[epsilon]^{([alpha]-[gamma])x} + [alpha]i/([alpha] - [gamma]),
where C is a constant of integration. If there is no emission of
positive ions from the anode enu = i, when x = d. Determining C from
this condition we find
i / \
enu = ----------------- {[alpha][epsilon]^{([alpha]-[gamma])(x-d)} - [gamma] },
[alpha] - [gamma] \ /
[alpha]i / \
emw = ----------------- {1 - [epsilon]^{([alpha]-[gamma])(x-d)} }.
[alpha] - [gamma] \ /
If the cathode did not emit any corpuscles owing to the bombardment by
positive ions, the condition that the charge should be maintained is
that there should be enough positive ions at the cathode to carry the
current i.e. that emw = i; when x = 0, the condition gives
i / \
----------------- {[alpha][epsilon]^{-([alpha]-[gamma])d} - [gamma] } = 0,
[alpha] - [gamma] \ /
or
[epsilon]^{[alpha]d}/[alpha] = [epsilon]^{[gamma]d}/[gamma].
Since [alpha] and [gamma] are both of the form pf(X/p) and X = V/d, we
see that V will be a function of pd, in agreement with Paschen's law.
If we take into account both the ionization of the gas and the
emission of corpuscles by the metal we can easily show that
_
[alpha]-[gamma][epsilon]^{([alpha]-[gamma])d} k[alpha]Ve | 1
--------------------------------------------- = ---------- | ------------------------- -
[alpha] - [gamma] d |_ ([beta]+[gamma]-[alpha])²
_
/ 1 d \ |
[epsilon]^{-([beta]+[gamma]-[alpha])d} { ------------------------ + ---------------------- } |,
\([beta]+[gamma]-[alpha])² [beta]+[gamma]-[alpha]/ _|
where k and [beta] have the same meaning as in the previous
investigation. When d is large, [epsilon]^{([alpha]-[gamma])d} is also
large; hence in order that the left-hand side of this equation should
not be negative [gamma] must be less than [alpha]/[epsilon]^
{([alpha]-[gamma])d}; as this diminishes as d increases we see that when
the sparks are very long discharge will take place, practically as soon
as [gamma] has a finite value, i.e. as soon as the positive ions begin
to produce fresh ions by their collisions.
In the preceding investigation we have supposed that the electric field
between the plates was uniform; if it were not uniform we could get
discharges produced by very much smaller differences of potential than
are necessary in a uniform field. For to maintain the discharge it is
not necessary that the positive ions should act as ionizers all along
their path; it is sufficient that they should do so in the neighbourhood
of cathode. Thus if we have a strong field close to the cathode we might
still get the discharge though the rest of the field were comparatively
weak. Such a distribution of electric force requires, however, a great
accumulation of charged ions near the cathode; until these ions
accumulate the field will be uniform. If the uniform field existing in
the gas before the discharge begins were strong enough to make the
corpuscles produce ions by collision, but not strong enough to make the
positive ions act as ionizers, there would be some accumulation of ions,
and the amount of this accumulation would depend upon the number of free
corpuscles originally present in the gas, and upon the strength of the
electric field. If the accumulation were sufficient to make the field
near the cathode so strong that the positive ions could produce fresh
ions either by collision with the cathode or with the gas, the discharge
would pass though the gas; if not, there will be no continuous
discharge. As the amount of the accumulation depends on the number of
corpuscles present in the gas, we can understand how it is that after a
spark has passed, leaving for a time a supply of corpuscles behind it,
it is easier to get a discharge to pass through the gas than it was
before.
[Illustration: Fig. 15.]
The inequality of the electric field in the gas when a continuous
discharge is passing through it is very obvious when the pressure of the
gas is low. In this case the discharge presents a highly differentiated
appearance of which a type is represented in fig. 15. Starting from the
cathode we have a thin velvety luminous glow in contact with the
surface; this glow is often called the "first cathode layer." Next this
we have a comparatively dark space whose thickness increases as the
pressure diminishes; this is called the "Crookes's dark space," or the
"second cathode layer." Next this we have a luminous position called the
"negative glow" or the "third cathode layer." The boundary between the
second and third layers is often very sharply defined. Next to the third
layer we have another dark space called the "Faraday dark space." Next
to this and reaching up to the anode is another region of luminosity,
called the "positive column," sometimes (as in fig. 15, a) continuous,
sometimes (as in fig. 15, b) broken up into light or dark patches called
"striations." The dimensions of the Faraday dark space and the positive
column vary greatly with the current passing through the gas and with
its pressure; sometimes one or other of them is absent. These
differences in appearances are accompanied by great difference in the
strength of the electric field. The magnitude of the electric force at
different parts of the discharge is represented in fig. 16, where the
ordinates represent the electric force at different parts of the tube,
the cathode being on the right. We see that the electric force is very
large indeed between the negative glow and the cathode, much larger than
in any other part of the tube. It is not constant in this region, but
increases as we approach the cathode. The force reaches a minimum either
in the negative glow itself or in the part of the Faraday dark space
just outside, after which it increases towards the positive column. In
the case of a uniform positive column the electric force along it is
constant until we get quite close to the anode, when a sudden change,
called the "anode fall," takes place in the potential.
[Illustration:
_Discharge in Hydrogen
Pressure 2.25 m.m. Current 0.568·10^-3 ampere_
FIG. 16.]
The difference of potential between the cathode and the negative glow is
called the "cathode potential fall" and is found to be constant for wide
variations in the pressure of the gas and the current passing through.
It increases, however, considerably when the current through the gas
exceeds a certain critical value, depending among other things on the
size of the cathode. This cathode fall of potential is shown by
experiment to be very approximately equal to the minimum potential
difference. The following table contains a comparison of the
measurements of the cathode fall of potentials in various gases made by
Warburg (_Wied. Ann._, 1887, 31, p. 545, and 1890, 40, p. 1), Capstick
(_Proc. Roy. Society_, 1898, 63, p. 356), and Strutt (_Phil. Trans._,
1900, 193, p. 377), and the measurements by Strutt of the smallest
difference of potential which will maintain a spark through these gases.
+---------+-----------------------------------------+-----------------+
| | Cathode fall in Volts. |Least potential |
| Gas. +-----------------------------+-----------+ difference |
| | Platinum Electrodes. |Aluminium | required to |
| | |Electrodes.|maintain a Spark.|
+---------+-----------+---------+-------+-----------+-----------------+
| | Warburg. |Capstick.|Strutt.| Warburg. | Strutt. |
+---------+-----------+---------+-------+-----------+-----------------+
|Air | 340-350 | .. | .. | .. | 341 |
|H2 | about 300 | 298 | .. | 168 | 302-308 |
|O2 | .. | 369 | .. | .. | .. |
|N2 |230 if free| 232 | .. | 207 | 251 |
| |from oxygen| | | | |
|Hg vapour| 340 | .. | .. | .. | .. |
|Helium | .. | .. | 226 | .. | 261-326 |
|H2O | .. | 469 | .. | .. | .. |
|NH3 | .. | 582 | .. | .. | .. |
+---------+-----------+---------+-------+-----------+-----------------+
Thus in the cases in which the measurements could be made with the
greatest accuracy the agreement between the cathode fall and the minimum
potential difference is very close. The cathode fall depends on the
material of which the terminals are made, as is shown by the following
table due to Mey (_Verh. deutsch. physik. Gesell._, 1903, 5, p. 72).
+------+---------------------------------------------+
| Gas. | Electrode. |
+------+---+---+---+---+---+---+---+---+---+-----+---+
| | Pt| Hg| Ag| Cu| Fe| Zn| Al| Mg| Na| Na-K| K |
+------+---+---+---+---+---+---+---+---+---+-----+---+
|O2 |369| ..| ..| ..| ..| ..| ..| ..| ..| .. | ..|
|H2 |300| ..|295|280|230|213|190|168|185|169 |172|
|N2 |232|226| ..| ..| ..| ..| ..|207|178|125 |170|
|He |226| ..| ..| ..| ..| ..| ..| ..| 80| 78.5| 69|
|Argon |167| ..| ..| ..| ..| ..|100| ..| ..| .. | ..|
+------+---+---+---+---+---+---+---+---+---+-----+---+
The dependence of the minimum potential required to produce a spark upon
the metal of which the cathode is made has not been clearly established,
some observers being unable to detect any difference between the
potential required to spark between electrodes of aluminium and those of
brass, while others thought they had detected such a difference. It is
only with sparks not much longer than the critical spark length that we
could hope to detect this difference. When the current through the gas
exceeds a certain critical value depending among other things on the
size of the cathode, the cathode fall of potential increases rapidly and
at the same time the thickness of the dark spaces diminishes. We may
regard the part of the discharge between the cathode and the negative
glow as a discharge taking place under minimum potential difference
through a distance equal to the critical spark length. An inspection of
fig. 16 will show that we cannot regard the electric field as constant
even for this small distance; it thus becomes a matter of interest to
know what would be the effect on the minimum potential difference
required to produce a spark if there were sufficient ions present to
produce variations in the electric field analogous to those represented
in fig. 16. If the electric force at a distance x from the cathode were
proportional to [epsilon]^-px we should have a state of things much
resembling the distribution of electric force near the cathode. If we
apply to this distribution the methods used above for the case when the
force was uniform, we shall find that the minimum potential is less and
the critical spark length greater than when the electric force is
uniform.
_Potential Difference required to produce a Spark of given Length._--We
may regard the region between the cathode and the negative glow as a
place for the production of corpuscles, these corpuscles finding their
way from this region through the negative glow. The parts of this glow
towards the anode we may regard as a cathode, from which, as from a hot
lime cathode, corpuscles are emitted. Let us now consider what will
happen to these corpuscles shot out from the negative glow with a
velocity depending on the cathode fall of potential and independent of
the pressure. These corpuscles will collide with the molecules of the
gas, and unless there is an external electric field to maintain their
velocity they will soon come to rest and accumulate in front of the
negative glow. The electric force exerted by this cloud of corpuscles
will diminish the strength of the electric field in the region between
the cathode and the negative glow, and thus tend to stop the discharge.
To keep up the discharge we must have a sufficiently strong electric
field between the negative glow and the anode to remove the corpuscles
from this region as fast as they are sent into it from the cathode. If,
however, there is no production of ions in the region between the
negative glow and the anode, all the ions in this region will have come
from near the cathode and will be negatively charged; this negative
electrification will diminish the electric force on the cathode side of
it and thus tend to stop the discharge. This back electric field could,
however, be prevented by a little ionization in the region between the
anode and glow, for this would afford a supply of positive ions, and
thus afford an opportunity for the gas in this region to have in it as
many positive as negative ions; in this case it would not give rise to
any back electromotive force. The ionization which produces these
positive ions may, if the field is intense, be due to the collisions of
corpuscles, or it may be due to radiation analogous to ultra-violet, or
soft Röntgen rays, which have been shown by experiment to accompany the
discharge. Thus in the most simple conditions for discharge we should
have sufficient ionization to keep up the supply of positive ions, and
an electric field strong enough to keep the velocity of the negative
corpuscle equal to the value it has when it emerges from the negative
glow. Thus the force must be such as to give a constant velocity to the
corpuscle, and since the force required to move an ion with a given
velocity is proportional to the pressure, this force will be
proportional to the pressure of the gas. Let us call this force ap; then
if l is the distance of the anode from the negative glow the potential
difference between these points will be alp. The potential difference
between the negative glow and the cathode is constant and equals c;
hence if V is the potential difference between the anode and cathode,
then V = c + alp, a relation which expresses the connexion between the
potential difference and spark length for spark lengths greater than the
critical distance. It is to be remembered that the result we have
obtained applies only to such a case as that indicated above, where the
electric force is constant along the positive column. Experiments with
the discharge through gases at low pressure show the discharge may take
other forms. Thus the positive column may be striated when the force
along it is no longer uniform, or the positive column may be absent;
the discharge may be changed from one of these forms to another by
altering the current. The relation between the potential and the
distance between the electrodes varies greatly, as we might expect, with
the current passing through the gas.
The connexion between the potential difference and the spark length has
been made the subject of a large number of experiments. The first
measurements were made by Lord Kelvin in 1860 (_Collected Papers on
Electrostatics and Magnetism_, p. 247); subsequent experiments have been
made by Baille (_Ann. de chimie et de physique_, 5, 25, p. 486), Liebig
(_Phil. Mag._ [5], 24, p. 106), Paschen (_Wied. Ann._ 37, p. 79), Peace
(_Proc. Roy. Soc._, 1892, 52, p. 99), Orgler (_Ann. der Phys._ 1, p.
159), Strutt (_Phil. Trans._ 193, p. 377), Bouty (_Comptes rendus_, 131,
pp. 469, 503), Earhart (_Phil. Mag._ [6], 1, p. 147), Carr (_Phil.
Trans._, 1903), Russell (_Phil. Mag._ [5], 64, p. 237), Hobbs (_Phil.
Mag._ [6], 10, p. 617), Kinsley (_Phil. Mag._ [6], 9, 692), Ritter
(_Ann. der Phys._ 14, p. 118). The results of their experiments show
that for sparks considerably longer than the critical spark length, the
relation between the potential difference V and the spark length l may
be expressed when the electrodes are large with great accuracy by the
linear relation V = c + blp, where p is the pressure and c and b are
constants depending on the nature of the gas. When the sparks are long
the term blp is the most important and the sparking potential is
proportional to the spark length. Though there are considerable
discrepancies between the results obtained by different observers, these
indicate that the production of a long spark between large electrodes in
air at atmospheric pressure requires a potential difference of 30,000
volts for each centimetre of spark length. In hydrogen only about half
this potential difference is required, in carbonic acid gas the
potential difference is about the same as in air, while Ritter's
experiments show that in helium only about one-tenth of this potential
difference is required.
In the case when the electric field is not uniform, as for example when
the discharge takes place between spherical electrodes, Russell's
experiments show that the discharge takes place as soon as the maximum
electric force in the field between the electrodes reaches a definite
value, which he found was for air at atmospheric pressure about 38,000
volts per centimetre.
_Very Short Sparks._--Some very interesting experiments on the potential
difference required to produce exceedingly short sparks have been made
by Earhart, Hobbs and Kinsley; the length of these sparks was comparable
with the wave length of sodium light. With sparks of these lengths it
was found that it was possible to get a discharge with less than 330
volts, the minimum potential difference in air. The results of these
observers show that there is no diminution in the minimum potential
difference required to produce discharge until the spark length gets so
small that the average electric force between the electrodes amounts to
about one million volts per centimetre. When the force rises to this
value a discharge takes place even though the potential difference is
much less than 330 volts; in some of Earhart's experiments it was only
about 2 volts. This kind of discharge is determined not by the condition
that the potential difference should have a given value, but that the
electric force should have a given value. Another point in which this
discharge differs from the ordinary one is that it is influenced
entirely by the nature of the electrodes and not by the nature or
pressure of the gas between them, whereas the ordinary discharge is in
many cases not affected appreciably by changes in the metal of the
electrodes, but is always affected by changes in the pressure and
character of the gas between them. Kinsley found that when one of these
small sparks passed between the electrodes a kind of metallic bridge was
formed between them, so that they were in metallic connexion, and that
the distance between them had to be considerably increased before the
bridge was broken. Almy (_Phil. Mag._, Sept. 1908), who used very small
electrodes, was unable to get a discharge with less than the minimum
spark potential even when the spark length was reduced to one-third of
the wave length of sodium light. He suggests that the discharges
obtained with larger electrodes for smaller voltages are due to the
electrodes being dragged together by the electrostatic attraction
between them.
_Constitution of the Electric Spark._--Schuster and Hemsalech (_Phil.
Trans._ 193, p. 189), Hemsalech (_Comptes Rendus_, 130, p. 898; 132, p.
917; _Jour. de Phys._ 3. 9, p. 43, and Schenck, _Astrophy. Jour._ 14, p.
116) have by spectroscopic methods obtained very interesting results
about the constitution of the spark. The method employed by Schuster and
Hemsalech was as follows: Suppose we photograph the spectrum of a
horizontal spark on a film which is on the rim of a wheel rotating about
a horizontal axis with great velocity. If the luminosity travelled with
infinite speed from one electrode to the other, the image on the film
would be a horizontal line. If, however, the speed with which the
luminosity travelled between the electrodes was comparable with the
speed of the film, the line would be inclined to the horizontal, and by
measuring the inclinations we could find the speed at which the
luminosity travelled. In this way Schuster and Hemsalech showed that
when an oscillating discharge passed between metallic terminals in air,
the first spark passes through the air alone, no lines of the metal
appearing in its spectrum. This first spark vaporizes some of the metal
and the subsequent sparks passing mainly through the metallic vapour;
the appearance of the lines in the film shows that the velocity of the
luminous part of the vapour was finite. The velocity of the vapour of
metals of low atomic weight was in general greater than that of the
vapour of heavier metals. Thus the velocity of aluminium vapour was 1890
metres per second, that of zinc and cadmium only about 545. Perhaps the
most interesting point in the investigation was the discovery that the
velocities corresponding to different lines in the spectrum of the same
metal were in some cases different. Thus with bismuth some of the lines
indicated a velocity of 1420 metres per second, others a velocity of
only 550, while one ([lambda] = 3793) showed a still smaller velocity.
These results are in accordance with a view suggested by other phenomena
that many of the lines in a spectrum produced by an electrical discharge
originate from systems formed during the discharge and not from the
normal atom or molecule. Schuster and Hemsalech found that by inserting
a coil with large self induction in the primary circuit they could
obliterate the air lines in the discharge.
Schenck, by observing the appearance presented when an alternating
current, produced by discharging Leyden jars, was examined in a rapidly
rotating mirror, found it showed the following stages: (1) a thin bright
line, followed in some cases at intervals of half the period of the
discharge by fainter lines; (2) bright curved streamers starting from
the negative terminal, and diminishing rapidly in speed as they receded
from the cathode; (3) a diffused glow lasting for a much longer period
than either of the preceding. These constituents gave out quite
different spectra.
The structure of the discharge is much more easily studied when the
pressure of the gas is low, as the various parts which make up the
discharge are more widely separated from each other. We have already
described the general appearance of the discharge through gases at low
pressures (see p. 657). There is, however, one form of discharge which
is so striking and beautiful that it deserves more detailed
consideration. In this type of discharge, known as the striated
discharge, the positive column is made up of alternate bright and dark
patches known as _striations_. Some of these are represented in fig. 17,
which is taken from a paper by De la Rue and Müller (_Phil. Trans._,
1878, Pt. 1). This type of discharge only occurs when the current and
the pressure of the gas are between certain limits. It is most
beautifully shown when a Wehnelt cathode is used and the current is
produced by storage cells, as this allows us to use large currents and
to maintain a steady potential difference between the electrodes. The
striations are in consequence very bright and steady. The facts which
have been established about these striations are as follows: The
distance between the bright parts of the striations is greater at low
pressures than at high; it depends also upon the diameter of the tube,
increasing as the diameter of the tube increases. If the discharge tube
is wide at one place and narrow in another the striations will be
closer together in the narrow parts than in the wide. The distance
between the striations depends on the current through the tube. The
relation is not a very simple one, as an increase of current sometimes
increases while under other circumstances it decreases the distance
between the striations (see Willows, _Proc. Camb. Phil. Soc._ 10, p.
302). The electric force is not uniform along the striated discharge,
but is greater in the bright than in the dark parts of the striation. An
example is shown in fig. 16, due to H. A. Wilson, which shows the
distribution of electric force at every place in a striated discharge.
In experiments made by J. J. Thomson (_Phil. Mag._, Oct. 1909), using a
Wehnelt cathode, the variations in the electric force were more
pronounced than those shown in fig. 16. The electric force in this case
changed so greatly that it actually became negative just on the cathode
side of the bright part of the striation. Just inside the striation on
the anode side it rose to a very high value, then continually diminished
towards the bright side of the next striation when it again increased.
This distribution of electric force implies that there is great excess
of negative electricity at the bright head of the striation, and a small
excess of positive everywhere else. The temperature of the gas is higher
in the bright than in the dark parts of the striations. Wood (_Wied.
Ann._ 49, p. 238), who has made a very careful study of the distribution
of temperature in a discharge tube, finds that in those tubes the
temperature varies in the same way as the electric force, but that this
temperature (which it must be remembered is the average temperature of
all the molecules and not merely of those which are taking part in the
discharge) is by no means high; in no part of the discharge did the
temperature in his experiments exceed 100° C.
[Illustration: FIG. 17.]
_Theory of the Striations._--We may regard the heaping up of the
negative charges at intervals along the discharge as the fundamental
feature in the striations, and this heaping up may be explained as
follows. Imagine a corpuscle projected with considerable velocity from a
place where the electric field is strong, such as the neighbourhood of
the cathode; as it moves towards the anode through the gas it will
collide with the molecules, ionize them and lose energy and velocity.
Thus unless the corpuscle is acted on by a field strong enough to supply
it with the energy it loses by collision, its speed will gradually
diminish. Further, when its energy falls below a certain value it will
unite with a molecule and become part of a negative ion, instead of a
corpuscle; at this stage there will be a sudden and very large
diminution in its velocity. Let us now follow the course of a stream of
corpuscles starting from the cathode and approaching the anode. If the
speed falls off as the stream proceeds, the corpuscles in the rear will
gain on those in front and the density of the stream in the front will
be increased. If at a certain place the velocity receives a sudden check
by the corpuscles becoming loaded with a molecule, the density of the
negative electricity will increase at this place with great rapidity,
and here there will be a great accumulation of negative electricity, as
at the bright head on the cathode side of a striation. Now this
accumulation of negative electricity will produce a large electric force
on the anode side; this will drive corpuscles forward with great
velocity and ionize the gas. These corpuscles will behave like those
shot from the cathode and will accumulate again at some distance from
their origin, forming the bright head of the next striation, when the
process will be repeated. On this view the bright heads of the
striations act like electrodes, and the discharge passes from one bright
head to the next as by a number of stepping stones, and not directly
from cathode to anode. The luminosity at the head of the striations is
due to the recombination of the ions. These ions have acquired
considerable energy from the electric field, and this energy will be
available for supplying the energy radiated away as light. The
recombination of ions which do not possess considerable amounts of
energy does not seem to give rise to luminosity. Thus, in an ionized gas
not exposed to an electric field, although we have recombination between
the ions, we need not have luminosity. We have at present no exact data
as to the amount of energy which must be given to an ion to make it
luminous on recombination; it also certainly varies with the nature of
the ion; thus even with hot Wehnelt cathodes J. J. Thomson has never
been able to make the discharge through air luminous with a potential
less than from 16 to 17 volts. The mercury lamps, however, in which the
discharge passes through mercury vapour are luminous with a potential
difference of about 12 volts. It follows that if the preceding theory be
right the potential difference between two bright striations must be
great enough to make the corpuscles ionize by collision and also to give
enough energy to the ions to make them luminous when they recombine. The
difference of potential between the bright parts of successive
striations has been measured by Hohn (_Phys. Zeit._ 9, p. 558); it
varies with the pressure and with the gas. The smallest value given by
Hohn is about 15 volts. In some experiments made by J. J. Thomson, when
the pressure of the gas was very low, the difference of potential
between two adjacent dark spaces was as low as 3.75 volts.
_The Arc Discharge._--The discharges we have hitherto considered have
been characterized by large potential differences and small currents. In
the arc discharge we get very large currents with comparatively small
potential differences. We may get the arc discharge by taking a battery
of cells large enough to give a potential difference of 60 to 80 volts,
and connecting the cells with two carbon terminals, which are put in
contact, so that a current of electricity flows round the circuit. If
the terminals, while the current is on, are drawn apart, a bright
discharge, which may carry a current of many amperes, passes from one to
the other. This arc discharge, as it is called, is characterized by
intense heat and by the brilliant luminosity of the terminals. This
makes it a powerful source of light. The temperature of the positive
terminal is much higher than that of the negative. According to Violle
(_Comptes Rendus_, 115, p. 1273) the temperature of the tip of the
former is about 3500° C, and that of the latter 2700° C. The temperature
of the arc itself he found to be higher than that of either of its
terminals. As the arc passes, the positive terminal gets hollowed out
into a crater-like shape, but the negative terminal remains pointed.
Both terminals lose weight.
The appearance of the terminals is shown in fig. 18, given by Mrs
Ayrton (_Proc. Inst. Elec. Eng._ 28, p. 400); a, b represent the
terminals when the arc is quiet, and c when it is accompanied by a
hissing sound. The intrinsic brightness of the positive crater does
not increase with an increase in the current; an increased current
produces an increase in the area of the luminous crater, but the
amount of light given out by each unit of area of luminous surface is
unaltered. This indicates that the temperature of the crater is
constant; it is probably that at which carbon volatilizes. W. E.
Wilson (_Proc. Roy. Soc._ 58, p. 174; 60, p. 377) has shown that at
pressures of several atmospheres the intrinsic brightness of the
crater is considerably diminished.
[Illustration: FIG. 18.]
[Illustration: FIG. 19.]
The connexion between V, the potential difference between the
terminals, and l, the length of the arc, is somewhat analogous to that
which holds for the spark discharge. Fröhlich (_Electrotech. Zeit._ 4,
p. 150) gives for this connexion the relation V = m + nl, where m and
n are constants. Mrs Ayrton (_The Electric Arc_, chap. iv.) finds that
both m and n depend upon the current passing between the terminals,
and gives as the relation between V and l, V = [alpha] + [beta]/I +
([gamma] + [delta]/I)l, where [alpha], [beta], [gamma], [delta] are
constants and I the current. The relation between current and
potential difference was made the subject of a series of experiments
by Ayrton (_Electrician_, 1, p. 319; xi. p. 418), some of whose
results are represented in fig. 19. For a quiet arc an increase in
current is accompanied by a fall in potential difference, while for
the hissing arc the potential difference is independent of the
current. The quantities m and n which occur in Fröhlich's equation
have been determined by several experimenters. For carbon electrodes
in air at atmospheric pressure m is about 39 volts, varying somewhat
with the size and purity of the carbons; it is diminished by soaking
the terminals in salt solution. The value of n given by different
observers varies considerably, ranging from .76 to 2 volts when l is
measured in millimetres; it depends upon the current, diminishing as
the current increases. When metallic terminals are used instead of
carbons, the value of m depends upon the nature of the metal, m in
general being larger the higher the temperature at which the metal
volatilizes. Thus v. Lang (_Wied. Ann._ 31, p. 384) found the
following values for m in air at atmospheric pressure:--C = 35; Pt =
27.4; Fe = 25; Ni = 26.18; Cu = 23.86; Ag = 15.23; Zn = 19.86; Cd =
10.28. Lecher (_Wied. Ann._ 33, p. 609) gives Pt = 28, Fe = 20, Ag =
8, while Arons (_Wied. Ann._ 31, p. 384) found for Hg the value 12.8;
in this case the fall of potential along the arc itself was abnormally
small. In comparing these values it is important to remember that
Lecher (loc. cit.) has shown that with Fe or Pt terminals the arc
discharge is intermittent. Arons has shown that this is also the case
with Hg terminals, but no intermittence has been detected with
terminals of C, Ag or Cu. The preceding measurements refer to mean
potentials, and no conclusions as to the actual potential differences
at any time can be drawn when the discharge is discontinuous, unless
we know the law of discontinuity. The ease with which an arc is
sustained depends greatly on the nature of the electrodes; when they
are brass, zinc, cadmium, or magnesium it is exceedingly difficult to
get the arc.
[Illustration: FIG. 20.]
[Illustration: FIG. 21.]
The potential difference between the terminals is affected by the
pressure of the gas. The most extensive series of experiments on this
point is that made by Duncan, Rowland, and Tod (_Electrician_, 31, p.
60), whose results are represented in fig. 20. We see from these
curves that for very short arcs the potential difference increases
continuously with the pressure, but for longer ones there is a
critical pressure at which the potential difference is a minimum, and
that this critical pressure seems to increase with the length of arc.
The nature of the gas also affects the potential difference. The
magnitude of this effect may be gathered from the following values
given by Arons (_Ann. der Phys._ 1, p. 700) for the potential
difference required to produce an arc 1.5 mm. long, carrying a current
of 4.5 amperes, between terminals of different metals in air and pure
nitrogen.
+-----------+------+-----------+
| Terminal. | Air. | Nitrogen. |
+-----------+------+-----------+
| Ag | 21 | ? |
| Zn | 23 | 21 |
| Cd | 25 | 21 |
| Cu | 27 | 30 |
| Fe | 29 | 20 |
| Pt | 36 | 30 |
| Al | 39 | 27 |
| Pb | .. | 18 |
| Mg | .. | 22 |
+-----------+------+-----------+
Thus, with the discharge for an arc of given length and current, the
nature of the terminals is the most important factor in determining
the potential difference. The effects produced by the pressure and
nature of the surrounding gas, although quite appreciable, are not of
so much importance, while in the spark discharge the nature of the
terminals is of no importance, everything depending upon the nature
and pressure of the gas.
The potential gradient in the arc is very far from being uniform. With
carbon terminals Luggin (_Wien. Ber._ 98, p. 1192) found that, with a
current of 15 amperes, there was a fall of potential of 33.7 close to
the anode, and one 8.7 close to the cathode, so that the curve
representing the distribution of potential between the terminals would
be somewhat like that shown in fig. 21. We have seen that a somewhat
analogous distribution of potential holds in the case of conduction
through flames, though in that case the greatest drop of potential is
in general at the cathode and not at the anode. The difference between
the changes of potential at the anode and cathode is not so large with
Fe and Cu terminals as with carbon ones; with mercury terminals, Arons
(_Wied. Ann._ 58, p. 73) found the anode fall to be 7.4 volts, the
cathode fall 5.4 volts.
The case of the arc when the cathode is a pool of mercury and the anode
a metal wire placed in a vessel from which the air has been exhausted is
one which has attracted much attention, and important investigations on
this point have been made by Hewitt (_Electrician_, 52, p. 447), Wills
(_Electrician_, 54, p. 26), Stark, Retschinsky and Schnaposnikoff (_Ann.
der Phys._ 18, p. 213) and Pollak (_Ann. der Phys._ 19, p. 217). In this
arrangement the mercury is vaporized by the heat, and the discharge
which passes through the mercury vapour gives an exceedingly bright
light, which has been largely used for lighting factories, &c. The
arrangement can also be used as a rectifier, for a current will only
pass through it when the mercury pool is the cathode. Thus if such a
lamp is connected with an alternating current circuit, it lets through
the current in one direction and stops that in the other, thus
furnishing a current which is always in one direction.
_Theory of the Arc Discharge._--An incandescent body such as a piece of
carbon even when at a temperature far below that of the terminals in an
arc, emits corpuscles at a rate corresponding to a current of the order
of 1 ampere per square centimetre of incandescent surface, and as the
rate of increase of emission with the temperature is very rapid, it is
probably at the rate of many amperes per square centimetre at the
temperature of the negative carbon in the arc. If then a piece of carbon
were maintained at this temperature by some external means, and used as
a cathode, a current could be sent from it to another electrode whether
the second electrode were cold or hot. If, however, these negatively
electrified corpuscles did not produce other ions either by collision
with the gas through which they move or with the anode, the spaces
between cathode and anode would have a negative charge, which would tend
to stop the corpuscles leaving the cathode and would require a large
potential difference between anode and cathode to produce any
considerable current. If, however, there is ionization either in the gas
or at the anode, the positive ions will diffuse into the region of the
discharge until they are sensibly equal in number to the negative ions.
When this is the case the back electromotive force is destroyed and the
same potential difference will carry a much larger current. The arc
discharge may be regarded as analogous to the discharge between
incandescent terminals, the only difference being that in the arc the
terminals are maintained in the state of incandescence by the current
and not by external means. On this view the cathode is bombarded by
positive ions which heat it to such a temperature that negative
corpuscles sufficient to carry the current are emitted by it. These
corpuscles bombard the anode and keep it incandescent. They ionize also,
either directly by collision or indirectly by heating the anode, the gas
and vapour of the metal of which the anode is made, and produce in this
way the supply of positive ions which keep the cathode hot.
_Discharge from a Point._--A very interesting case of electric discharge
is that between a sharply pointed electrode, such as a needle, and a
metal surface of considerable area. At atmospheric pressures the
luminosity is confined to the immediate neighbourhood of the point. If
the sign of the potential of the point does not change, the discharge is
carried by ions of one sign--that of the charge on the pointed
electrode. The velocity of these ions under a given potential gradient
has been measured by Chattock (_Phil. Mag._ 32, p. 285), and found to
agree with that of the ions produced by Röntgen or uranium radiation,
while Townsend (_Phil. Trans._ 195, p. 259) has shown that the charge on
these ions is the same as that on the ions streaming from the point. If
the pointed electrode be placed at right angles to a metal plane serving
as the other electrode, the discharge takes place when, for a given
distance of the point from the plane, the potential difference between
the electrodes exceeds a definite value depending upon the pressure and
nature of the gas through which the discharge passes; its value also
depends upon whether, beginning with a small potential difference, we
gradually increase it until discharge commences, or, beginning with a
large potential difference, we decrease it until the discharge stops.
The value found by the latter method is less than that by the former.
According to Chattock's measurements the potential difference V for
discharge between the point and the plate is given by the linear
relation V = a + bl, where l is the distance of the point from the plate
and a and b are constants. From v. Obermayer's (_Wien. Ber._ 100, 2, p.
127) experiments, in which the distance l was greater than in
Chattock's, it would seem that the potential for larger distances does
not increase quite so rapidly with l as is indicated by Chattock's
relation. The potential required to produce this discharge is much less
than that required to produce a spark of length l between parallel
plates; thus from Chattock's experiments to produce the point discharge
when l = .5 cm. in air at atmospheric pressure requires a potential
difference of about 3800 volts when the pointed electrode is positive,
while to produce a spark at the same distance between plane electrodes
would require a potential difference of about 15,000 volts. Chattock
showed that with the same pointed electrode the value of the electric
intensity at the point was the same whatever the distance of the point
from the plane. The value of the electric intensity depended upon the
sharpness of the point. When the end of the pointed electrode is a
hemisphere of radius a, Chattock showed that for the same gas at the
same pressure the electric intensity f when discharge takes place is
roughly proportioned to a^-0.8. The value of the electric intensity at
the pointed electrode is much greater than its value at a plane
electrode for long sparks; but we must remember that at a distance from
a pointed electrode equal to a small multiple of the radius of curvature
of its extremity the electric intensity falls very far below that
required to produce discharge in a uniform field, so that the discharge
from a pointed electrode ought to be compared with a spark whose length
is comparable with the radius of curvature of the point. For such short
sparks the electric intensity is very high. The electric intensity
required to produce the discharge from a gas diminishes as the pressure
of the gas diminishes, but not nearly so rapidly as the electric
intensity for long sparks. Here again the discharge from a point is
comparable with short sparks, which, as we have seen, are much less
sensitive to pressure changes than longer ones. The minimum potential at
which the electricity streams from the point does not depend upon the
material of which the point is made; it varies, however, considerably
with the nature of the gas. The following are the results of some
experiments on this point. Those in the first two columns are due to
Röntgen, those in the third and fourth to Precht:--
+------+-----------------------------+--------------------+
| |Discharge Potential. Point +.| Pressure 760. |
| Gas. +--------------+--------------+----------+---------+
| | Pressure 205.| Pressure 110.| Point +. | Point -.|
+------+--------------+--------------+----------+---------+
| | Volts. | Volts. | Volts. | Volts. |
| H2 | 1296 | 1174 | 2125 | 1550 |
| O2 | 2402 | 1975 | 2800 | 2350 |
| CO | 2634 | 2100 | .. | .. |
| CH4 | 2777 | 2317 | .. | .. |
| NO | 3188 | 2543 | .. | .. |
| CO2 | 3287 | 2655 | 3475 | 2100 |
| N2 | .. | .. | 2600 | 2000 |
| Air | .. | .. | 2750 | 2050 |
+------+--------------+--------------+----------+---------+
We see from this table that in the case of the discharge from a
positively electrified point the greater the molecular weight of the gas
the greater the potential required for discharge. Röntgen concluded from
his experiments that the discharging potential from a positive point in
different gases at the same pressure varies inversely as the mean free
path of the molecules of the gas. In the same gas, however, at different
pressures the discharging potential does not vary so quickly with the
pressure as does the mean free path. In Precht's experiments, in which
different gases were used, the variations in the discharging potential
are not so great as the variations in the mean free path of the gases.
The current of electrified air flowing from the point when the
electricity is escaping--the well-known "electrical wind"--is
accompanied by a reaction on the point which tends to drive it
backwards. This reaction has been measured by Arrhenius (_Wied. Ann._
63, p. 305), who finds that when positive electricity is escaping from a
point in air the reaction on the point for a given current varies
inversely as the pressure of the gas, and for different gases (air,
hydrogen and carbonic acid) inversely as the square root of the
molecular weight of the gas. The reaction when negative electricity is
escaping is much less. The proportion between the reactions for positive
and negative currents depends on the pressure of the gas. Thus for equal
positive and negative currents in air at a pressure of 70 cm. the
reaction for a positive point was 1.9 times that of a negative one, at
40 cm. pressure 2.6 times, at 20 cm. pressure 3.2 times, at 10.3 cm.
pressure 7 times, and at 5.1 cm. pressure 15 times the reaction for the
negative point. Investigation shows that the reaction should be
proportional to the quotient of the current by the velocity acquired by
an ion under unit potential gradient. Now this velocity is inversely
proportional to the pressure, so that the reaction should on this view
be directly proportional to the pressure. This agrees with Arrhenius'
results when the point is positive. Again, the velocities of an ion in
hydrogen, air and carbonic acid at the same pressure are approximately
inversely proportional to the square roots of their molecular weights,
so that the reaction should be directly proportional to this quantity.
This also agrees with Arrhenius' results for the discharge from a
positive point. The velocity of the negative ion is greater than that of
a positive one under the same potential gradient, so that the reaction
for the negative point should be less than that for a positive one, but
the excess of the positive reaction over the negative is much greater
than that of the velocity of the negative ion over the velocity of the
positive. There is, however, reason to believe that a considerable
condensation takes place around the negative ion as a nucleus after it
is formed, so that the velocity of the negative ion under a given
potential gradient will be greater immediately after the ion is formed
than when it has existed for some time. The measurements which have been
made of the velocities of the ions relate to those which have been some
time in existence, but a large part of the reaction will be due to the
newly-formed ions moving with a greater velocity, and thus giving a
smaller reaction than that calculated from the observed velocity.
With a given potential difference between the point and the neighbouring
conductor the current issuing from the point is greater when the point
is negative than when it is positive, except in oxygen, when it is less.
Warburg (_Sitz. Akad. d. Wissensch. zu Berlin_, 1899, 50, p. 770) has
shown that the addition of a small quantity of oxygen to nitrogen
produces a great diminution in the current from a negative point, but
has very little effect on the discharge from a positive point. Thus the
removal of a trace of oxygen made a leak from a negative point 50 times
what it was before. Experiments with hydrogen and helium showed that
impurities in these gases had a great effect on the current when the
point was negative, and but little when it was positive. This suggests
that the impurities, by condensing round the negative ions as nuclei,
seriously diminish their velocity. If a point is charged up to a high
and rapidly alternating potential, such as can be produced by the
electric oscillations started when a Leyden jar is discharged, then in
hydrogen, nitrogen, ammonia and carbonic acid gas a conductor placed in
the neighbourhood of the point gets a negative charge, while in air and
oxygen it gets a positive one. There are two considerations which are of
importance in connexion with this effect. The first is the velocity of
the ions in the electric field, and the second the ease with which the
ions can give up their charges to the metal point. The greater velocity
of the negative ions would, if the potential were rapidly alternating,
cause an excess of negative ions to be left in the surrounding gas. This
is the case in hydrogen. If, however, the metal had a much greater
tendency to unite with negative than with positive ions, such as we
should expect to be the case in oxygen, this would act in the opposite
direction, and tend to leave an excess of positive ions in the gas.
_The Characteristic Curve for Discharge through Gases._--When a current
of electricity passes through a metallic conductor the relation between
the current and the potential difference is the exceedingly simple one
expressed by Ohm's law; the current is proportional to the potential
difference. When the current passes through a gas there is no such
simple relation. Thus we have already mentioned cases where the current
increased as the potential increased although not in the same
proportion, while as we have seen in certain stages of the arc discharge
the potential difference diminishes as the current increases. Thus the
problem of finding the current which a given battery will produce when
part of the circuit consists of a gas discharge is much more complicated
than when the circuit consists entirely of metallic conductors. If,
however, we measure the potential difference between the electrodes in
the gas when different currents are sent through it, we can plot a
curve, called the "characteristic curve," whose ordinates are the
potential differences between the electrodes in the gas and the
abscissae the corresponding currents. By the aid of this curve we can
calculate the current produced when a given battery is connected up to
the gas by leads of known resistance.
For let E0 be the electromotive force of the battery, R the resistance
of the leads, i the current, the potential difference between the
terms in the gas will be E0 - Ri. Let ABC (fig. 22) be the
"characteristic curve," the ordinates being the potential difference
between the terminals in the gas, and the abscissae the current. Draw
the line LM whose equation is E = E0 - Ri, then the points where this
line cuts the characteristic curves will give possible values of i and
E, the current through the discharge tube and the potential difference
between the terminals. Some of these points may, however, correspond
to an unstable position and be impossible to realize. The following
method gives us a criterion by which we can distinguish the stable
from the unstable positions. If the current is increased by [delta]i,
the electromotive force which has to be overcome by the battery is
R[delta]i + dE/di · [delta]i. If R + dE/di is positive there will be
an unbalanced electromotive force round the circuit tending to stop
the current. Thus the increase in the current will be stopped and the
condition will be a stable one. If, however, R + dE/di is negative
there will be an unbalanced electromotive force tending to increase
the current still further; thus the current will go on increasing and
the condition will be unstable. Thus for stability R + dE/di must be
positive, a condition first given by Kaufmann (_Ann. der Phys._ 11, p.
158). The geometrical interpretation of this condition is that the
straight line LM must, at the point where it cuts the characteristic
curve, be steeper than the tangent to characteristic curve. Thus of
the points ABC where the line cuts the curve in fig. 22, A and C
correspond to stable states and B to an unstable one. The state of
things represented by a point P on the characteristic curve when the
slope is downward cannot be stable unless there is in the external
circuit a resistance greater than that represented by the tangent of
the inclination of the tangent to the curve at P to the horizontal
axis.
[Illustration: FIG. 22.]
If we keep the external electromotive force the same and gradually
increase the resistance in the leads, the line LM will become steeper
and steeper. C will move to the left so that the current will
diminish; when the line gets so steep that it touches the curve at C',
any further increase in the resistance will produce an abrupt change
in the current; for now the state of things represented by a point
near A' is the only stable state. Thus if the BC part of the curve
corresponded to a luminous discharge and the A part to a dark
discharge, we see that if the electromotive force is kept constant
there is a minimum value of the current for the luminous discharge. If
the current is reduced below this value, the discharge ceases to be
luminous, and there is an abrupt diminution in the current.
_Cathode Rays._--When the gas in the discharge tube is at a very low
pressure some remarkable phenomena occur in the neighbourhood of the
cathode. These seem to have been first observed by Plücker (_Pogg. Ann._
107, p. 77; 116, p. 45) who noticed on the walls of the glass tube near
the cathode a greenish phosphorescence, which he regarded as due to rays
proceeding from the cathode, striking against the sides of the tube, and
then travelling back to the cathode. He found that the action of a
magnet on these rays was not the same as the action on the part of the
discharge near the positive electrode. Hittorf (_Pogg. Ann._ 136, p. 8)
showed that the agent producing the phosphorescence was intercepted by a
solid, whether conductor or insulator, placed between the cathode and
the sides of the tube. He regarded the phosphorescence as caused by a
motion starting from the cathode and travelling in straight lines
through the gas. Goldstein (_Monat. der Berl. Akad._, 1876, p. 24)
confirmed this discovery of Hittorf's, and further showed that a
distinct, though not very sharp, shadow is cast by a small object placed
near a large plane cathode. This is a proof that the rays producing the
phosphorescence must be emitted almost normally from the cathode, and
not, like the rays of light from a luminous surface, in all directions,
for such rays would not produce a perceptible shadow if a small body
were placed near the plane. Goldstein regarded the phosphorescence as
due to waves in the ether, for whose propagation the gas was not
necessary. Crookes (_Phil. Trans._, 1879, pt. i. p. 135; pt. ii. pp.
587, 661), who made many remarkable researches in this subject, took a
different view. He regarded the rays as streams of negatively
electrified particles projected normally from the cathode with great
velocity, and, when the pressure is sufficiently low, reaching the sides
of the tube, and by their impact producing phosphorescence and heat. The
rays on this view are deflected by a magnet, because a magnet exerts a
force on a charged moving body.
These rays striking against glass make it phosphorescent. The colour of
the phosphorescence depends on the kind of glass; thus the light from soda
glass is a yellowish green, and that from lead glass blue. Many other
bodies phosphoresce when exposed to these rays, and in particular the
phosphorescence of some gems, such as rubies and diamonds, is exceedingly
vivid. The spectrum of the phosphorescent light is generally continuous,
but Crookes showed that the phosphorescence of some of the rare earths,
such as yttrium, gives a spectrum of bright bands, and he founded on this
fact a spectroscopic method of great importance. Goldstein (_Wied. Ann._
54, p. 371) discovered that the haloid salts of the alkali metals change
colour under the rays, sodium chloride, for example, becoming violet. The
coloration is a surface one, and has been traced by E. Wiedemann and
Schmidt (_Wied. Ann._ 54, p. 618) to the formation of a subchloride.
Chlorides of tin, mercury and lead also change colour in the same way. E.
Wiedemann (_Wied. Ann._ 56, p. 201) discovered another remarkable effect,
which he called thermo-luminescence; he found that many bodies after being
exposed to the cathode rays possess for some time the power of becoming
luminous when their temperature is raised to a point far below that at
which they become luminous in the normal state. Substances belonging to
the class called by van 't Hoff solid solutions exhibit this property of
thermo-luminescence to a remarkable extent. They are formed when two
salts, one greatly in excess of the other, are simultaneously precipitated
from a solution. A trace of MnSO4 in CaSO4 shows very brilliant
thermo-luminescence. The impact of cathode rays produces after a time
perceptible changes in the glass. Crookes (_Phil. Trans._ pt. ii. 1879, p.
645) found that after glass has been phosphorescing for some time under
the cathode rays it seems to get tired, and the phosphorescence is not so
bright as it was initially. Thus, for example, when the shadow of a
Maltese cross is thrown on the walls of the tube as in fig. 23, if after
the discharge has been going on for some time the cross is shaken down or
a new cathode used whose line of fire does not cut the cross, the pattern
of the cross will still be seen on the glass, but it will now be brighter
instead of darker than the surrounding portion. The portions shielded by
the cross, not being tired by being made to phosphoresce for a long time,
respond more vigorously to the stimulus than those portions which have not
been protected. Skinner (_Proc. Camb. Phil. Soc._ ix. p. 371) and Thomson
found on the glass which had been exposed to the rays gelatinous
filaments, apparently silica, resulting from the reduction of the glass. A
reducing action was also noticed by Villard (_Journ. de phys._ 3, viii. p.
140) and Wehnelt (_Wied. Ann._ 67, p. 421). It can be well shown by
letting the rays fall on a plate of oxidized copper, when the part struck
by the rays will become bright. The rays heat bodies on which they fall,
and if they are concentrated by using as a cathode a portion of a
spherical surface, the heat at the centre becomes so great that a piece of
platinum wire can be melted or a diamond charred. Measurements of the
heating effects of the rays have been made by Thomson (_Phil. Mag._ [5],
44, p. 293) and Cady (_Ann. der Phys._ 1, p. 678). Crookes (_Phil.
Trans._, 1879, pt. i. p. 152) showed that a vane mounted as in a
radiometer is set in rotation by the rays, the direction of the rotation
being the same as would be produced by a stream of particles proceeding
from the cathode. The movement is not due to the momentum imparted to the
vanes by the rays, but to the difference in temperature between the sides
of the vanes, the rays making the side against which they strike hotter
than the other.
[Illustration: FIG. 23.]
_Effect of a Magnet._--The rays are deflected by a magnet, so that the
distribution of phosphorescence over the glass and the shape and
position of the shadows cast by bodies in the tube are altered by the
proximity of a magnet. The laws of magnetic deflection of these rays
have been investigated by Plücker (_Pogg._ _Ann._ 103, p. 88), Hittorf
(_Pogg. Ann._ 136, p. 213), Crookes (_Phil. Trans._, 1879, pt. 1, p.
557), and Schuster (_Proc. Roy. Soc._ 47, p. 526). The deflection is the
same as that of negatively electrified particles travelling along the
path of the rays. Such particles would in a magnetic field be acted on
by a force at right angles to the direction of motion of the particle
and also to the magnetic force, the magnitude of the force being
proportional to the product of the velocity of the particle, the
magnetic force, and the sine of the angle between these vectors. In this
case we have seen that if the particle is not acted on by an
electrostatic field, the path in a uniform magnetic field is a spiral,
which, if the magnetic force is at right angles to the direction of
projection of the particle, becomes a circle in the plane at right
angles to the magnetic force, the radius being mv/He, where m, v, e are
respectively the mass, velocity and charge on the particle, and H is the
magnetic force. The smaller the difference of potential between the
electrodes of the discharge tube the greater the deflection produced by
a magnetic field of given strength, and as the difference of potential
rapidly increases with diminution of pressure, after a certain pressure
has been passed, the higher the exhaustion of the tube the less the
magnetic deflection of the rays. Birkeland (_Comptes rendus_, 1896, p.
492) has shown that when the discharge is from an induction coil the
cathode rays produced in the tube at any one time are not equally
deflected by a magnet, but that a narrow patch of phosphorescence when
deflected by a magnet is split up into several distinct patches, giving
rise to what Birkeland calls the "magnetic spectrum." Strutt (_Phil.
Mag._ 48, p. 478) has shown that this magnetic spectrum does not occur
if the discharge of a large number of cells is employed instead of the
coil. Thomson (_Proc. Camb. Phil. Soc._ 9, p. 243) has shown that if the
potential difference between the electrodes is kept the same the
magnetic deflection is independent of the nature of the gas filling the
discharge tube; this was tested with gases so different as air,
hydrogen, carbonic acid and methyl iodide.
_Charge of Negative Electricity carried by the Rays._--We have seen that
the rays are deflected by a magnet, as if they were particles charged
with negative electricity. Perrin (_Comptes rendus_, 121, p. 1130)
showed by direct experiment that a stream of negative electricity is
associated with the rays. A modification made by Thomson of Perrin's
experiment is sketched in fig. 24 (_Phil. Mag._ 48, p. 478).
[Illustration: FIG. 24.]
The rays start from the cathode A, and pass through a slit in a solid
brass rod B fitting tightly into the neck of the tube. This rod is
connected with earth and used as the anode. The rays after passing
through the slit travel through the vessel C. D and E are two
insulated metal cylinders insulated from each other, and each having a
slit cut in its face so as to enable the rays to pass into the inside
of the inner cylinder, which is connected with an electrometer, the
outer cylinder being connected with the earth. The two cylinders are
placed on the far side of the vessel, but out of the direct line of
fire of the rays. When the rays go straight through the slit there is
only a very small negative charge communicated to the inner cylinder,
but when they are deflected by a magnet so that the phosphorescent
patch falls on the slit in the outer cylinder the inner cylinder
receives a very large negative charge, the increase coinciding very
sharply with the appearance of the phosphorescent patch on the slit.
When the patch is so much deflected by the magnet that it falls below
the slit, the negative charge in the cylinder again disappears. This
experiment shows that the cathode rays are accompanied by a stream of
negative electrification. The same apparatus can be used to show that
the passage of cathode rays through a gas makes it a conductor of
electricity. For if the induction coil is kept running and a stream of
the rays kept steadily going into the inner cylinder, the potential
of the inner cylinder reaches a definite negative value below which it
does not fall, however long the rays may be kept going. The cylinder
reaches a steady state in which the gain of negative electricity from
the cathode rays is equal to the loss by leakage through the
conducting gas, the conductivity being produced by the passage of the
rays through it. If the inner cylinder is charged up initially with a
greater negative charge than corresponds to the steady state, on
turning the rays on to the cylinder the negative charge will decrease
and not increase until it reaches the steady state. The conductivity
produced by the passage of cathode rays through a gas diminishes
rapidly with the pressure. When rays pass through a gas at a low
pressure, they are deflected by an electric field; when the pressure
of the gas is higher the conductivity it acquires when the cathode
rays pass through it is so large that the potential gradient cannot
reach a sufficiently high value to produce an appreciable deflection.
Thus the cathode rays carry a charge of negative electricity; the
experiment described on page 875 (fig. 13) shows that they are deflected
by an electric field as if they were negatively electrified, and are
acted on by a magnetic force in just the way this force would act on a
negatively electrified body moving along the path of the rays. There is
therefore every reason for believing that they are charges of negative
electricity in rapid motion. By measuring the deflection produced by
magnetic and electric fields we can determine the velocity with which
these particles moved and the ratio of the mass of the particle to the
charge carried by it.
We may conclude from the experiments that the value of m/e for the
particles constituting the cathode rays is of the order 1/1.7 × 10^7,
and we have seen that m/e has the same value in all the other cases of
negative ions in a gas at low pressure for which it has been
measured--viz. for the ions produced when ultra-violet light falls on a
metal plate, or when an incandescent carbon filament is surrounded by a
gas at a low pressure, and for the [beta] particles given out by
radio-active bodies. We have also seen that the value of the charge on
the gaseous ion, in all cases in which it has been measured--viz. the
ions produced by Röntgen and uranium radiation, by ultra-violet light,
and by the discharge of electrification from a point--is the same in
magnitude as the charge carried by the hydrogen atom in the electrolysis
of solutions. The mass of the hydrogen alone is, however, 10^-4 times
this charge, while the mass of the carriers of negative electrification
is only 1/1.7 × 10^7 times the charge; hence the mass of the carriers of
the negative electrification is only 1/1700 of the mass of the hydrogen
atom. We are thus, by the study of the electric discharge, forced to
recognize the existence of masses very much smaller than the smallest
mass hitherto recognized.
Direct determinations of the velocity of the cathode rays have been
made by J. J. Thomson (_Phil. Mag._ 38, p. 358), who measured the
interval between the appearance of phosphorescence on two pieces of
glass placed at a known distance apart, and by Maiorana (_Nuovo
Cimento_, 4, 6, p. 336) and Battelli and Stefanini (_Phys. Zeit._ 1,
p. 51), who measured the interval between the arrival of the negative
charge carried by the rays at two places separated by a known
distance. The values of the velocity got in this way are much smaller
than the values got by the indirect methods previously described: thus
J. J. Thomson at a fairly high pressure found the velocity to be 2 ×
10^7 cm./sec. Maiorana found values ranging between 10^7 and 6 × 10^7
cm./sec, and Battelli and Stefanini values ranging from 6 × 10^6 to
1.2 × 10^7. In these methods it is very difficult to eliminate the
effect of the interval which elapses between the arrival of the rays
and the attainment by the means of detection, such as the
phosphorescence of the glass or the deflection of the electrometer, of
sufficient intensity to affect the senses.
[Illustration: FIG. 25.]
_Transmission of Cathode Rays through Solids--Lenard Rays._--It was for
a long time believed that all solids were absolutely opaque to these
rays, as Crookes and Goldstein had proved that very thin glass, and even
a film of collodion, cast intensely black shadows. Hertz (_Wied. Ann._
45, p. 28), however, showed that behind a piece of gold-leaf or
aluminium foil an appreciable amount of phosphorescence occurred on the
glass, and that the phosphorescence moved when a magnet was brought
near. A most important advance was next made by Lenard (_Wied. Ann._ 51,
p. 225), who got the cathode rays to pass from the inside of a discharge
tube to the air outside. For this purpose he used a tube like that shown
in fig. 25. The cathode K is an aluminium disc 1.2 cm. in diameter
fastened to a stiff wire, which is surrounded by a glass tube. The anode
A is a brass strip partly surrounding the cathode. The end of the tube
in front of the cathode is closed by a strong metal cap, fastened in
with marine glue, in the middle of which a hole 1.7 mm. in diameter is
bored, and covered with a piece of very thin aluminium foil about .0026
mm. in thickness. The aluminium window is in metallic contact with the
cap, and this and the anode are connected with the earth. The tube is
then exhausted until the cathode rays strike against the window. Diffuse
light spreads from the window into the air outside the tube, and can be
traced in a dark room for a distance of several centimetres. From the
window, too, proceed rays which, like the cathode rays, can produce
phosphorescence, for certain bodies phosphoresce when placed in the
neighbourhood of the window. This effect is conveniently observed by the
platino-cryanide screens used to detect Röntgen radiation. The
properties of the rays outside the tube resemble in all respects those
of cathode rays; they are deflected by a magnet and by an electric
field, they ionize the gas through which they pass and make it a
conductor of electricity, and they affect a photographic plate and
change the colour of the haloid salts of the alkali metals. As, however,
it is convenient to distinguish between cathode rays outside and inside
the tube, we shall call the former Lenard rays. In air at atmospheric
pressure the Lenard rays spread out very diffusely. If the aluminium
window, instead of opening into the air, opens into another tube which
can be exhausted, it is found that the lower the pressure of the gas in
this tube the farther the rays travel and the less diffuse they are. By
filling the tube with different gases Lenard showed that the greater the
density of the gas the greater is the absorption of these rays. Thus
they travel farther in hydrogen than in any other gas at the same
pressure. Lenard showed, too, that if he adjusted the pressure so that
the density of the gas in this tube was the same--if, for example, the
pressure when the tube was filled with oxygen was 1/16 of the pressure
when it was filled with hydrogen--the absorption was constant whatever
the nature of the gas. Becker (_Ann. der Phys._ 17, p. 381) has shown
that this law is only approximately true, the absorption by hydrogen
being abnormally large, and by the inert monatomic gases, such as helium
and argon, abnormally small. The distance to which the Lenard rays
penetrate into this tube depends upon the pressure in the discharge
tube; if the exhaustion in the latter is very high, so that there is a
large potential difference between the cathode and the anode, and
therefore a high velocity for the cathode rays, the Lenard rays will
penetrate farther than when the pressure in the discharge tube is higher
and the velocity of the cathode rays smaller. Lenard showed that the
greater the penetrating power of his rays the smaller was their magnetic
deflection, and therefore the greater their velocity; thus the greater
the velocity of the cathode rays the greater is the velocity of the
Lenard rays to which they give rise. For very slow cathode rays the
absorption by different gases departs altogether from the density law,
so much so that the absorption of these rays by hydrogen is greater than
that by air (Lenard, _Ann. der Phys._ 12, p. 732). Lenard (_Wied. Ann._
56, p. 255) studied the passage of his rays through solids as well as
through gases, and arrived at the very interesting result that the
absorption of a substance depends only upon its density, and not upon
its chemical composition or physical state; in other words, the amount
of absorption of the rays when they traverse a given distance depends
only on the quantity of matter they cut through in the distance.
McClelland (_Proc. Roy. Soc._ 61, p. 227) showed that the rays carry a
charge of negative electricity, and M'Lennan measured the amount of
ionization rays of given intensity produced in different gases, finding
that if the pressure is adjusted so that the density of the different
gases is the same the number of ions per cubic centimetre is also the
same. In this case, as Lenard has shown, the absorption is the same, so
that with the Lenard rays, as with uranium and probably with Röntgen
rays, equal absorption corresponds to equal ionization. A convenient
method for producing Lenard rays of great intensity has been described
by Des Coudres (_Wied. Ann._ 62, p. 134).
_Diffuse Reflection of Cathode Rays._--When cathode rays fall upon a
surface, whether of an insulator or a conductor, cathode rays start from
the surface in all directions. This phenomenon, which was discovered by
Goldstein (_Wied. Ann._ 62, p. 134), has been investigated by Starke
(_Wied. Ann._ 66, p. 49; _Ann. der Phys._ 111, p. 75), Austin and Starke
(_Ann. der Phys._ 9, p. 271), Campbell-Swinton (_Proc. Roy. Soc._ 64, p.
377), Merritt (_Phys. Rev._ 7, p. 217) and Gehrcke (_Ann. der Phys._ 8,
p. 81); it is often regarded as analogous to the diffuse reflection of
light from such a surface as gypsum, and is spoken of as the diffuse
reflection of the cathode rays. According to Merritt and Austin and
Starke the deviation in a magnetic field of these reflected rays is the
same as that of the incident rays. The experiments, however, were
confined to rays reflected so that the angle of reflection was nearly
equal to that of incidence. Gehrcke showed that among the reflected rays
there were a large number which had a much smaller velocity than the
incident ones. According to Campbell-Swinton the "diffuse" reflection is
accompanied by a certain amount of "specular" reflection. Lenard, who
used slower cathode rays than Austin and Starke, could not detect in the
scattered rays any with velocities comparable with that of the incident
rays; he obtained copious supplies of slow rays whose speed did not
depend on the angle of incidence of the primary rays (_Ann. der Phys._
15, p. 485). When the angle of incidence is very oblique the surface
struck by the rays gets positively charged, showing that the secondary
rays are more numerous than the primary.
_Repulsion of two Cathode Streams._--Goldstein discovered that if in a
tube there are two cathodes connected together, the cathodic rays from
one cathode are deflected when they pass near the other. Experiments
bearing on this subject have been made by Crookes and Wiedemann and
Ebert. The phenomena may be described by saying that the repulsion of
the rays from a cathode A by a cathode B is only appreciable when the
rays from A pass through the Crookes dark space round B. This is what we
should expect if we remember that the electric field in the dark space
is far stronger than in the rest of the discharge, and that the gas in
the other parts of the tube is rendered a conductor by the passage
through it of the cathode rays, and therefore incapable of transmitting
electrostatic repulsion.
Scattering of the Negative Electrodes.--In addition to the cathode rays,
portions of metal start normally from the cathode and form a metallic
deposit on the walls of the tube. The amount of this deposit varies very
much with the metal. Crookes (_Proc. Roy. Soc._ 50, p. 88) found that
the quantities of metal torn from electrodes of the same size, in equal
times, by the same current, are in the order Pd, Au, Ag, Pb, Sn, Pt, Cu,
Cd, Ni, In, Fe.... In air there is very little deposit from an Al
cathode, but it is abundant in tubes filled with the monatomic gases,
mercury vapour, argon or helium. The scattering increases as the density
of the gas diminishes. The particles of metal are at low pressures
deflected by a magnet, though not nearly to the same extent as the
cathode rays. According to Grandquist, the loss of weight of the cathode
in a given time is proportional to the square of the current; it is
therefore not, like the loss of the cathode in ordinary electrolysis,
proportional to the quantity of current which passes through it.
[Illustration: FIG. 26.]
_Positive Rays or "Canalstrahlen."_--Goldstein (_Berl. Sitzungsb._ 39,
p. 691) found that with a perforated cathode certain rays occurred
behind the cathode which were not appreciably deflected by a magnet;
these he called Canalstrahlen, but we shall, for reasons which will
appear later, call them "positive rays."
Their appearance is well shown in fig. 26, taken from a paper by Wehnelt
(_Wied. Ann._ 67, p. 421) in which they are represented at B. Goldstein
found that their colour depends on the gas in which they are formed,
being gold-colour in air and nitrogen, rose-colour in hydrogen,
yellowish rose in oxygen, and greenish gray in carbonic acid.
The colour of the luminosity due to positive rays is not in general the
same as that due to anode rays; the difference is exceptionally well
marked in helium, where the cathode ray luminosity is blue while that
due to the positive rays is red. The luminosity produced when the rays
strike against solids is also quite distinct. The cathode rays make the
body emit a continuous spectrum, while the spectrum produced by the
positive rays often shows bright lines. Thus lithium chloride under
cathode rays gives out a steely blue light and the spectrum is
continuous, while under the positive rays the salt gives out a brilliant
red light and the spectrum shows the red helium line. It is remarkable
that the lines on the spectra of the alkali metals are much more easily
produced when the positive rays fall on the oxide of the metal than when
they fall on the metal itself. Thus when the positive rays fall on a
pool of the liquid alloy of sodium and potassium the specks of oxide on
the surface shine with a bright yellow light while the untarnished part
of the surface is quite dark.
W. Wien (_Wied. Ann._ 65, p. 445) measured the values of e/m for the
particles forming the positive rays. Other measurements have been made
by Ewers (_Wied. Ann._ 69, p. 167) and J. J. Thomson (_Phil. Mag._ 13,
p. 561). The differences between the values of e/m for the cathode and
positive rays are very remarkable. For cathode rays whose velocity does
not approach that of light, e/m is always equal to 1.7 × 10^8, while for
the positive rays the greatest value of this quantity yet observed is
10^4, which is also the value of e/m for the hydrogen ions in the
electrolysis of dilute solutions. In some experiments made by J. J.
Thomson (_Phil. Mag._, 14, p. 359) it was found that when the pressure
of the gas was not too low the bright spot produced by the impact of a
pencil of these rays on a phosphorescent screen is deflected by electric
and magnetic forces into a continuous band extending on both sides of
the undeflected position. The portion on one side is in general much
fainter than that on the other. The direction of this deflection shows
that it is produced by particles charged with negative electricity,
while the brighter band is due to particles charged with positive
electricity. The negatively electrified particles which produce the band
c.c are not corpuscles, for from the electric and magnetic deflections
we can find the value of e/m. As this proves to be equal to 10^4, we see
that the mass of the carrier of the negative charge is comparable with
that of an atom, and so very much greater than that of a corpuscle. At
very low pressures part of the phosphorescence disappears, while the
upper portion breaks up into two patches (fig. 27). For one of these the
maximum value of e/m is 10^4 and for the other 5 × 10³. At low pressures
the appearance of the patches and the values of e/m are the same whether
the tube is filled originally with air, hydrogen or helium. In some of
the experiments the tube was exhausted until the pressure was too low to
allow the discharge to pass. A very small quantity of the gas under
investigation was then admitted into the tube, just sufficient to allow
the discharge to pass, and the deflection of the phosphorescent patch
measured. The following gases were admitted into the tube, air, carbonic
oxide, oxygen, hydrogen, helium, argon and neon, but whatever the gas
the appearance of the phosphorescence was the same; in every case there
were two patches, for one of which e/m = 10^4 and for the other e/m =
5 × 10³. In helium at higher pressures another patch was observed, for
which e/m = 2.5 × 10^8. The continuous band into which the
phosphorescent spot is drawn out when the pressure is not exceedingly
low, which involves the existence of particles for which the mean value
of e/m varies from zero to 10^4, can be explained as follows. The rays
on their way to the phosphorescent screen have to pass through gas which
is ionized by the passage through it of the positive rays; this gas will
therefore contain free corpuscles. The particles which constitute the
rays start with a charge of positive electricity. Some of these
particles in their journey through the gas attract a corpuscle whose
negative charge neutralizes the positive charge on the particle. The
particles when in this neutral state may be ionized by collision and
reacquire a positive charge, or by attracting another particle may
become negatively charged, and this process may be repeated several
times on their journey to the phosphorescent screen. Thus some of the
particles, instead of being positively charged for the whole of the time
they are exposed to the electric and magnetic forces, may be for a part
of that time without a charge or even have a negative charge. The
deflection of a particle is proportional to the average value of its
charge whilst under the influence of the deflecting forces. Thus if a
particle is without a charge for a part of the time, its deflection will
be less than that of a particle which has retained its positive charge
for the whole of its journey, while the few particles which have a
negative charge for a longer time than they have a positive will be
deflected in the opposite direction to the main portion and will produce
the tail (fig. 27).
[Illustration: Fig. 27.]
A similar explanation will apply to the positive rays discovered by
Villard (_Comptes rendus_, 143, p. 674) and J. J. Thomson (_Phil. Mag._
13, p. 359), which travel in the opposite direction to the rays we have
been considering, i.e. they travel away from the cathode and in the
direction of the cathode's rays; these rays are sometimes called
"retrograde" rays. These as far as has been observed have always the
same maximum value of e/m, i.e. 10^4, and there are a considerable
number of negative ones always mixed with them. The maximum velocity of
both the positive and retrograde rays is about 2 × 10^8 cm./sec. and
varies very little with the potential difference between the electrodes
in the tube in which they are produced (J. J. Thomson, _Phil. Mag._,
Dec. 1909).
The positive rays show, when the pressure is not very low, the line
spectrum of the gas through which they pass. An exceedingly valuable set
of observations on this point have been made by Stark and his pupils
(_Physik. Zeit._ 6, p. 892; _Ann. der Phys._ 21, pp. 40, 457). Stark has
shown that in many gases, notably hydrogen, the spectrum shows the
Doppler effect, and he has been able to calculate in this way the
velocity of the positive rays.
_Anode Rays._--Gehrcke and Reichenhein (_Ann. der Phys._ 25, p. 861)
have found that when the anode consists of a mixture of sodium and
lithium chloride raised to a high temperature either by the discharge
itself or by an independent heating circuit, very conspicuous rays come
from the anode when the pressure of the gas in the discharge tube is
very low, and a large coil is used to produce the discharge. The
determination of e/m for these rays showed that they are positively
charged atoms of sodium or lithium, moving with very considerable
velocity; in some of Gehrcke's experiments the maximum velocity was as
great as 1.8 × 10^7 cm./sec. though the average was about 10^7 cm./sec.
These velocities are less than those of the positive rays whose maximum
velocity is about 2 × 10^8 cm./sec. (J. J. T.)
FOOTNOTES:
[1] The values for nickel and bismuth given in the table are much
higher than later values obtained with pure electrolytic nickel and
bismuth.
[2] The value here given, namely 12.885, for the electric
mass-resistivity of liquid mercury as determined by Matthiessen is
now known to be too high by nearly 1%. The value at present accepted
is 12.789 ohms per metre-gramme at 0° C.
[3] The value (1630) here given for hard-drawn copper is about ¼%
higher than the value now adopted, namely, 1626. The difference is
due to the fact that either Jenkin or Matthiessen did not employ
precisely the value at present employed for the density of hard-drawn
and annealed copper in calculating the volume-resistivities from the
mass-resistivities.
[4] Matthiessen's value for nickel is much greater than that obtained
in more recent researches. (See Matthiessen and Vogt, _Phil. Trans._,
1863, and J. A. Fleming, _Proc. Roy. Soc._, December 1899.)
[5] Matthiessen's value for mercury is nearly 1% greater than the
value adopted at present as the mean of the best results, namely
94,070.
[6] The samples of silver, copper and nickel employed for these tests
were prepared electrolytically by Sir J. W. Swan, and were
exceedingly pure and soft. The value for volume-resistivity of nickel
as given in the above table (from experiments by J. A. Fleming,
_Proc. Roy. Soc._, December 1899) is much less (nearly 40%) than the
value given by Matthiessen's researches.
[7] The electrolytic bismuth here used was prepared by Hartmann and
Braun, and the resistivity taken by J. A. Fleming. The value is
nearly 20% less than that given by Matthiessen.
[8] In 1899 a committee was formed of representatives from eight of
the leading manufacturers of insulated copper cables with delegates
from the Post Office and Institution of Electrical Engineers, to
consider the question of the values to be assigned to the resistivity
of hard-drawn and annealed copper. The sittings of the committee were
held in London, the secretary being A. H. Howard. The values given in
the above paragraphs are in accordance with the decision of this
committee, and its recommendations have been accepted by the General
Post Office and the leading manufacturers of insulated copper wire
and cables.
[9] Platinoid is an alloy introduced by Martino, said to be similar
in composition to German silver, but with a little tungsten added. It
varies a good deal in composition according to manufacture, and the
resistivity of different specimens is not identical. Its electric
properties were first made known by J. T. Bottomley, in a paper read
at the Royal Society, May 5, 1885.
[10] An equivalent gramme molecule is a weight in grammes equal
numerically to the chemical equivalent of the salt. For instance, one
equivalent gramme molecule of sodium chloride is a mass of 58.5
grammes. NaCl = 58.5.
[11] F. Kohlrausch and L. Holborn, _Das Leitvermögen der Elektrolyte_
(Leipzig, 1898).
[12] It should be noticed that the velocities calculated in
Kohlrausch's theory and observed experimentally are the average
velocities, and involve both the factors mentioned above; they
include the time wasted by the ions in combination with each other,
and, except at great dilution, are less than the velocity with which
the ions move when free from each other.