V = 1/ke[alpha]d;_Encyclopaedia Britannica, 11th Edition, "Conduction, Electric" Volume 6, Slice 8

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

--(nu) = [alpha]nu + [gamma]mw ,

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] \ /

[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 |

+---------+-----------+---------+-------+-----------+-----------------+

+---------+-----------+---------+-------+-----------+-----------------+

|Air | 340-350 | .. | .. | .. | 341 |

|H2 | about 300 | 298 | .. | 168 | 302-308 |

|O2 | .. | 369 | .. | .. | .. |

|N2 |230 if free| 232 | .. | 207 | 251 |

|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 Rontgen 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 Muller (_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 deg. 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 deg. C, and that of the latter 2700 deg. 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. Frohlich (_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 Frohlich'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 Rontgen 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

Rontgen, those in the third and fourth to Precht:--

+------+-----------------------------+--------------------+

| |Discharge Potential. Point +.| Pressure 760. |

| Gas. +--------------+--------------+----------+---------+

+------+--------------+--------------+----------+---------+

| 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. Rontgen 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 Plucker (_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 Plucker (_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 X 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 Rontgen 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 X 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 X

10^7 cm./sec. Maiorana found values ranging between 10^7 and 6 X 10^7

cm./sec, and Battelli and Stefanini values ranging from 6 X 10^6 to

1.2 X 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 Rontgen 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 Rontgen

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 X 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 X 10^3. 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 X 10^3. In helium at higher pressures another patch was observed, for

which e/m = 2.5 X 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 X 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 X 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 X 10^8 cm./sec. (J. J. T.)

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