Electrical Properties Of Gases - Encyclopedia




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"ELECTRICAL PROPERTIES OF GASES 6.864 for Electric Conduction Through Gases). - The electrical properties of gases vary greatly with the conditions to which the gas is exposed.

A gas in its normal condition is a non-conductor of electricity even though it is the vapour of a good conductor like mercury. On the other hand, when it is exposed to such influences as Röntgen rays, intense electrical forces or the radiation from radioactive substances, it becomes a conductor of electricity. Radioactive radiations are so wide-spread and so difficult to eliminate that it has not been found possible to obtain gases which do not show traces of conductivity under tests as delicate as some of those now at our command. This residual conductivity is, however, so small that we may here leave it out of account. The most important electrical property of a gas in a normal state is its specific inductive capacity. The significance of this property is best illustrated from the relation K-1/47r= NM, between the specific inductive capacity K, N the number of molecules per unit volume, and M the electrostatic moment which a molecule acquires under unit electric force. As we know N, we can if we know the value of K deduce the value of M, and this will tell us a good deal about the shape and size of the molecule. For example, if we regard the molecules as solid conducting spheres, M = r 3 where r is the radius of the sphere. Thus, on this hypothesis we can find the radius of the molecule, if we know the value of K, and though the hypothesis itself does not throw much light on the structure of the atom, it is probable that the radius of a conducting sphere which would produce the same electrical moment would be of the same order of magnitude as the linear dimensions of the molecule: the radii of metallic spheres which would give the specific inductive capacities possessed by hydrogen, nitrogen, oxygen and chlorine, are respectively 1.19 X 10-8, 1.60 X i 08, 1.48 X 10 -8, 2 04 X i 08 centimetres. On the more probable hypothesis that the atoms and molecules consist of electrons arranged in equilibrium round centres of positive electricity, the electric force will displace the electrons relatively to the positive centres and thus cause the molecule to have a finite electrical moment. The more rigidly the electrons are connected to the positive charge, the smaller will be this moment and the smaller the specific inductive capacity of the gas.

The values of K - I for the elements belonging to the same family are connected by a remarkably simple and interesting relation, which was discovered by Mr. Cuthbertson (Phil. Trans.

N

0

F

297

270

192

P

S

CI

1197

II 0 I

768

=299X4 As 1J50 =258 X6

=275X4 Se =261 X6 Te 2495 =249 X10

=192X4 Br 1125 =187X6

1920

= 192 X 10

A.207, p. 1 35). It is shown in the following table, where the numbers under the symbols denoting the elements are the values of - (K - i) X 106: - Thus the values of K - i for successive elements of the same family - (N.P.As): (O,S ,Se,Te): (F.C1.Br.I): (Ne,Ar,Kr,X) - are in all cases very nearly in the proportion i, 4, 6, io. In the simple theory, where the molecules are regarded as conductors, this would indicate that the volumes of the molecules of the successive elements in the same family are in the proportion i, 4, 6, io, for each of these types of elements. On the theory which regards the atom as built up of electrons arranged round positive centres, the configuration of the outer layer of electrons for different members of the same family would be similar, and it is easy to show that for similar configurations of electrons the value of K - i would be proportional to the cube of the linear dimensions, i.e. to the volume enclosed by the outer layer of electrons; so that again on this theory Cuthbertson's result shows that volumes of successive elements in the same family are in the same ratio whether the family be that of the inert gases, the halogens, or the oxygen or nitrogen groups.

Another example of the information as to the nature of the molecule afforded by determinations of the specific inductive capacity is that, while the specific inductive capacity of many gases, e.g. H2, N 2, 02, CO, C02, C12, is equal (as Maxwell's Electromagnetic Theory of Light suggests) to the square of the refractive index, there are, as Badeker (Zeitschrift Physik. Chem. 3 6, p. 305) has shown, others, such as NH 3, HC1, S02, the vapours of water and the alcohols, whose specific inductive capacity is far in excess of the value given by this rule, and moreover the specific inductive capacity of these gases diminishes much more rapidly as the temperature increases than that of gases of the first type. The difference can be accounted for by supposing that the molecules of gases of the first type have no electrical moment when they are free from the action of an external electrical force, while those of the second type have an intrinsic electrical moment apart from that which may be produced by the external force. When there is no electrical field, the collisions between the molecules will cause the axes of electrical moments of the different molecules to be uniformly distributed, so that the average effect will be zero. An electric force will tend to drag the axes of the different molecules into alignment, and the assemblage of molecules will have a finite electrical moment which will be a measure of the specific inductive capacity. Inasmuch as the collisions between the molecules tend to knock their axes out of line and diminish the specific inductive capacity, the latter will diminish as the temperature and with it the vigour of the encounters increases. The substances which have an intrinsic electrical moment have exceptionally active chemical properties and are good solvents, dissociating the salts dissolved in them.

Argon .

Hydrogen

Nitrogen

Air .

Oxygen

Carbon dioxide .

Nitrous oxide .

0.46%

3.83%

4.06%

5.00%

9.40%

11.70%

15.40%

If the distribution of electrons in a molecule were not symmetrical about three axes at right angles to each other, the specific inductive capacity of a single molecule would vary with the direction of the electric force, but as the molecules in a gas are orientated in equal numbers in all directions we should not detect this by direct measurements of the specific inductive capacity. We can however detect this effect in another way; for if the molecules have different specific inductive capacities in different directions the light scattered by the molecules at right angles to the incident unpolarized light will not be plane polarized as it would be if the molecule were symmetrical (J. J. Thomson, Phil. Mag. 40, p. 393), and if the incident light is plane polarized the scattered light will not vanish in any direction. Strutt (Proc. Roy. Soc. 98A. 57) has measured the departure from plane polarization for different gases with the result shown in the following table: This shows that the molecule of argon is very symmetrical, while the nitrogen molecule is more symmetrical than the oxygen, and this again more symmetrical than that of C02.

Table of contents

Ionized Gases

Gases may in various ways be put into a state in which they conduct electricity on an altogether different scale from the normal gas. They acquire this conductivity when Röntgen rays or the rays from radioactive substances pass through them, or when they are traversed by cathode or positive rays. Ultra-violet light of very short wave length can impart this property to a gas, while gases recently driven from flames or from near arcs or sparks or bubbled through certain liquids or passed slowly over phosphorus also possess this property.

The conductivity of gases possesses interesting characteristics. In the first place it persists for some time after the agent which made the gas a conductor has ceased to act; it always however diminishes after the agent is removed, in some cases very rapidly, and finally disappears. The conducting gas loses its conductivity if it is sucked through glass-wool, or made to bubble through water. The conductivity may also be removed by making the gas traverse a strong electric field so that a current of electricity passes through it. The removal of the conductivity by filtering the gas through glass-wool or water shows that the conductivity is due to something mixed with the gas which can be removed by filtration, while the removal of the conductivity by the electrical field shows that this something is charged with electricity and moves under the action of the electric force. Since the gas when in the conducting state shows as a whole no charge of electricity, the charges mixed with the gas must be both positive and negative. We conclude that the conductivity of the gas is due to the presence of electrified particles; some of these particles are positively, others negatively, electrified. These electrified particles are called ions, and the process ionization.

The passage of electricity through a conducting gas does not follow the same laws as the flow through metals and liquid electrolytes; in these the current is proportional to the electromotive force, while for gases the relation is represented by a graph like fig. r, where the ordinates are proportional to the current and 20 ' '10. 100. Z00.300.400.500.600700.800.9001000.1100.1200.1300.1400 1500 Volts FIG.1 the abscissa to the electromotive forces. We see that when the electromotive force is small, the current is proportional to the electromotive force, as in the case of metallic conduction; as the electromotive force increases, the current after a time does not increase nearly so rapidly, and a stage is reached where the current remains constant in spite of the increase in the electromotive force. There is a further stage, which we shall consider later, where the current again increases with the electromotive force, and does so much more rapidly than at any previous stage. The He 14 137 Ar.

568 =142X4 Kr.

850 =142X6 X 1 37 8 =138X10 50 current in the stage when it does not depend upon the electromotive force is said to be saturated. The reason for this saturation is that the passage of a current of electricity through the gas involves the removal of a number of ions proportional to the quantity of electricity passing through the gas. Thus the gas is losing ions at a rate proportional to the current; it cannot go on losing more ions than are produced, so that the current cannot increase beyond a critical value which is proportional to the rate of production of ions. This sometimes produces a state of things which seems anomalous to those accustomed to look at conduction of electricity exclusively from the point of Ohm's law. For example, when gases are exposed to Röntgen rays, the number of ions produced per second is proportional to the volume of the gas, so that, if two parallel plates are immersed in such a gas and a current sent from one to the other, when the distance between the plates is increased the number of ions available for carrying the current and therefore the saturation current will be increased also. Thus apparent " resistance " will diminish as the length of 'the gaseous conductor is increased.

The Nature of the Ions

The question arises, what is the nature of the particles which carry the charges of electricity? Are they the atoms or molecules of the gas, or, for the negative charges, electrons? Information on these points is afforded by measuring the velocity of the ions under given electric forces.

It follows from the kinetic theory of gases that the velocity V of an ion due to an electric force X is given by the equation :- e X V=X(i) - v Here X is the mean free path of the ion through the surrounding molecules, v the average velocity of the ion due to its thermal agitation, this velocity depending only on the mass of the ion and the temperature of the gas, and m is the mass of the ion and e the electric charge carried by it. If we calculate by this formula the velocity of an ion in hydrogen, assuming that the mass of the ion and its free path are the same as those for a molecule of hydrogen, we find that it would be 26 cm/sec. for an electric force of a volt per cm.; the value found by experiment is 6.7 cm/sec. for the positive and 7.9 cm/sec. for the negative ion. The assumption that both X and m are the same for the ion as for the molecule is therefore wrong. It is clear that if, as we have every reason to believe, the normal hydrogen molecule is made up of positively and negatively electrified parts, the ion in virtue of its charge, even if its mass is the same as that of the hydrogen molecule, will exert a greater force upon a neighbouring molecule than would an uncharged molecule, and this increase in the force implies a diminution in the free path, and therefore by equation (i) a diminution in V. That a part of the discrepancy between the results given by the equation and those found by experiment is due to this cause cannot be questioned; the point which is still doubtful is whether the attraction due to the charge on the ion may not cause some of the hydrogen molecules to cling to it, forming a cluster of molecules with a greater mass and smaller free path than a single molecule. It would follow from the general principles of thermodynamics that, if the work required to separate a neutral molecule of hydrogen from a positive charge in its near neighbourhood were comparable with the average energy of translation of the molecules at the temperature of the gas, some such clusters would be formed, and that, if the work of separation were large compared with the energy of agitation, practically all the ions would consist of such clusters. This work would be greater for molecules which, like those of ammonia, or the vapours of water and alcohol, have a finite electrical moment, than for those which, like the molecules of hydrogen, oxygen and nitrogen, have no such moment, so that it is quite possible that, though there may be no clustering with these very permanent gases, there may be some when gases of the other type are present. This differentiation seems borne out by experiment, for no clear indications of clustering seem to have been found for the permanent gases. Since clustering is analogous to chemical combination, we should expect the mobilities, if they depended upon clusters, to have very large temperature coefficients. The mobilities of some of the permanent gases at constant density have been measured by Erikson over a considerable range of temperature, and though there is a considerable temperature effect it is not nearly so large as we should expect if it depended on chemical combination. Again, since clustering is a process of condensation, it would be favoured by an increase in pressure; thus a decrease in pressure would be accompanied by a simplification of the ion, and would increase its mean free path beyond the natural increase due to the diminution in the number of molecules with which the ion comes into collision. If there were no change in the character of the ion with the pressure, the mobility would vary inversely as the pressure; if the character of the ion changes, the mobility at low pressures will be greater than that given by this law. Now experiments show that for the positive ion the mobility is, very accurately, inversely proportional to the pressure over a wide range of pressures; this again is inconsistent with the existence of clusters. On the other hand, it is found that the addition of small quantities of gases which, like the vapours of water and alcohol, have a finite electrical moment produce a marked diminution in the mobility; this effect is more pronounced for the negative than for the positive ion, but as Zeleny has shown it exists for both ions. This effect is readily explained by supposing the water molecules to cluster round the ion. It would seem in accordance with the evidence to conclude that, though there is no evidence of clustering for the permanent gases, it does occur when certain easily condensible gases are present.

The behaviour of negative ions is in many respects quite different from that of the positive ones. In the first place the mobility of the negative ions is for the permanent gases greater than that of the positive; thus, for example, in dry hydrogen the velocities of the negative and positive ions, when the electric force is one volt per cm., are 7:95 and 6.7 respectively, and for air 1.87 and 1.36. The difference is less for moist gases than for dry, while for complex vapours which have comparatively small mobilities Wellisch found that there was very little difference between the mobilities of the positive and negative ions.

For the permanent gases the ratio of the mobilities of the negative and positive ions varies but little with the pressure, until the pressure is reduced below that represented by about 10 cm. of mercury. For lower pressures than this, the mobility of the negative ion increases, as Langevin showed, more rapidly than that of the positive; at the pressure of a mm. or so the mobility of the negative ion in air may be three or four times that of the positive.

An even more interesting result was discovered by Franck and Hertz, who, when they experimented with very carefully purified nitrogen or argon, found that the mobility of the negative ion was more than 100 times that of the positive. The mobilities in these gases are extremely sensitive to traces of oxygen, and a fraction of 1% of oxygen added to the pure gas will reduce the mobility of the negative ion to less than one-tenth of its maximum value. The enormous mobility of the negative ion in nitrogen and argon as compared with that of the positive shows that in them the negative electricity must be carried by electrons and not by atoms or molecules, while the effect of introducing traces of oxygen shows that these electrons readily attach themselves to the molecules of oxygen though they are unable to adhere to molecules of nitrogen or argon. The same effect has also been observed in helium and hydrogen.

These properties of the negative ion are of great importance in connexion with the mechanism of ionization in gases and the structure of atoms and molecules. In the first place, they furnish strong evidence in support of the view that the first stage in the ionization of a gas is the ejection of an electron from the molecule of the gas rather than the separation of the molecule into atoms of which some are charged with positive and others with negative electricity. On this view the negative ion begins its career as an electron and not as an atom, while the positive ion from the beginning is of molecular dimensions. As an electron has much greater mobility than a molecule the mobility of the negative ion will at first be much greater than that of the positive. In some gases, such as oxygen, the electron soon gets attached to a molecule, and its mass and mobility become comparable with those of the positive one. The mobility we measure is the average mobility of the negative ion during its life; part of the time its mobility, being that of an electron, is very much larger than that of the positive ion, while in the other part the two mobilities will be much the same. The excess of mobility of the negative over the positive ion will depend upon the fraction of its life which the negative ion spends as a free electron - a fraction which would tend to increase as the pressure of the gas diminished.

To calculate the mobility of an electron as compared with that of a molecule, we must make some assumption as to the effect of the charge on the mean free path of an electron. We saw that there were some grounds for supposing that, in the case of the positive ions, the mean free path was determined rather by the charge of the ion than by the dimensions of the molecule carrying the charge. Since the magnitude of the charge on the electron is the same as that on the positive ion, we might expect, if this were the case, that the mean free path of an electron would be much the same as that of an ion, so that in equation (i) it would be the factor my which would differentiate the mobility of the ion from that of the electron. If the electron is in thermal equilibrium with the surrounding gas, m y 2 will be the same for the ion and the electron, and thus the mobility will be inversely proportional to the square root of the mass; as the mass of the hydrogen molecule is 3.6 X io 3 times that of the electron, the mobility of the electron in hydrogen should be 60 times that of the positive ion; in nitrogen the mobility of the electron would be about 220 times that of the positive ion. If the positive ion were a cluster of molecules instead of a single molecule, the mobility of the electron as compared with that of the positive electron would be much larger than the preceding figures would indicate.

The difference between the behaviour of the electron in nitrogen or argon and in oxygen is of great importance in connexion with the structure of the atom and molecule, for it indicates that, while a molecule of oxygen can accommodate another electron in addition to those already present, the molecules of nitrogen and argon are unable to do so. It is instructive therefore to consider the results in connexion with the power of the atoms and molecules of the different elements to acquire a negative charge obtained by the study of the positive rays. These show that, while the atoms of hydrogen, carbon, oxygen, fluorine or chlorine readily acquire a negative charge, those of helium, nitrogen, neon, and argon do not; and again that, while it is very exceptional for a molecule whether of a compound or an elementary gas to acquire a negative charge, the molecule of oxygen is able to do so. We see that this result is in accordance with the behaviour of the carrier of the negative charge in an ionized gas. Since the atoms in the positive rays show so much greater affinity for the electrons than the molecules, it follows that if the agent producing ionization were to dissociate some of the molecules of the gas into neutral atoms (and to do this would require the expenditure of much less energy than to ionize the gas), these atoms would be much more effective traps for the electrons than the undissociated molecules. Loeb has shown that even in oxygen an electron collides on the average with about 50,000 molecules of oxygen before it is captured; thus if the oxygen atom could capture an electron at the first encounter, if only one molecule in 50,000 were dissociated into atoms, the effect of the atoms would be as efficacious as that of the molecules in capturing the electrons. When this dissociation takes place the abnormal velocity of the negative ion will only occur in gases like nitrogen and the inert gases whose atoms cannot receive an electron.

Recombination of the Ions

Even when the ions are not removed from a gas by sending a current of electricity through it, their number will not increase indefinitely with the time of exposure of the gas to the ionizing agent. This is due to the recombination which takes place between the positive and negative ions; these ions as they move about in the gas sometimes come into collision with each other, and by forming electrically neutral systems cease to act as ions. The gas will reach a steady state with regard to ionization when the number of ions which disappear in one second as the result of the collisions is equal to the number produced in the same time by the ionizing agent.

If there are n ions of either kind per cub. cm., the number of collisions between the positive and negative ions in one second in a cub. cm. of the gas will be proportional to n 2; hence the number of ions of either sign which are lost by recombination in one second will be represented by an t when a is called the coefficient of recombination. If the ionizing agent produces q ions per cub. cm. per second, then dn _ dt = q - ant.

The solution of this equation, if we reckon t from the instant the ionizing agent begins to act, so that n =o when 1=0, and where K 2 =q/a, is - / n =K(E2Ka1 - I)/(€2hal+I) We see that, when the gas reaches a steady state, n = K = .1 q/a, and that the gas will not approximate to this state until t is large compared with 1Ka, i.e. to Znoa where no is the value of n in the steady state. Thus when the ionization is very weak it may take a considerable time for the gas to reach a steady state.

Town-

send

Mc-

Clung

Lan-

gevin

Thir-

kill

Hen-

dren

Ret-

schin-

sky

Rume-

lin

Riint-

Ront-

Ront-

Ront-

Gas

gen

rays

gen

rays

gen

rays

gen

rays

a rays

a rays

a. rays 0 rays

Air

3420

3380

3200

3580

3300

4200

4240 5820

CO 2

35 20

349 0

34 00

35 00

..

..

H 2 3020

2940

..

..

..

..

..

2

3380

. .

..

..

..

..

SO

..

..

..

3000

..

..

N 2 0.

..

..

2960

..

..

C

..

..

1780

..

..

When the ionizing agent is removed, the ions do not disappear at once, but decay at the rate given by the equation dn dt = q - an2. - ant. The solution of this, where t is the time which has elapsed since the removal of the ionizing agents, and no the number of ions when t=o, is The results as ascribed to Thirkill were obtained by extrapolation from experiment made at lower pressures. Since e, in electrostatic measure, is 4.8 X I o 10, the value of a for air is about I. 6 X to °, so that, when there are n positive and n negative ions per cub. cm., the number of ions which recombine per second is I. 6X Io °n2.

This shows very markedly the influence of the electric charge in increasing the number of collisions between the particles, for the number of collisions in a second between 2n, uncharged molecules in a cub. cm. of air is only - which is only about I/4,000 of 4 th X e io num 1°n2, ber of recombinations between the same number of ions.

It is a very remarkable fact, and one which has not yet received a satisfactory explanation, that the values of a for gases of such different molecular weights as H2, 02, C02, S02 should be so nearly equal, while the value of a for CO is only about one-half of that for the other gases.

For pressures less than one atmosphere Thirkill has shown that a diminishes as the pressure p diminishes, and that the relation between a and p is a linear one. Langevin showed that a for air attained a maximum value at a pressure about two atmospheres, and that at higher pressures it diminished somewhat rapidly as the pressure increased.

When the density is constant the value of a diminishes as the temperature increases. The connexion between a and the absolute temperature T seems to be expressed with fair accuracy by the equation a = cT -n.

According to Erikson, n is equal to 2.3, 2.42, 2.35 for hydrogen, air and CO 2 respectively, while Phillips' experiments gave n = 2.

Large Ions

The ions we have been considering are those produced in dust-free gases by Röntgen or cathode rays. In some cases, however, ions with very much lower mobilities are to be found in gases. Thus Langevin found in air from the top of the Eiffel Tower two types of ions, one consisting of ions of the kind we have been considering, with a mobility of about i5 cm/sec., the other of ions with a mobility of 1/3,000 cm/sec. Ions with mobilities of the same order as this second type may be produced by bubbling air through water, by passing air over phosphorus, or by drawing air from the neighbourhood of flames. They are probably charged particles of dust of various kinds, held in suspension in gas which is exposed to some kind of ionizing agent which gives a supply of ions of the first type; these settle on the particles of dust and form the slow ions. The number of these slow ions when the gas is in a steady state will only depend on the number of dust particles in the gas, and will not be affected by the strength of the ionizing agent. This follows from the principle that in the steady state the number of dust particles which acquire a positive charge must equal the number which lose such a charge. A positively electrified dust particle might lose its charge by meeting and coalescing with a negative small ion or by coalescing with a negatively electrified dust particle. These dust particles are, however, so sluggish in their movements that, unless the dust particles are enormously more numerous than the small ions, we may neglect the second source of loss in comparison with the first.

Thus if U is the number of uncharged dust particles in a cub. cm. of the gas, P and N the number of those with positive and negative charges respectively, and p, n the number of positive and negative small ions, the number of dust particles which acquire per second a positive charge will be aUp and the number losing such a charge by coalescing with a negative ion 13Pn, where a and (3 are constants; hence for equilibrium aUp = 13Pn.

Similarly by considering the negatively charged particles we geta'Un = R'Np. Hence we see that the proportion between the charged and uncharged particles of dust depends only upon the ratio of p to n, and not upon the absolute magnitude of either of these quantities. Thus, though it would take much longer to reach the steady state with a feeble source of ionization than with a strong one, when that state was reached there would be as much dust electrified in one case as in the other. De Broglie estimates that in this state about one-tenth of the particles would be electrified.

Relation between the Potential Difference and the Current through an Ionized Gas

We shall take the case of two infinite parallel metal plates maintained at different potentials and immersed in an ionized gas; the line at right angles to these plates we shall take as the axis of x, it being evidently parallel to the direction of the electric force X. Let ni, n 2 be respectively the number of positive and negative n = no/ (I +mat). Thus the number of ions will be reduced to one-half their initial value after a time I/ano. We may therefore take I/an as the measure of the life of an ion when there are n ions per cub. centimetre. The values of a/e, where e is the charge on an ion, have been measured by various experimenters, and for different methods of ionization the results are given in the following table: - Values of ale for various gases at atmospheric pressure and ordinary temperature. ions at the place fixed by the coordinate x; u l and u 2 the velocities of these ions. The volume density of the electrification in the gas, if it is entirely due to the ions, is (n i - n 2)e when e is the charge on an ion, hence where q is the number of ions produced per second in a cub. cm. of gas, and a is the coefficient of recombination; if K 1 , ate the mobilities of the positive and negative ions respectively, then u 1 =K 1 X, u2=K2X.

From equations (I), (5) and (6) we get - 2 2 x = 87re(g - an,n 2) C KI + K2, d and, substituting the values of n 1 and n 2, we ge(t - l d2X dx' = 87re (k i -IK2/ q e 2 X 2 (K 1 a +K2) 2 + 8 2 d d 2 / C K1 dX2 / 87r No general solution of this equation has been obtained, but when e is small compared with the saturation current qle, an approximate solution is represented by the graph in fig. 2.

If, as is more convenient in this case, x is the distance from the cathode instead of from the anode, as we have hitherto assumed, the solution of this equation is - 2= 6`2 +C e -87re2K2Qx gg_e2 (9)as The second term on the right-hand side diminishes very rapidly as x increases and soon gets negligible, so that we see that the electric force will be constant except in the immediate neighbourhood of the cathode. To find the value close to the cathode we must find the value of C in equation (9). We have from equation (7) - [87re I dX 2 K,K2 l xi_ xI (q - an, n 2) dx (IO). dx (Kid]-K2)io - The right-hand side of this equation is the excess of ionization over recombination in the region between the cathode and x; it must therefore be equal to the excess of number of the negative ions passing through the gas at x; it must therefore be equal to (t - to)/e where co is the amount of negative electricity emitted by unit area of the cathode in unit time. Putting this value for the right-hand side of equation (Io) we find approximately, since K 1 is small compared with K2, - C _ at (t - to) K 1 -f-K 2_ at (c - co). gK1 K ("Kt K2 Substituting this value for C, we find - 2_ a C 1 - to - 8 7re2K2gx () X gKZe? I +KI c ac I I .

This distribution of force is represented by the graph in fig. 4; the force at some distance from the cathode is equal tot a 1 Kek q and is thus proportional to the current; the force at the cathode itself is { K2(t - to)/ K i t } I times greater than this. The fall of potential be tween the electrodes is made up of two parts, one arising from the constant force; as this force is proportional to t, this part of the potential fall will be proportional to it when 1 is the distance between the electrodes, and may be represented by Ail when A is a constant; the other part of the potential fall is that which occurs close to the cathode. We find from equation (I I) that this is proportional to t2 dX - dx = 47r(nl - n2)e (I). If c is the current through unit area of the gas c = e (n i u l - -n 2 u 2) (2). Hence from (I) and (2) we have - I u2 dX nle + 47r + u dx t I u 1 dX nee = (3), (4).

47r u l +u2 dx When things are in a steady state, neglecting any loss of ions by diffusion we have - x(nlw2) =q - anin2 - dx(n 2 u 2) = q - anin2 FIG.

'FIG. 2 The force is practically constant, and equal to - C 'a';: q / 'e( K I f K2)' except close to the electrode, where it increases; and as the mobil ity of the negative ion is greater than that of the positive the increase in the force will be greater at the cathode than at the anode. As the potential difference between the electrodes increases, and the current approaches more nearly the saturation value, the flat part of the graph diminishes, and the graph for X takes the form given in fig. 3. When the potential difference is so large that the current is FIG. 3 nearly saturated, X is very approximately constant from one electrode to another.

In one extremely important case, that in which the negative ions are electrons and have a mobility which may be regarded as infinite in comparison with that of the positive ions, equation (7) admits of integration: for by putting K l /K 2 = o in equation (8) it becomes dX 2 8re 2 K 2 gX 2 _ 87rt dx at Distance from Cathode and does not depend upon 1. Thus, if V is the potential difference between the electrodes when A and B are constants V =Atl+Br. 2 (12).

H. A. Wilson has shown that an equation of this type represents the relation between the current and potential difference for conduction through flames. In many cases the drop of potential at the cathode is much greater than the fall in the rest of the circuit; when this is so we see that the current is proportional to the square root of the potential difference. The value of B increases with the pressure and decreases with the amount of the ionization.

Current from Hot Wires

A case of great importance from its industrial application in hot wire valves is one where all the ions are negative and are emitted from the cathode. Metal wires raised to incandescence emit electrons, and if they are used as cathodes can transmit across a vacuum or gas at a low pressure very considerable currents. No currents will pass if they are used as anodes.

Take the hot cathode as the origin from which x is measured; let V be the potential at the point x, n the density of the negative ions at this point, and c the current through unit area. If a is the velocity of the negative ion, we have 2 nue = c and dx2 There are two cases to be considered; the first is when the hot wire is surrounded by gas of sufficient density to make the velocity (7)

(8).

of the ions proportional to the electric force; the second is when the hot wire is surrounded by a vacuum, and the motion of the ions is not affected by the gas.

In the first case u =K 2 d x , when K2 is the mobility of the nega tive ion, and the equation nue =1 is equivalent to - K2 dV d2V 47r dx dx 2 - The solution of this is - 87rc + C dx) K2 Therefore if V is the difference of potential between the anode and cathode, and 1 the distance between them, - V '=' r 87rc1 +C _01 127ra K If uo is the velocity of the negative ions at the cathode, a=neuo; hence _ 1167ruo

- c (15).  I So that, unless c is small compared with I, uo will be comparable with c; in this case, however, the velocity of the ion is no longer proportional to the electric force so that equation (13) no longer holds. Again, when the current approaches saturation, t/(I - c) is large, and therefore by (15) uo will be large compared with c. For the negative ion to acquire a velocity of this magnitude the electric field would have to be so strong that sparks would pass through the gas unless the pressure were very low. Thus saturation currents from hot bodies are only obtainable at very low pressures.

Since uo = K J, c2 C = 67rK 2 (I - c)2 Comparing this with the value of 87rc1/K we find, by substituting the values of K and c, that if the current is far from saturation, C will be negligible compared with 87rcl/K, unless 11, when 1 is measured in centimetres and i in milliamperes, is small compared with unity. When C can be neglected, equation 02) gives q V2 - 327r l3 (r6).

Thus the current is proportional to the square of the potential difference. A remarkable thing about this expression is that for these very small currents the intensity of the current is independent of the temperature of the wire, although, of course, the range of currents over which this formula is applicable is wider the higher the temperature of the wire.

When the hot body is in a vacuum, we have, if the ions have no initial velocity, - 3mu2 =Ve, where m is the mass and e the charge on an ion; hence the equation nue = c is equivalent to d 2V dx2 V3 = 47rcy 1 a solution of which is V = (97rc)3 (m/2e)ixi (18). Hence, if V is the potential difference and l the distance between the electrodes 1 = 97 r 12 yn) V? We see from this equation that the electric force vanishes at the cathode, and that the density of the negative electrification is proportional to x-1; thus it is infinite close to the cathode and diminishes as the distance from the anode diminishes. The total quantity of electricity between the anode and cathode is proportional to 1c2. We see again that for a given potential difference the current does not depend on the temperature of the hot wire; this law only holds when the currents are less than the maximum currents which can pass between the electrodes. When the current approaches this value, the current instead of increasing as VI becomes independent of V and the negative electricity between the electrodes diminishes as V increases. Langmuir, who has made a very complete investigation of the currents from hot wires, finds that the expression (7) represents, with considerable accuracy, the relation between the current and potential over a wide range in the values of the currents. The curves in fig. 5 given by him represent the relation between the current and potential for wires at different temperatures. They illustrate the point that a colder wire, until it is approaching the stage of saturation, gives as large a current as a hotter one, though the hotter one, of course, has a wider range of currents.

Ionization by Collision

The curve representing the relation between the currents through a gas ionized (say) by Röntgen rays and the difference of potential between the electrodes is found to be of the form already shown in fig. r, where the ordinates represent the currents and the abscissae the potential difference. The fiat part represents the state of saturation when the potential difference is large enough to send all the ions produced by the rays to the electrode before they can recombine. When the potential difference is still further increased we see that a stage is 005 004 1500 1800 2000 2200 Temperature reached when the current begins to increase with great rapidity with the potential difference, and reaches values much greater than could be attained by the ions produced by the Röntgen rays. Thus in addition to the ions produced by the rays there must be other ions, and some other source of ionization associated with the strong electric fields. Now the processes going on in a gas while it is conveying an electric current are: - (I) the ionization of the gas by the external agent - in this an electron is liberated from the molecule and the residue forms a positive ion; (2) the electron and the positive ion acquire energy under the action of the electric forces; (3) in many gases the electron finally unites with an uncharged molecule to form a negative ion. As the most noticeable change in the conditions when the intensity of the electric field increases is in the energy of the electrons and ions, it is natural to look to these as the source of the additional ionization. We have moreover direct experimental evidence that rapidly moving electrons and ions are able to ionize a gas through which they are passing. Hot wires and metals exposed to ultraviolet light yield a supply of electrons which when they leave the metal have very little energy; by applying suitable electric fields these electrons can be endowed with definite amounts of energy and can then be sent through a gas from which all extraneous ionizing agencies are shielded off. When this is done it is found that, when the energy of the electrons exceeds a certain critical value, depending upon the nature of the gas, the gas is ionized by the electrons, but no ionization occurs when the energy of the electron falls below this limit. It is convenient to measure the energy of the electron in terms of the difference of electrical potential through which the electron has to fall in order to acquire this energy. The potential difference which would give to the electron the energy at which it begins to ionize the gas is called the ionizing potential. The values of the ionizing potential have been found for several gases, as will be seen from the following table. There is, however, considerable discrepancy between the results obtained by different observers.

Gas

Stead &

Gosling

Franck

& Hertz

ii

Davis &

Goucher

I I and 15

Horton

& Davis

Tate &

Foote

Hughes

& Dixon

10.2

He

0 2

20.8

20.5

9

25.6

9.2

N

17.2

7'5

17

7.7

CO

Arg.

15

12.5

12

7.2

15

Ne

16.7& 20

& 22.8

Hg

10.8

10.2

Cd

8.9

Na

5. I

K

4I

Zn

9'5

.003 240 Volts 120 lofts 60 Volts 2400 2600 (13). (14). The most obvious view to take of this ionization by moving electrons is that the moving electron comes so near to an electron in a molecule of the gas that the latter receives from the collision enough energy to enable it to escape from the molecule and start as a free electron. If the electrons repel each other with forces varying inversely as the square of the distance between them, and if T is the energy of the moving electron, and d the length of the perpendicular from the electron in the molecule on the initial direction of motion of the moving electron, then the energy communicated to the electron in the molecule by its collision with the moving electron is T equal to d where e is the charge of electricity on an elec I-}-e4 T2 tron. This is on the supposition that the electron is moving so rapidly that the time while it is in close proximity to the electron in the molecule is small compared with the time of vibration of that electron; if this time is comparable with the duration of the collision, the energy taken from the moving electron will be considerably less, and it will become vanishingly small when the duration of the collision is large compared with the time of vibration. The energy given to the electron in the molecule does not increase indefinitely with that of the moving molecule, for it vanishes when T is infinite as well as when T is zero; it has the maximum value when T =e 2 /d. In order that the electron in the molecule should receive an amount of energy Q, - T, or d 2= e4(T/Q - I) d2 T2 d4 T2 e If Q is the ionizing potential, d 2 must be less than the value given by this expression. If n is the number of electrons in unit volume of the gas, and if the spheres with radius d described round the different electrons do not overlap, the probability that the moving electrons should come within this distance of one of them, when moving through a distance Ax, is n-ird 2 :zx, or n-rre4(T/Q - I) T2 The coefficient of Ax is the number of ions made per unit path by a moving electron with energy T. The maximum is when T =2Q.

Experiments on ionization by moving electrons have been made by KSssel (Ann. der Phys. 37, p. 406) and by Mayer 45, p. 1), who found that the maximum ionization per unit path occurred when the energy of the moving electron was in the neighbourhood of 200 volts. Mayer's results are 125 for hydrogen, 130 for air, and 140 for carbon dioxide. These numbers are much greater than twice the potential at which the ionization begins, as this potential is of the order of II volts. It must be remembered, however, that, though there may be some electrons in the atom which can be ejected by II volt electrons, there may be other electrons of different types which require more energy for their expulsion, so that, as the energy of the moving electrons increases beyond the energy required to liberate these electrons, fresh sources of detachable electrons will be trapped, and these may more than counterbalance the falling off in the ionization of the more easily detached electrons. Again, some of the electrons ejected by the primary electrons may have enough energy to ionize on their own account; the total ionization may thus be increased by ionization due to the secondary electrons, and also by radiation excited by the impact of the primary electrons against the molecules of the gas.

When, as in the case of cathode rays in highly exhausted tubes or in that of the R rays from radioactive substances, T is very large compared with Q, the number of ions produced per unit path is nae 4 /QT, and so varies inversely as the energy of the moving electrons. The experiments of Glasson on ionization by cathode rays, and of Durack on that by J3 particles, seem to be in accordance with this result. If we measure the number of ions produced per centimetre in a gas at known pressure, for which we know the value of Q, we could determine n, the number of electrons in unit volume; as the pressure gives us the number of molecules, we could deduce in this way the number of electrons in each molecule.

Ionization by Moving Ions

When the moving systems are ions instead of electrons, the collision between them and the electrons are collisions between masses of very different magnitudes, and in consequence a very much smaller fraction of the energy of the moving body is transferred to the electron than when the colliding bodies have equal masses.

The amount of energy transferred to the electron when the moving body has a mass M is equal to: - // 4141142 T (M 1+ M 2) 2= 4d 2 T 2 M2 2' 1 I e2E2 (M1+M2) when is the mass of the electron and E the charge on the moving body. When, as in the case of the collision between an ion and an electron, M 2 is very small compared with M 1, this becomes 4M 2 T m 1 +4 d2T2 M e 2 E 2 M 12 Thus, if Q is the ionizing potential, the minimum value of T, which will communicate this energy to the electron is 4 - ' Q, For the smallest possible ion, an atom of hydrogen, 114 1 /M 2 =1,700, so that the minimum energy that will enable an ion to ionize a gas by knocking out an electron from a molecule is equal to 425Q. Q for many gases is about Io volts; thus a positive ion must have at least energy represented by 4,250 volts to ionize the gas. With more massive ions the energy required for ionization would be still greater.

An ion with a mass equal to that of a molecule of oxygen would not ionize unless its energy were greater than 136,000 volts. Thus if any ionization by ions takes place in discharge tubes it must be due to ions of the lighter elements hydrogen or helium.

If the ion came into collision with the ion of the atom instead of with one of its electrons, it could, since its mass is comparable with that of the ion, give up to this a large fraction of its energy, a very much larger fraction than it is able to give to an electron. Inasmuch as it requires less work to dissociate a molecule into neutral atoms than to dissociate it into positively and negatively electrified ions, the result of such a collision is more likely to be the production of neutral atoms than of electrified ions.

An ion is, however, a much more complex thing than the simple charge of electricity which has in the preceding considerations been taken to represent the forces it exerts; and it may be that some strongly electronegative ions have such a strong attraction for an electron that when they pass through the molecule of a more electropositive element they are able to capture one of its electrons and carry it away with them. This type of ionization would differ from the ordinary type, inasmuch as in it the electron is never free; it produces negative ions, the other negative electrons.

It is evident from the preceding considerations that except in very intense fields it must be the electrons and not the ions which produce ionization by collision. Let us consider what are the chances of an electron acquiring sufficient energy in a uniform electric field; if the electron moved freely under the electric force X for a distance 1 it would acquire Xel units of energy. The electron in its course through the gas will come into collision with other bodies; its path will be deflected, possibly reversed, and in moving against the electric field it may lose all the energy it had previously acquired. Thus a collision of this type will destroy any ionizing power given to the electron by the electric force before the collision.

Let X be the average distance passed over by an electron between two collisions; then the chance of an electron moving through a distance 1 without a collision --1; but if it moves through a distance 1 it will acquire energy =T = hence the chance of an T electron acquiring energy equal or greater than T is e ?' CA, and the chance that it should acquire energy between T and T+dT is I Y) dT. If it possess this amount of energy the chance 4 that it makes one ion per centimetre of path is n14 22 (T/Q - I); hence the chance that an electron should make one pair of ions per centimetre of path is: - T n?re4J o dT E eA) (T/Q - I)dl, - r.

_ Q n7re 4 E `'ex /Q F(- o eA), co XeX -xx where F = X eA dx.

+ 0 Thus if a is the chance that an electron may produce one electron per unit path, since X for the same gas is inversely proportioned to the pressure p, a will be of the form of (p): and since n is proportional to the number of molecules per unit volume, a may be written as pf (p). When the spheres described round the electrons with radius d do not overlap, n will also be proportional to the number of electrons in the molecule. The greatest value of d is e /2Q; hence if D, the distance between two electrons, is greater than e /2Q, there can be no overlapping; if D is less than this quantity there may be overlapping; since the value of d diminishes as the kinetic energy of the electron increases, n for very fast electrons will be proportional to the number of electrons in the molecule.

Some of the electrons will by adhesion to a neutral molecule become negative ions. Let the chance of an electron doing so while passing over i centimetre be -yp. If N be the number of electrons per c.c. at a place fixed by the coordinate x, then +d x (NU) =rate of increase of number of ions per c.c., where U is the velocity of the electron parallel to x.

X =volts per

CM.

Pressure (mm.)

20

17

24

.38

..

1.10

2.1

4.1,

40

65

'34

..

80

1'35

1'3

'45

'13

120

1.8

2.0

11

-42

13

160

2I

2.8

2.0

9

-28

20

..

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

21

400

..

50

6.8

60

36

480

3.15

5.4

8.o

7.8

5.3

560

5.8

9.3

9.4

7.1

6 40

3.25

6.2

106

108

8.9

The number of electrons passing through the unit of area in unit time is NU. The new electrons produced by the passage of them through the unit volume is NUa, while NUyp will disappear; hence: dN d where q is the ionization due to external sources; when things are in a steady state dN/dt=o, and the solution of the equation, when the electric field may be taken as constant from one electrode to another, is NU=Ce(a-YP)x- 4 a-yp' Most of the experiments on this subject have been made without external ionization; a supply of electrons has been obtained from the cathode, either by raising it to incandescence or by exposing it to ultra-violet light. In such cases q=0, and NU = - (20), where to is the number of electrons emitted in unit time from the cathode. Townsend, and Townsend and Kirkby have determined the value of a-7p for various gases and over a considerable range of pressure. A series of these values for air are given in the following table It will be seen that, when X is given, the increase in the number of electrons reaches a maximum for a particular pressure. From general reasoning this must be so, for if p =o there will be no collisions to make fresh electrons, and if p is infinite the free path of the electrons will be so small that they cannot acquire sufficient energy to X ionize the gas. Since a is of the form pf(-), and y does not depend upon p, a-yp will be a maximum when - le ( p ') p2 or when f (-) - y This equation determines X/p; hence the critical pressure will be proportional to the electric force.

At this critical pressure XeX bears to Q a ratio which depends upon the way in which the chance of an electron ionizing by a collision depends upon the energy of the electron. If, for example, the chance were independent of this energy, provided the energy were greater than Q, the maximum current would be when XeX =Q; this relation would not hold for other and more probable laws connecting ionizing power with the energy, but we should expect that for any such law the ratio of XeX to Q would neither be very large nor very small.

Since the electrons cannot begin to ionize until their energy is equal to Q, and to attain this energy they must pass through a distance Q/Xe, it is clear that we ought in such an equation as (19) to write x-Q/Xe in place of x. If V is the potential difference between the plates, X=V/d, so that x- Q/Xe=x-dQ/V if Q is measured in volts. Thus in finding the current between two elec trodes we must, if we use equation (19), write d(i -Q) instead of d. Partz (Verh. d. Deutsch. Phys. Gesell. xiv, p. 60) has shown that theory and experiment agree better by this change.

Spark Discharge.-The production of ions by moving electrons will not by itself explain why a current of electricity can be maintained through a gas by an electric field when all other sources of ionization are excluded. The electrons are continually being driven towards the anode, and unless there is some source of supply near the cathode the ionization and therefore the current will rapidly come to an end. One way in which the electrons could be supplied by the action of the electric field would be by the positive ions which strike against the cathode communicating so much energy to the anode that it is raised to incandescence. Since an incandescent metal gives out large quantities of electrons there will be a continuous supply of electrons from the cathode, which will ionize the gas and produce fresh positive ions to strike against the cathode and keep it hot. This is what happens in the arc discharge when the cathode is kept in a state of incandescence by the discharge. In this case there is a large amount of energy put into the arc. There are, however, other forms of continuous discharge where the cathode does not become incandescent, so that there must be other ways in which the supply of electrons is maintained. From what we know about ions there are several ways in which this might occur.

It has been found by experiment-(Ftichtbauer, Ann. der Phys. 23, p. 301 (1907); Saxen, Ann. der Phys. 38, p. 319 (1912); Baerwald, Ann. der Phys. 41, p. 643 (1913); 42, p. 1207 (1913)-that electrons are emitted from metals when these are bombarded by highspeed positive ions even though the metal is not raised to incandescence. According to Baerwald the emissions of electrons from metals bombarded by positive hydrogen atoms does not become appreciable until these have an amount of energy exceeding that represented by 900 volts. We know too that, when the electric discharge passes through a gas, radiation capable of ionizing a gas through which it passes, or of ejecting electrons from a metal on which it falls, is an accompaniment of the discharge. Again positive ions ionize a gas through which they pass. This was shown by McClelland, who found that the relation between the potential difference and the current from a hot wire anode surrounded by gas at low pressure was represented by a curve like that shown in 0 40 80 120 160 200 FIG. 6 fig. 6. The hot wire furnishes positive ions as well as negative ones, and the curve shows that fresh ions are formed when the potential difference is greater than about zoo volts. This is a much greater potential difference than that needed to produce ionization by electrons, but it is smaller than would be expected by the considerations given above. As it requires less work to eject an electron from a metal than from a molecule, we should expect that if 200 volts ions could eject electrons from a gas through which they pass they would be able to do so from a metal against which they strike, but from Baerwald's experiments much more energy than 200 volts 240 280 360 320 is required for this purpose. In McClelland's experiments the ionization might have been into positive and negative ions rather than into positive ions and electrons; before the negative ions could be efficient for ionization by collision they would have to undergo further dissociation into electrons and uncharged molecules. Curves similar to that in fig. 6 have also been obtained by O. W. Richardson. Pawlow (Proc. Roy. Soc. A. 90, p. 398) and also Franck and E. v. Bahr (Verh. d. Deutsch. Phys. Ges. xvi, p. 57, 1914) came to the conclusion from their experiments, that ionization was produced by positive ions even when their energy did not exceed a few volts; indeed they could not get any evidence of a minimum to the ionizing voltage. Horton and Davies (Proc. Roy. Soc. 95, p. 333) could not detect any ionization in a gas by positive helium ions when the energy was due to 200 volts. They ascribe the ionization observed by Pawlow and Bahr and Franck to photo-electric effects; they consider, however, that positive helium ions can liberate electrons from a metal against which they strike if their energy exceeds 20 volts. Baerwald considers that it requires an energy measured by 900 volts before positive ions can liberate electrons from metals.

There are thus at least four methods by which the supply of electrons near the cathode necessary to maintain the discharge can be obtained. The gas near the cathode may be ionized by positive ions or by radiation, or the cathode itself may emit electrons under the impact of positive ions or by the incidence of radiation.

When the gas is at a low pressure the appearance of the discharge has well-marked characteristics which may throw light on the method by which the electrons are produced and the place from which they start. The discharge near the cathode is represented in fig. 7; near the cathode we have a velvety glow, then a space comparatively dark called the cathode dark space; this joins on to a brightly luminous region called the negative glow; passing through this region, and making themselves evident by the luminosity they excite when they strike against the glass wall of the vessel in which the gas is contained, are the cathode rays. These have been shown to be electrons moving with high velocity. These electrons have been liberated by the action of the electric field and have acquired their velocity under the action of that field. The velocity of the cathode rays has been measured, and it has been found that practically all of them have the same velocity. This shows that they must have all fallen through the same potential. They would do this if they all started from the cathode itself, but if they had originated by the ionization of the gas in the dark space in front of the cathode, some would have started from one place and some from another, and they would have acquired different velocities. This is strong evidence in favour of the cathode itself being the primary source of the electrons which maintain the discharge. When a supply of electrons is produced by processes taking place at the cathode, ionization by collisions of electrons with the molecules of the gas is sufficient to maintain the discharge through the interval between the negative glow and the anode. This interval, as will be seen from fig. 7, is made up of a short part next the negative glow in which there is comparatively little light, called the Faraday dark space, and then a long uniform portion reaching right up to the anode. Unless the pressure is very low or the spark very short this position, which is called the positive column, forms by far the larger part of the discharge. The discharge here will be maintained if the rate at which electrons are produced by collision is equal to the number lost by recombination. When this is the case, equation (19) gives a =yp, or, since a is of the form Pf Q (XeX) (X Q e0 =7' thus XeX=cQ, where c is a quantity which does not depend upon the pressure or strength of the field; as X is inversely proportioned to the pressure, this equation is equivalent to X =c i p, when c 1 is a quantity which will depend on the nature of the gas and possibly on the intensity of the current. If 1 is the length of the positive column the difference in potential between the anode and the end of the positive column next the cathode is IX, i.e. lcip. Between the cathode itself and the negative glow there is a fall of potential, called the cathode potential fall, which, when the current carried by the discharge is not large, is independent of the current and the pressure of the gas; it depends upon the nature of the gas and the material of which the electrodes are made. If Vo is the cathode fall, then (neglecting the change in potential in the negative glow and the Faraday dark space, which has been found by experiments to be very small) V, the potential difference between the anode and cathode will be given by the equation V =Vo+cilp (21).

It is assumed that the length of the spark is greater than that of the dark space D: at pressures comparable with that of the atmosphere, D is a very small fraction of a millimetre, but at the low pressures which can easily be obtained in highly exhausted vessels D may be several centimetres. It is to be noticed that V is a linear function of 1p, and 1p is proportional to the mass of gas between the electrodes; hence as long as the mass of gas between the electrodes remains unaltered the potential difference required to maintain the spark will be constant. This law, which was discovered by Paschen in 1889 as the result of a long series of experiments, is known as "Paschen's law." It has been found to be in agreement with the very numerous investigations which have been made on the potential difference required to produce a discharge in an approximately uniform electric field such as that which exists between two slightly curved electrodes.

The relation (21) does not give any indication of the relation between the potential difference and the spark length when the latter is exceedingly small. When the spark length falls below a critical value which is inversely proportional to the pressure, and which in air at atmospheric pressure is about oi mm., the spark potential increases rapidly as the spark length diminishes; this was first observed by Peace. A simple way of demonstrating it is to use slightly curved electrodes and to observe the path of the spark as these are brought closer together. Until the electrodes get very close together the spark passes along the shortest line between them, but as they approach each other a stage is reached where the spark no longer passes along the shortest line but goes to one side, taking a longer path, showing that it is easier to produce a long spark than a short one. The relation between the potential difference and the spark length for several gases has been determined by Carr, who finds that Paschen's law that the potential difference depends only on pd is also true for very short sparks; Paschen's own experiments were made with sparks considerably longer than the critical value. Fig. 8 represents Carr's results for 2000 1800 1600 1400 1200 1000 200: ? 0 .. ?

Air .

Nitrogen

Oxygen

Hydrogen. .

Carbonic acid .

Sulphur dioxide .

Nitrous oxide. .

Sulphuretted hydrogen

Acetylene .

Helium

34 1 S

251 S

455 C

J 302-308

278 C

4 1 9 C

457 C

4 1 4 C

468 C

. 261 S

S

5.7

6.7

14.4

5.1

3.3

5

6

35

FIG. 8 the relation between V and pl. The results of Carr and Strutt's experiment for the minimum spark potential, and the value of pl, at which it occurs, are given in the following table :- Minimum Spark Potential in volts. The curves are very flat in the neighbourhood of the minima, so that the critical values of pl may be subject to considerable errors. Strutt found that even very small traces of impurity produced very large increases in the values of the minimum spark potential in nitrogen and helium; these are gases where, as we have seen, such traces produce large diminutions in the mobility of the negative ion. The existence of a minimum for the spark potential and a critical spark length follow from the view that the spark is maintained by the emission of electrons from the cathode owing to its bombardment by positive ions. For if to be the number of cathode rays emitted from unit area of the cathode per second, at a distance x from the cathode Loeax electrons will stream through unit area per second and will produce 7 2 3 4 5 6 Product of Pressure and distance between Electrodes 800 600 400 Gas. p1.

per second ioae a x positive ions per c.c. These positive ions will proceed up to the cathode, and a certain percentage will react and bombard it. Let the chance of the ion reaching the cathode with undiminished energy be e -0x; then the energy with which it strikes the cathode is Ve. when V is the potential at x, so that the energy in the ions striking unit area of the cathode per second is, o f l a xe - s x Vedx. The rate of emission to will be proportional oa.

to this energy, so that, = KLo j l eax (22). o a when K is a quantity that may depend on the material of which the cathode is made and on the kind of positive ions which strike against it, but will not depend on the pressure of the gas. If W be the potential difference between the anode and cathode, and 1 the distance by which they are separated, V may be written in the form Wf (x/e), where f(o) = o and AI) =1. Putting x11= y, equation (7) gives i 1 =KWale e-0 3 - x) l Yf (y)dy Now both a and 13 are proportional to the pressure p of the gas, so that l and p only occur in the combination 1p; thus in the most general case W the spark potential will be a function of 1p; this is Paschen's law, which has been shown by Carr to hold, down to very low pressures and spark lengths. When 1p is very small (23) reduces to W - Kale f a f (y)dy. Thus the potential required to produce very short sparks varies inversely asthe length of the spark, so that to produce an infinitely small spark would require an infinitely large potential. The rapid increase in the spark potential as the spark length diminishes is shown by the curve in fig. 8. The spark potential will also be infinite when 1 is infinite so for some intermediate spark length the potential must be a minimum. We see from the form of equation (23) that if Wo is the minimum potential, KW 0 a/(1 3 - a) is a constant, depending only on the form of the function f, and also that, if L is the spark length when the potential is a minimum, L(1 3 - a)is another constant depending also on the form of the function; if f(y) =y we get L = 18, thus the critical spark length will depend upon the - a gas, but not upon the material of which the cathode is made: the minimum potential Wo is equal in this case to (/3 - a)22/Kea or Kea Now I/Ke is the potential difference, u, through L which a positive ion must fall to get enough energy to liberate one electron from the cathode, and aL is the number of electrons produced when an electron passes over the critical spark length. If 2u this number is n, Wo = n. We may summarize the argu ment as follows: if P l is the chance of a positive ion liberating an electron from the cathode, pi, the chance of that electron making an ion in the space d, then the probability that the original positive ion will be replaced by a new one is pipe, and if the process is to be regenerative P i pe must be unity.

Since K may depend on the metal against which the ion strikes as well as upon the ion itself, the minimum potential might depend upon the material of which the cathode is made. Baerwald found, however, that for many of the ordinary metals there was not much difference in the numbers of electrons they emitted when bombarded by positive ions, so that with all such metals for cathodes the critical spark should be the same. There is very considerable evidence that the minimum potential required to produce a spark is equal to the cathode fall of potential when the length of discharge is much greater than the critical spark length, and Mey has shown that the cathode fall of potential is appreciably less when the cathode is made of Al, Mg, Na or K, than when it is made of Pt, Hg, Cu or Ag.

The mechanism we have hitherto considered involves the ionization of the gas between the electrodes, and no spark could pass across a vacuum. There are, however, other methods by which a discharge might pass across a vacuum. For suppose there was a stray electron between two parallel electrodes in a vacuum; then under the action of the electric field it would be driven against the anode; by the impact Röntgen radiation would be generated, which would fall on the cathode and if it were intense enough to liberate one electron from the cathode the original electron would be replaced and the passage of negative electricity from the cathode to the anode would be repeated. From these considerations it is probable that even the highest vacuum would not act as a perfect insulator for the very intense fields.

The linear relation V = Vo+cilp has been obtained on the assumption that the direction of the electric force was the same in all parts of the field; this is only true when the dimensions of the electrodes are large compared with the distance between them. The potential difference required to produce a spark of a particular length depends upon the size of the electrodes between which the spark passes, and is not a linear function of 1p, where p is the pressure and 1 the spark length, unless 1 is small compared with the linear dimensions of the electrodes. If these are spheres, the spark potential will depend upon their radii, and for small spheres may be considerably less than for large ones. Thus, for example, the spark potential in air for a five centimetre spark is 26,000 volts for electrodes .5 cm. in diameter, and 105,000 volts when the diameter of the electrodes is 5 centimetres.

In this connexion it may be noted that, if the electric field is sufficiently intense at any place to produce there a local supply of ions, these may redistribute themselves between the electrodes, and by their electrostatic action produce a change in the distribution of the electric force more favourable to the passage of the spark than that prior to the production of the ions. To illustrate this, take the very simple case when the electrodes are two parallel plates: if there are any ions available these may distribute themselves so that the force between the plates is no longer uniform. Thus let us suppose that there are enough positive ions to congregate round the cathode in sufficient numbers to produce within the distance of the " critical spark length " or thickness of the cathode dark space a difference of potential equal to the minimum spark potential. This would ensure that from close to the cathode there was a continual emission of electrons, and even though the electric field from this place to the anode was too feeble to give an electron enough energy to ionize the gas, the electrons coming from the cathode would be able to carry a small current, though this part of the discharge might not be luminous. The ions here would be all of one sign, so that the electric force will increase up to the anode. If the current is gradually increased, the place where the electric force will just rise to the value necessary to make the electrons ionize will be close to the anode. When this occurs a supply of positive ions will start from the anode and move towards the cathode, accompanied by luminosity close to the anode and very faint luminosity through the rest of the tube. The introduction of the positive ions into the region between the anode and cathode will diminish the retarding effect of the negative space charge which existed in this region, so that the current will increase. This increase in current will again increase the ionization at the anode, and thus the supply of positive ions. In this way there might be a supply of electrons coming from the cathode, and of positive ions from close to the anode, which will maintain the current in spite of the fact that between these places there was a region where the electric force was below that required to produce ionization by collision, and the potential difference between the electrodes less than that calculated on the supposition that the electric force was uniform from one to the other. We should expect from these considerations that, if the electric force at any point were intense enough to produce ionization by collision, some discharge would take place.

Russell (Phil. Mag. 6. xi., p. 237) states that the results of the different experiments made on the potential difference required to produce sparks of various lengths between spherical electrodes of various radii are in good agreement with the rule that the discharge takes place in air at atmospheric pressure if the electric force at any point in the field before discharge begins is as great as 37,000 volts per centimetre. This value agrees well with that required to make electrons produce in air at atmospheric pressure other ions by collisions.

The curious lag observed by Warburg between the application of the potential difference and the passage of the spark, which may amount in extreme cases to several seconds, e.g. when the applied potential is only a very little greater than that required to produce the spark, is naturally explained as the time necessary for the ions to distribute themselves so as to produce the distribution of potential required for the discharge.

The discharge of electricity from points affords a good illustration of the preceding considerations. Suppose that the electrodes are a needle point and a plane. When the discharge first begins the only place where any light is to be seen is close to the point; the current between the electrodes is very small; as the potential difference increases a stage is reached where light begins to appear close to the points, the space between the point and plate being quite dark. This stage is marked by a large increase in the current. With further increase in current the luminosity extends into the gas and ultimately stretches from one electrode to another.

The potential required to start the discharge is less where the point is negative than where it is positive. This is what might be expected, for to maintain the discharge from the negative point there must be (I) ionization of the gas by the outgoing electrons, and (2) liberation of electrons by the incoming positive ions, while when the point is positive there must be (I) ionization of the gas by outgoing positive ions, and (2) liberation of positive ions by the impact of incoming electrons; as the process is not the same as for the negative point we should expect that there would be a difference between the potentials. It is not only the potential difference which is affected but the type of discharge. This can be shown by allowing the point discharge to pass in the neighbourhood of a photographic plate. Beautiful figures are found on developing the (23).

plate, and the character of these is different according as the point is positive or negative. Figures 9 and io represent discharges from positive and negative points respectively.

The discharge from a negative point is in some gases very much influenced by the purity of the gas; thus Warburg found that the discharge from a negative point in nitrogen increased about fifty times by removing the last trace of oxygen from the nitrogen, though this had little or no effect upon the discharge from a positive point. This can be accounted for by the discovery of Franck and Hertz that in very pure nitrogen the electron does not become a negative ion and has a very high mobility. This is true for the inert gases as well as for nitrogen, and Pryzibram has shown that the difference between the discharges from positive and negative points is exceptionally large in these gases.

Electrical Wind

The electrified ions starting from the point in a point discharge sets the gas in the neighbourhood of the point in motion producing a current of air, called the " electrical wind." The momentum gained by the air is lost by the point, so that there is a backward force acting on the point, which has often been measured. This force, as well as the electrical wind, is smaller when the point is negative than when it is positive; this difference is especially marked at pressures low enough to make the negative ion have an abnormally large mobility.

Relation between Potential Difference and Current

The potential difference required to maintain a discharge will depend upon the current passing in the discharge. The relation between the current and potential difference for discharge through gases is often a very complicated one. We should expect that this would be so, for in the spark discharge, for example, the potential difference is made up of the cathode fall of potential (this increases with the current) and a uniform force along the rest of the discharge, and this force in many cases diminishes as the current increases. Thus whether increases of current produce an increase or decrease in the potential difference will depend on the relative contributions of these two parts.

Current A curve of which the ordinates are the potential difference between the electrodes and the abscissae the current through the gas is called the " characteristic curve " for the discharge. Suppose that the current sent through a gas by a battery of cells of electromotive force E 0 is required. If R is the resistance of the curves connecting the battery with the electrodes in the gas, then E 0 - Rt. is the potential difference between the electrodes in the gas, and one relation between this potential V and the current is represented by the straight line V = Eo - Rt. The other relation is that represented by the characteristic curve; the values of the current through the gas and the potential difference between the electrodes will be determined by the points of intersection of this straight line and the characteristic curve. Unless the straight line cuts the curve there can be no discharge through the gas; on the other hand, the straight line may cut the characteristic curve in more than one point, indicating that there is more than one type of discharge. Some of these types may, however, be unstable and thus impossible to realize. Thus, for example, if the current is increased by Se the difference of potential given by the battery between the electrodes is diminished by RSI; if V is the potential difference between the electrodes required to send a current t through the gas, then, when the current is increased by It, the increase in the potential required is dV Sc; thus unless dV r dr at is less than - RSt, or - (da -1-R) St be positive, the dimin ished potential supplied by the battery will not be sufficient to maintain the increase in the current, this increase will stop, the current will return to its original value, and the discharge will be stable; thus if R -{ d V is positive the discharge will be stable. If, however, RHdV is negative the fall in potential required to main tain the increased current is so great that, in spite of the diminution of the potential difference supplied by the battery, the residue is great enough to maintain the increased current, the increase in the current will continue, and the discharge will be unstable. Thus the condition for stability is that -F dV should be positive, a re sult first given by Kaufman. This result is equivalent to the condition that for stability the straight line must, at the point where it cuts the characteristic curve, fall more steeply than the tangent to the curve at that point. Thus if Apqb is the characteristic curve, and if the straight line cuts it at PQ, the type of discharge represented by P is unstable, and that by Q stable. Keeping the electromotive force of the battery constant and increasing the resistance will make the straight line steeper, and Q will move to the left and the current through the tube will decrease; when the line gets so steep that it touches the curve at S, the minimum value of the current consistent with the maintenance of this type of discharge by the electromotive force supplied by the battery will be reached, and any further diminution of the current will result in the extinction of this type of discharge. It is a well-known fact that the existence of most types of luminous discharges requires the current to be above a certain critical value which depends upon the external force. The electric arc is perhaps the most familiar example of this; as the characteristic curve for the arc discharge is a rectangular hyperbola represented by the equation V =a-1-- b ' We can easily show that if the external electric force is E, the maximum resistance which can be introduced into the circuit without extinguishing the arc is (E - a) 2 /4b, and the smallest current compatible with the existence of the arc 2b/(E - a). For any stable type of discharge we see that an increase in the external electromotive force will result in an increase of current; at a point corresponding to an unstable condition it produces a diminution.

Structure of the Discharge

The structure of the discharge at atmospheric pressure is on so fine a scale that its details can only be made out with difficulty; as the pressure is reduced the scale gets larger and larger, until, when the pressure is reduced to that due to a millimetre or so of mercury, the details of the structure become very conspicuous. The appearance of the discharge at such a pressure is shown in fig. 12, and we see that it is built up of several constituents of very different types. We have already when considering the spark discharge given a general description of some of them; there are, however, some features which require further discussion.

Starting from the cathode we find a thin layer of luminous gas, the colour of which depends on the kind of gas through which the discharge is passing. In most gases the light appears to reach right up to the cathode, but in helium Aston has shown it is separated from it by an exceedingly thin dark space. This luminous layer is sometimes called " Goldstein's first layer "; next to this we have a region where there is comparatively little luminosity called " Crookes' dark space," the boundary of this space being approximately the surface traced out by normals to the surface of the cathode of constant length. The thickness of the dark space, which is of the order of the critical spark length, depends upon the pressure of the gas, varying approximately as the reciprocal of the pressure for air; at the pressure of 1 mm. of mercury the thickness of the dark space is about 2 mm., so that at atmospheric pressure the thickness would not be much more than about 1/400 of a millimetre. If the pressure remains constant and the current through the tube is increased, the thickness of the dark space remains unaltered until the current is large enough to cover the whole of the cathode with the luminous glow; after this stage is reached any further increase in the current causes a diminution in the thickness of the dark space. Starting from the boundary of the dark space there is a brightly luminous region called " the negative glow." The function of the parts of the discharge from the cathode to the negative glow is to produce the supply of electrons from the neighbourhood of the cathode necessary to keep the discharge going. The dimensions of this part of the discharge are independent of the distance between the cathode and anode; at very low pressures this part may occupy a length of several centimetres, but at atmospheric pressure they are crowded into a very small fraction of a millimetre and as far as length goes occupy a negligible portion of the sparks at such pressures. The Crookes' dark space, though it appears dark in contrast to the negative glow, is not devoid of luminosity; indeed Seeliger, who has made a spectroscopic examination of the dark space, finds that there are some lines, such as the Balmer series lines, which are almost as bright in the dark space as in the negative glow. But many lines are much stronger in the negative glow than in the dark space.

Beyond the negative glow there is another comparatively dark region called the " Faraday dark space "; the length of this is very variable even when the pressure is constant, as it is sensitive to any change in current. Beyond this and reaching right up to the anode is a luminous column, called the positive column. The luminosity in some cases is fairly uniform in intensity, but when the pressure and current are between certain limits this column may exhibit remarkable alternations of dark and bright spaces called striations, such as are shown in fig. 13. Under some circumstances a dark space round the anode has been detected by several observers.

When the distance between the electrodes is considerable and the pressure not very low, the positive column forms by far the greater part of the discharge; thus at atmospheric pressures all but a fraction of a millimetre of the discharge next the cathode will consist of the positive column.

Distribution of the Electric Force along the Discharge

The electric force is very large indeed in the part of the dark space next the cathode, but diminishes rapidly towards the negative glow. In the negative glow itself it is smaller than in any other part of the discharge; passing the negative glow, the electric force increases in the Faraday dark space, until the positive column is reached. When the positive column is of uniform luminosity the electric force in the column is constant until quite close to the anode, when there is an abrupt change of potential of about 20 volts, called the anode fall of potential. When the positive column is striated, the alternations of luminosity in the positive column are accompanied by alternations in the intensity of the electric force, the maxima of the electric force occurring at the bright parts of the striae, the minima at the dark. From the equation dX 4 = irp, where X is the electric force in the direction of x and dx p the density of the electrification, we see that there is an excess of positive electricity in the cathode dark space and of negative in the Faraday dark space; in a uniform positive column there is no appreciable excess of electricity of one sign over that of the opposite, while in the striated positive column there is an excess of negative electricity on the cathode side of a bright part of a striation and of positive on the anode side.

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Cathode Fall of Potential

Until the glow next the cathode covers the whole of the electrode. the difference of potential between the cathode and the negative glow is constant, depending on the gas and the material of which the cathode is made, but being independent of the pressure of the gas and the strength of the current. This constant difference of potential is called the " cathode fall of potential," and there is evidence to show that it is equal to the minimum potential that can produce a spark through the gas. Its value, as determined by Mey for different gases and different electrodes, is given in the following table, which includes also Matthies' results for C1 2, Br 2, 12: - When the current is so large that the luminous glow completely covers the cathode, the potential difference between the cathode and the negative glow increases as the current increases, while the thickness of the dark space diminishes. Mr. Aston, as the result of experiments made with very large parallel plate electrodes, found the following relations between V the cathode fall of potential, c the intensity of the current, D the thickness of the dark space, and p the pressure of the gas - D= p }i F These relations are empirical, and must not be taken to imply that the dark space would increase indefinitely if the current were diminished without limit. Aston also found that the thickness of the dark space as well as the cathode fall of potential depended upon the material of which the cathode is made. If the space round the cathode is restricted so that the dark space has not room to develop (for example, if the cathode is placed in a narrow tube), then, as soon as the dark space reaches the walls of the tube, the cathode fall begins to increase, and increases very rapidly as the pressure diminishes and the thickness of the free dark space exceeds more and more the space available round the cathode. This is due to the same cause as that which makes the spark potential increase rapidly when the spark length falls below the critical value. This result is utilized to make " electric valves," i.e. tubes through which a current will only pass in one direction. For if electrodes are put in a tube which is narrow at one end and very wide at the other, the development of the negative glow will be restricted when the cathode is at the narrow, but not when it is at the wide end of the tube: a discharge through the bulb will pass much more easily when the wide end is cathode than when it is anode, so that even if the electrodes are made alternately positive and negative the discharge through the tube will only be in one direction.

A very important question in connexion with the cathode fall of potential is whether the fall is continuous throughout the dark space or whether an appreciable fraction of it occurs abruptly at the surface of the cathode: Aston, who measured the distribution of potential near a very large flat cathode, came to the conclusion that there was no abrupt fall at the cathode. Westphal, on the other hand, found in his experiments an abrupt fall of potential quite close to the cathode amounting to 20% or more of the total cathode fall. The question is important in connexion with the mechanism of the discharge, for if the fall is so abrupt that it occurs within molecular distances the electric force on the surface of the cathode might be so great that the electrons would be drawn out of the cathode without the necessity for the bombardment by positive ions. It is interesting in this connexion to notice that Skinner has shown that the anode " fall of potential " occurs quite abruptly, as far as can be tested by experiment; this, again, if the fall took place in molecular distances might be sufficient to drag positive ions out of the anode itself. By using a cathode heated to incandescence, and therefore emitting a plentiful supply of electrons, we can reduce the cathode fall of potential to a small fraction of its normal value; we cannot, however, with a luminous discharge get rid of the anode fall; thus in the arc discharge the anode fall of potential is greater than the cathode fall. Matthies has shown that, in chlorine, bromine and iodine, the anode fall of potential may rise to hundreds of volts, that in air or hydrogen being only about 18 volts. Reichenheim and Gehrke utilized this fact to get positive ions of sodium and potassium projected with great velocity. They made the anode of a mixture of the halogen salts of these metals and graphite, and worked at a very low pressure; under the action of the discharge the halogens were liberated from the anode, and the large anode fall they produced was sufficient to project sodium and potassium ions from the anode with great velocity; this stream of positive ions constitutes what is known as " anode rays." The electric force in the positive column is a linear function of the pressure; it depends slightly on the diameter of the tube through which the discharge is passing; it also depends on the current through the tube; in most cases, though not invariably, an increase of current produces a decrease in the electric force. The condition determining the electric force in the positive column is that it should give to an electron during its free path the amount of energy that will enable the electrons to produce by collisions as many ions per second as are lost during the same time by recombination.

Striated Discharge

The form of discharge when the positive column is striated is so beautiful and remarkable that it has attracted a great deal of attention. To get this type of discharge the current and pressure must be within certain limits. The striations are developed more readily in mixtures of gases than in a pure gas; in fact some physicists have advanced the view that they could not be obtained in an absolutely pure gas. There is no doubt, however, about their occurrence in gases in which great attention has been paid to purification. Nerbeck could not get them in pure nitrogen or pure helium, though they were conspicuous as soon as a trace of impurity was admitted. Nitrogen and helium are gases in which, when pure, the carrier of negative electricity is always an electron; in these gases the electron does not join on to a molecule and become a negative ion. Spottiswoode found that, in some cases when the positive column showed no signs of striation when observed in the usual way, striations moving rapidly down the tube could be seen when the discharge was observed after reflection in a rapidly rotating mirror. Aston and Kikuchi, who have studied this effect in neon and helium, are of opinion that the striations are moving in these gases with the velocity of sound; it must be remembered, however, that the velocity of sound in many gases is of the same order as the velocity of a positive ion under the electric forces in the positive column, so that this result does not necessarily prove that the moving striations are analogous to sound waves.

The distance between the striations increases as the pressure diminishes (in hydrogen the distance is inversely proportional to the square root of the pressure); it depends upon the size of the tube: the striations are nearer together in narrow tubes than they are in wide. The distance between the striations also depends upon the current. When several gases are in the tube, spectroscopic observation of the bright parts of the different striations shows that we may have one set of striations corresponding to one gas, another to another and so on. Thus Crookes observed in a tube containing hydrogen three sets of striations, one set red, another blue and a third grey; the spectroscope showed that the first was due to hydrogen, the second to mercury vapour and the third to hydrocarbons. The striations are often curved with their concavities turned to the anode.

To get a general idea of the causes which might give rise to strati fication, let us consider a case where the current is carried entirely by electrons, the positive ions being regarded as immovable in comparison with the electrons. Let us imagine a stream of electrons coming from the negative glow; the electric force in this region is exceedingly small, so that these electrons will have very little energy and will be unable to ionize the gas; the electrification in this part of the tube will be that due to the electrons and thus will be negative, so that the electric force will increase as we approach the anode; as the electric force increases the energy of the electron increases, and the electron will acquire enough energy to enable it to ionize the gas and produce positive ions and electrons; the increase in the number of ions will check the rate of increase in the electric force. The connexion between the ionization and this rate of increase is in the case we are considering represented by a very simple equation. For if n and y n represent respectively the number of negative and positive ions per unit volume, X the electric force, and x the distance from the cathode If the current c is carried, as we have supposed, by the electrons, neu = c, where u is the velocity of the electron, and if we neglect the current carried by the positive ions, then when things have reached a steady state the number of positive ions produced in any region per second must equal the number which disappear owing to recombination. Hence, if q is the rate of ionization, a the coefficient of recombination, q = amn or m = q/an. Hence we see that (24) is equivalent to dX _ 47rc 4-rrgeu dx _ eu ac Thus as long as q vanishes, dX/dx is positive, but as soon as q becomes finite the rate of increase will be retarded; as X increases q increases, and when e 2 qu 2 =ac e, dX /dx will vanish; but though X reaches its greatest value at this point, the values of u and q, which depend on the energy acquired by the electron, will continue to increase beyond it. For the energy acquired by an electron depends on fXdx, taken over a distance measured by the free path of the electron; at low pressures this may be a centimetre or more, and the place where fXdx is a maximum will be beyond that where X is a maximum by a length of this order. Thus after X has reached its maximum a and q will increase and dX/dx will become negative, so that X will diminish; the diminution in X will ultimately produce a diminution in fXdx and also in u and q; the rate of decrease will slow down; X will attain a minimum, and begin to increase again when similar changes will be repeated. Thus the curve which represents the relation between X and x will resemble fig. 14, giving alter FIG. 14 nate maxima and minima for the value of x. Thus fXdx, the energy acquired by an electron, will vary periodically along the path of the discharge. There are two values of this energy which are of special importance in connexion with discharge through gases, one the ionizing potential we have already referred to, the other, sometimes called the " radiation potential," is the energy which the electron must possess to make the gas luminous. The radiation potential is less than the ionizing potential, and electrons with energy between these potentials will make the gas luminous but will not ionize it. Thus the molecules of the gas will give out light but will not be charged. When the energy of the gas exceeds the ionizing potential the luminous molecules are or have been charged. If the variations in the energy along the line of discharge are large enough to make it sink below the radiation potential, then along the discharge we shall have: - (i) places where the energy is below the radiation potential, - these will be dark; (2) places where the potential is between the radiation potential and the ionizing potential, - the molecules here will be luminous and uncharged and will, therefore, not move under the electric field; (3) places where the molecules are luminous and charged, - these molecules will move down the tube towards the cathode with the velocity which the positive ion acquires under the electric field. This velocity, when the pressure is low and the field several volts a centimetre, as it is in the positive column, may be many thousand centimetres per second. Place (I) corresponds to the dark parts of the striations, (2) to the stationary luminous parts, while (3) is the origin of the striations moving down the tube observed by Wulner, Spottiswoode, Aston and Kikuchi.

Cathode Rays

In 1859 Pliick.er observed on the glass of a. highly exhausted tube in the neighbourhood of the cathode a.

dX . (24). dx - 4 7r (n - m)e . (25).

bright greenish yellow phosphorescence, which changed its position when a magnet was brought near to it. About io years afterwards Hittorf showed that a solid body placed between a pointed electrode and the walls of the tube cast a well-defined shadow of such a shape as to show that the agent producing the phosphorescence travels in straight lines at right angles to the surface of the cathode. The name " cathode rays " for the cause of the phosphorescence was introduced by Goldstein, who made many important investigations on their properties. The opinion held by Goldstein and generally in Germany was that cathode rays were waves in the ether. Varley and Crookes advanced the view that they were electrified molecules shot off at right angles to the cathode. The discovery by Hertz that the cathode rays could pass through thin layers of gold leaf was difficult to reconcile with this view. The evidence in favour of the cathode rays being electrified particles was much increased by Perrin's discovery that when a pencil of the rays entered the opening in a Faraday cylinder they gave a negative charge to the cylinder. One difficulty which had been urged against the rays being negatively electrified, viz. that, though they were deflected by a magnetic force, an electric force produced no effect upon their path - was removed by J. J. Thomson, who showed that the absence of deflection was due to the gas in the tube acting as a screen and protecting the particles from the electric force. As the gas in the vacuum tube is a conductor of electricity the rays move inside a conductor of electricity, and so will not be affected by an external electrified body. Thomson showed that when the vacuum was very high, so that there was but little gas in the tube, the cathode rays were deflected by an electric and magnetic field, and that the direction of the deflection indicated a negative charge on the particles. The measurement of the deflection by known electric and magnetic forces led to a determination of the mass of the particles which carried the charge, and showed that these particles were not atoms or molecules but something with a mass not one-thousandth part of the mass of the lightest atom known, that of hydrogen.

The deflection due to electric and magnetic forces can be calculated as follows. Suppose that the particles are travelling horizontally between two parallel horizontal metal plates A, B, maintained at a constant difference of potential, there will be a vertical electric force F acting between the plates, and if the axis of y is vertical the equation of motion of the electrified particle when it is between the plates is md d2y _ t" -Fe. If y and dt are both zero when the particle enters the region between the plates, then, when it leaves this region, after a time - y=- 2 m t2 and dt m t. Since the electric force is at right angles to the direction of motion of the particles, v the velocity of the particles will not alter, and if the deflection is small, t=1/v where 1 is the length of the plates. Thus Fe 1 2 d _ y _ F _ e l y= 2 m v2 and dv m 2 Suppose the particles strike a photographic plate or a screen covered with a phosphorescent substance at a distance L from the end of the plates, the y displacement at this plate produced by the electric force is given by the expression - t Fe 1 2 2 Fe lL _ Fel l y=- 2 m v- + 'm v 2 m y " C 2 +L Magnetic Deflection of the Rays. - If the rays go through a uniform magnetic field of length 1 and strength H, then if the magnetic force is vertical the force acting on the moving particles will be He y , and will be at right angles to the magnetic force and also to the direction of motion of the rays; i.e. it will be at right angles to the plane of the paper; if z is the displacement of the particle in this direction d2z m =Hey.

dt2 'From this we see' that the value of z at the screen is given by _Hel(1 + z L). n2v 2 1 z 2 F Y H 2 1 (+L) and v= z H.. (27). y Thus the measurements of y and z, the electric and magnetic deflections, give the values of elm and v. The expressions for y and z have been obtained on the supposition that the electric and magnetic fields acted one at a time and not simultaneously. If, however, y and z are small, their values will not to a first approximation be altered if the electric and magnetic deflections occur simultaneously. Thus by making the cathode rays pass through superposed electric and magnetic fields, elm and v can be got with one exposure by measuring y and z on the screen or photographic plate.

Since from the above equation (26) z 2 /y is constant as long as elm is constant, we see that all the particles of the same kind, whatever their velocity, would strike the screen or plate on a parabola, and that if the rays were a mixture of particles of different kinds each kind of particles would trace out a different parabola. Since z/y only depends upon v, all the particles moving with the same velocity will strike the screen or plate in a straight line.

The determination of elm for the cathode rays led to results of fundamental and far-reaching importance, for it was found that all the cathode rays had the same value for elm, and that moreover while for a charged atom of hydrogen in liquid electrolytes elm was equal to 10 4, when e was measured in electromagnetic units, the value of elm for the particles in the cathode rays was considerably more than one thousand times this value. Thus if e were the same for the particle as for the hydrogen atom (and we shall see later that this is the case), the mass of the cathode particle is only ,?aa of that of an atom of hydrogen, the smallest mass which hitherto had been recognized. Again it was found that whatever metal might be used for the cathode, or whatever might be the gas in the discharge tube, the value of elm was unaltered. As those particles must have come either from the electrode or the gas, it follows that the particles of the cathode rays are a constituent of the atoms of all the chemical elements. These particles are called " electrons." After the electrons had once been detected in the cathode rays, they were soon detected under many other conditions and found to be of very wide-spread occurrence. Thus, for example, it was found that streams of electrons are given out by incandescent metals, the rate of emission increasing very rapidly with the temperature. This has received a very important industrial application in what are known as " hot wire valves," at which a current from a hot cathode passes through a vessel in which the vacuum is so perfect that the gas takes no part in the discharge; the current, in some cases amounting to several amperes, is carried entirely by electrons. Lenard found that they were emitted by metals exposed to ultraviolet light. They are emitted when Röntgen rays strike against matter, and by radio-active substances. The speed of the electrons ejected either by ultra-violet light or by Röntgen rays does not depend upon the intensity of the radiation but only upon the wave length. The energy acquired by the electrons is = hn where n is the frequency of the radiation and h Planck's constant.

Since the cathode rays are deflected by electric and magnetic forces proportionally to the magnitude of these forces, we can use the deflection of the rays as a measure for electric and magnetic forces. As these rays have practically no inertia they are especially adapted to measure very rapidly alternating forces which could not be detected by any index having an appreciable mass. The cathode ray oscillograph, an instrument by which electric and magnetic forces are measured by the deflection of cathode rays, has already been used in many investigations, and is a very important aid to research. Another property of cathode rays is that when they strike against matter they generate Röntgen rays, the hardness of the latter increasing with the speed of the former.

Positive Rays. - Goldstein discovered in 1886 that, if the cathode on a highly exhausted tube was perforated, bundles of a luminous discharge streamed through the aperture into the space behind the cathode. The colour of this discharge depends upon the gas in the tube; thus in hydrogen it is rose colour; in air, yellowish. The colour of the light due to these rays is not the same as that produced when cathode rays pass through the gas. In some gases the difference is very striking: thus in neon the light due to the cathode rays is pale blue, while the discharge which streams through the cathode is a gorgeous red. Goldstein called the rays which stream through the hole in the cathode Kanalstrahlen; but as they have been proved to consist of positively charged particles it seems more natural to call them " positive rays." These rays produce phosphorescence when they strike against glass and many other substances, though the phosphorescence is generally of a different colour from that produced by cathode rays. They also affect a photographic Hence ' '. (26), plate. It was at first thought that the positive rays were not deflected by a magnet, as magnetic forces which produced large deflections of cathode rays had no appreciable effect upon positive ones. Wien showed, however, by using very strong magnetic fields, that they could be deflected, and that the direction of the deflection indicated that they carried a charge of positive electricity; they can also be deflected by electric forces.

By measuring the deflection provided by electric and magnetic fields we can determine the value of elm for the particles which constitute the rays. The result is of great interest. Instead of, as in the cathode rays, elm having the same value for all the carriers, we find that elm has many different values separated by finite intervals; and instead of elm being equal to 1.78 x ro 7, as in the cathode rays, we find the greatest value of elm is ro 4, which is the same as its value for a charged hydrogen atom. The values found for elm depend on the gases in the discharge tube; the outstanding result is that all these values of m correspond to masses of atoms or molecules of the chemical elements or compounds. Thus while the determination of elm for the cathode rays shows that in a gas at a very low pressure the carriers of the negative electricity are all of the one type, being electrons whose mass is exceedingly small compared with that of any atom, the determination of elm for the positive rays shows that the carriers of the positive electricity are of many different types; and that all these types correspond to atoms or molecules of the chemical elements or compounds. It has already been shown that if charged particles, after passing through electric and magnetic fields, are received on a screen or photographic plate, all particles, for which elm is the same, strike the plate on a parabola, and that for each different value of elm there is a separate parabola.

FIG.16

These parabolas are shown in fig. 15, which is a reproduction of a photograph made by allowing the positive rays in a tube containing gases liberated by heating a certain mineral to strike against a photographic plate; taken from the top downwards they correspond respectively to the atom of hydrogen, the molecule of hydrogen, the atom of helium, the atom of carbon with two charges, the atom of nitrogen with two charges, the atom of oxygen with two charges, the atom of carbon with one charge, the atom of nitrogen, the atom of oxygen, the molecule of water, the molecule of CO and that of N 2 (these form one parabola), the molecule of oxygen, the molecule of CO 2 and the atom of mercury. We find that many of the atoms can carry more than one charge, for when we find a parabola corresponding to one value of elm we frequently find another corresponding to twice this value; thus carbon, nitrogen, and oxygen occur very frequently with two charges, other atoms such as argon with two and three charges, while mercury atoms have been detected with I, 2, 3, 4, 5, 6, 7 charges. It is significant that the atom of hydrogen never occurs with more than one charge. Multiple charges generally occur on atoms but not on molecules; there are, however, some molecules such as CO on which double charges have been found. Some of the positive particles, after passing through the hole in the cathode, lose their positive charge and become uncharged, and some of these neutral particles acquire a negative charge; thus mixed with the positively electrified particles there are some negatively electrified ones. This power of acquiring a negative charge is confined to certain atoms; thus while the atoms of hydrogen, carbon, oxygen, fluorine occur with a negative charge, the atoms of nitrogen, helium, argon and neon do not. It is exceptional for a molecule to acquire a negative charge, the molecules of oxygen and carbon, however, can do so. The equation of a parabola formed by a particle on the photographic plate has already been given z 2 = - e yC where z is measured parallel to the displacement due to the magnetic field and y to that due to the electrostatic. C is a quantity which depends on the strength of the electric and magnetic fields and on the position of the photographic plate. If, as in fig. 16, we draw a A line parallel to the axis of z, the intercept made by a parabola on this line will be proportional to (elm)l; thus, if the top parabola is due to the atom of hydrogen, the next to the molecule of hydrogen, the third to the atom of helium and the fourth to that of_oxy gen, the intercepts AH, AH 2r AO are in the proportion of 1, r //2, r /4. Thus by comparing the intercept made by any parabola X with that made by the parabola due to the hydrogen atom we can find the molecular weight of the substance producing the parabola X.

Positive Rays as a Method of Chemical Analysis

Since from the measurement of the positive ray photographs we can determine the molecular weight of the gases in the discharge tube, we can analyze a gas by putting a small quantity of it in a discharge tube and taking a photograph of the positive rays. It is thus a method of chemical analysis, and its application has already led to the detection of several new substances. In fact, though it has only recently been introduced, more substances have been discovered by this method than have ever been discovered by spectrum analysis. The method has many advantages. In the first place only a very minute quantity of the gas is required; a small fraction of a cubic centimetre of gas at atmospheric pressure is all that is required to fill the discharge tube at the pressure at which the positive rays are produced. Again, the method is very sensitive, as it will detect the presence of a gas which only forms a small percentage of the gas in the tube. The method not only detects the presence of the gas, but at the same time determines its molecular weight. It indicates, if the gas is an element, whether it is monatomic or diatomic; for if it is diatomic it will give rise to two parabolas, one due to the atom, the other to the molecule. The absence of double or negative charges will suggest that it is a compound and not an elementary gas. The only ambiguity is that it does not distinguish between two substances of the same molecular weight; thus C02, and N 2 0 give the same parabolas, as also do CO and N2: we can often, however, remove this ambiguity by putting substances in the tube which would absorb one gas and not the other, and testing whether or not this has removed the parabola.

Use of Positive Rays to Determine Atomic Weight

The measurement of the parabolas give, as we have seen, the atomic weight of the elements producing them; they can therefore be used to determine the atomic weight of elements which can be introduced in a gaseous state into the discharge tube. This method has the great advantage that the presence of impurities does not affect the result. Mr. Aston has lately, by the use of a positive-ray method for determining atomic weights, found the very important fact that, if oxygen is taken as 16, the atomic weights of the elements with the exception of hydrogen are represented by whole numbers. Thus in working with chlorine he found no substance with an atomic weight of 35.4, but two substances with atomic weight of 35 and 37 respectively; he regards these substances as identical in chemical properties and inseparable by chemical reactions, and ordinary chlorine as a mixture of about 3 parts of (352) and one part of (371). Mr. Aston, by the method of positive ray analysis, has discovered isotopes of boron, silicon, bromine, krypton, xenon and mercury.

The Charge of Electricity Carried by Gaseous Ions and Electrons

The deflection of cathode and positive rays by electric and magnetic forces supplies a method for finding the value of elm; for the determination of e, the charge on an ion, other methods have to be employed. One such method used by J. J. Thomson is based on the important investigations of C. T. R. Wilson on the effect of ions on the deposition of clouds and fogs from supersaturated air. If dust-free air saturated wit h water vapour is suddenly cooled by expansion, no cloud or fog is deposited unless the supersaturation due to the cooling is very large. C. T. R. Wilson found that if ions are present in the gas they act as nuclei round which drops of water are deposited with a supersaturation much below that required for gas free from ions.

A beautiful application of this is the detection of the path of an a particle from a radioactive substance. The a particle produces by collision ions all along its path; if the damp gas through which the particle is passing is suddenly cooled by expansion, drops of water will deposit on the ions and thus mark out the path of the particle. One of Mr. Wilson's photographs of such a path is shown in fig. 17. Mr. Wilson found that less supersaturation is required to deposit water on negative than on positive ions. This result can be applied to find the number of ions in a moist gas, for if the gas is suddenly expanded by an amount sufficient to deposit drops on ions, but not sufficient to produce condensation in their absence, then each ion may be made the centre of a drop, and the problem of counting the ions is reduced to that of counting the drops.

We can calculate the amount of water that will be deposited by any given expansion of the air; hence, since we know the volume of the water we can determine the number of drops if we know the volume of a single drop. Observation of the rate at which a drop falls under gravity will give the size of the drop, for Stokes long ago showed that the velocity of a rain drop falling under gravity is given by the equation v= 3 - g (2 - P -; when v is the velocity of the drop, a its radius, µ the viscosity of the gas, g the acceleration due to gravity, and p is the density of the gas. It has been found that, with the exceedingly fine drops formed round ions where the radius of the drop is comparable with the free path of the molecules of the gas, the velocity is greater than that given by the above, equal in the proportion of (1 - a ) t 0 1, when C is a constant, and the pressure. But though this correction makes the relation between a and v a little more complicated, it still enables us to determine a when v is known. Thus the radius, and therefore the volume, of the drop can be determined, and from this, as we have seen, we can deduce the number of ions.

Let n be this number per unit volume; then if a current of electricity is sent through the gas by an electric force X, the current passing through unit area will be neU when U is the mean velocity of the positive and negative ions under the force X. We know that it is proportional to the force and for a force of one volt per centimetre is 1.5 cm./sec.; and hence when X is known U is known, the current neU can be measured, and hence ne deduced; as n has been found by the drops, the value of e can be determined immediately. This was the method used by J. J. Thomson; a simpler method used afterwards by H. A. Wilson was to get drops round the negative ions alone by using an expansion that would deposit moisture on negative but not on positive ions. He then showed the rate of fall of these drops, first under gravity alone, and then under a vertical electrical force X, acting on the drop in the same direction as gravity. Thus, when the electric field is acting, the force on the drop is Xe+ 3 irpa3g, and when it is off the force is only 3 irpa 3 g. Thus, if v1, v are respectively the velocities of the drop when the field is on and off, - Xe+ 3 ap a3g- v _ 3?pa3g or Xe= 3 7rpa3g (z1 -v), v From v, the rate of fall when the field is off, we can calculate as before the radius of the drop, and from the preceding equation we can determine e. Millikau, who has made most extensive and accurate investigations on the value of e, used a modification of the preceding method. Instead of producing water drops by expansion on the ions, he obtained, by means of a sprayer, minute drops of oil; he observed the motion of one of these under an electric field in a gas which was subject to some ionizing agent, and from time to time an ion would strike against the drop and alter the charge; this would alter the velocity, and from the alteration of the velocity he could by a formula similar to that just given calculate the charge communicated to the drop by the ion. The value obtained for e by this method is, in electrostatic units, e=4.77X10-10.

From the value of e we can obtain Avogadro's constant, the number of molecules in a cubic centimetre of gas at oc and 760 mm. pressure. For Townsend has shown that Ne = P X D where P is the pressure when the number of molecules is N, u the velocity of the ion when the force is X, and D the coefficient of diffusion of the ion into the gas. Townsend measured D, and found that the value of Ne determined by this equation was, within the limit of errors of experiment, equal to NE as determined by experiments on the quantities of hydrogen liberated by electrolysis. E is here the charge carried by an atom of hydrogen in the electrolysis of liquids. Thus the charge on the gaseous ion is equal to that on the liquid ion. Since one coulomb deposits 1.11827 milligrams of silver, and the atomic weight of silver is 108 and the density of hydrogen 8.987 X 105 at oc, NE= 1. 290X10 10, and as e= 4.77 X 10-10, N=2 7X1010.

The number of molecules in a gramme molecule of any substance is 606 X 1023.

Thus the study of the electrical property of gases has given the most accurate values available of two of the most important constants connected with the constitution of matter. By study, ing electrified atoms and molecules, we have been able to determine their masses and their properties with an accuracy far beyond that attainable by any method which can be used when they are in the normal state. (J. J. T.)

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