A History of the Theories of Aether and Electricity (1910) — part 24 of 29

A further consequence deduced by Helmholtz from this theory leads to a second method of determining the difference of potential between mercury and an electrolyte. If a mercury surface is rapidly extending, and electricity is not rapidly transferred through the electrolyte, the electric surface-density in the double layer must rapidly decrease, since the same quantity of electricity is being distributed over an increasing area. Thus it may be inferred that a rapidly extending mercury-surface in an electrolyte is at the same potential as the electrolyte.

This conception is realized in the dropping-electrode, in

• The conception of double layers of electricity at the surface of separation of two bodies had been already applied by Helmholtz to explain various other phenomena — e.g., the Volta contact-difference of potential of two metals, fiictional electricity, and *' electric endosmose," or the transport of fluid which occurs when an electric current is passed through two conducting liquids separated by a porous barrier. Cf. Helmholtz, Berlin Monatsberichte, February 27, 1879 ; -Ann. d. Phys. vii (1879), p. 337 ; Helmholtz, Wiss. Abh. i, p. 855.

380 Conduction in Solutions and Gases ,

which a jet of mercury, falling from a reservoir into an electro- lytic solution, is so adjusted that it breaks into drops when the jet touches the solution. According to Helmholtz's conclusion there is no difference of potential between the drops and the electrolyte ; and therefore the difference of potential between the electrolyte and a layer of mercury underlying it in the same vessel is equal to the difference of potential between this layer of mercury and the mercury in the upper reservoir, which difference is a measurable quantity.

It will be seen that according to the theories both of Gibbs and of Helmholtz, and indeed according to all other theories on the subject,* d^ldV is zero for an electrode whose surface is

• E.g., that of Warburg, Ann. d. Phys. xli (1890), p. 1. In this it is assumed that the electrolytic solution near the electrodes originally contains a salt of mercury in solution. When the external electromotive force is applied, a conduc- tion-current passes through the electrolyte, which in the hody of the electrolyte is carried by the acid and hydrogen ions. Warburg supposed that at the cathode the hydrogen ions react with the salt of mercury, reducing it to metallic mercury, which is deposited on the electrode. Thus a considerable change in concentration of the salt of mercury is caused at the cathode. At the anode, the acid ions carrying the current attack the mercury of the electrode, and thus increase the local concentration of the mercuric salt ; but on account of the size of the anode this increase is trivial and may be neglected.

Warburg thus supposed that the electromotive force of the polarized cell is really that of a concentration cell, depending on the different concentrations of mercuric salt at the electrodes. He found dy/dV to be equal to the amount of mercuric salt at the cathode per unit area of cathode, divided by the electro- chemical equivalent of mercury. The equation previously obtained is thus presented in a new physical interpretation.

Warburg connected the increase of the surface-tension with the fact that the surface-tension between mercury and a solution always increases when the con- centration of the solution is diminished. His theory, of course, leads to no conclusion regarding the absolute potential difference between the mercury and the solution, as Helmholtz' does.

Alan electrode whose surface is rapidly increasing — e.g., a dropping electrode — Warburg supposed that the surface-density of mercuric salt tends to zero, so dyldV is zero.

The explanation of dropping electrodes favoured by Nernst, Beilage zu den Ann. d. Phys. Iviii (1896), is that the difference of potential corresponding to the equilibrium between the mercury and the electrolyte is instantaneously established ; but that ions are withdrawn from the solution in order to form the double layer necessary for this, and that these ions are carried down with the drops

from Faraday to J. J . Thomson. 381

rapidly increasing — e.g., a dropping electrode; that is to say, the difference of potential between an ordinary mercury electrode and the electrolyte, when the surface-tension has its maximum value, is equal to the difference of potential between a dropping-electrode and the same electrolyte. This result has been experimentally verified by various investigators, who have shown that the applied electromotive force when the surface- tension has its maximum value in the capillary electrometer, is equal to the electromotive force of a cell having as electrodes a large mercury electrode and a dropping electrode.

Another memoir which belongs to the same period of Helmholtz' career, and which has led to important develop- ments, was concerned with a special class of voltaic cells. The most usual type of cell is that in which the positive electrode is composed of a different metal from the negative electrode, and the evolution of energy depends on the difference in the chemical affinities of these metals for the liquids in the cell. But in the class of cells now considered* by Helmholtz, the two electrodes are composed of the same metal (say, copper) ; and the liquid (say, solution of copper sulphate) is more con- centrated in the neighbourhood of one electrode than in the neighbourhood of the other. When the cell is in operation, the salt passes from the places of high concentration to the places of low concentration, so as to equalize its distribution ; and this process is accompanied by the flow of a current in the outer circuit between the electrodes. Such cells had been studied experimentally by James Moser a short time previously! to Helmholtz' investigation.

The activity of the cell is due to the fact that the available energy of a solution depends on its concentration ; the molecules

of mercury, until the upper layer of the solution is so much impoverished that the double layer can no longer be formed. The impoverishment of the upper layer of the solution has actually been observed by Palniaer, Zeitsch. Phys. Chem. xxv (1898), p. 265 ; xxviii (1899), p. 257 ; xxxvi (1901), p. 664.

• Berlin Monatsber., 1877, p. 713 ; Phil. Mag. (5) v (1878), p. 348; reprinted with additions in Ann. d. Phys. iii (1878), p. 201.

t Ann. d. Phys. iii (1878), p. 216.

382 Conduction in Solutions and Gases ,

of salt, in passing from a high to a low concentration, are therefore capable of supplying energy, just as a compressed gas is capable of supplying energy when its degree of compression is reduced. To examine the matter quantitatively, let nf(nf V) denote the term in the available energy of a solution, which is due to the dissolution of n gramme-molecules of salt in a volume V of pure solvent ; the function / will of course depend also on the temperature. Then when dn gramme-molecules of solvent are evaporated from the solution, the decrease in the available energy of the system is evidently equal to the available energy of dn gramme-molecules of liquid solvent, less the available energy of dn gramme-molecules of the vapour of the solvent, together with nf(n/ V) less nf{n/(V-v dn) } , where v denotes the volume of one gramme-molecule of the liquid. But this decrease in available energy must be equal to the mechanical work supplied to the external world, which is dn . p± (v - v), if pl denote the vapour-pressure of the solution at the temperature in question, and v denote the volume of one gramme-molecule of vapour. We have therefore

dn . pi (v' - v) = — available energy of dn gramme-molecules of

solvent vapour

• available energy of dn gramme-molecules of

liquid solvent

• nf(n/ V) - nf {n/( V-v dn) \ .

Subtracting from this the equation obtained by making n zero, we have

dn . (Pi - p0) (v - v) = nf(n/ V) - nf( n/( V - v dn) } ,

where pQ denotes the vapour-pressure of the pure solvent at the temperature in question ; so that

(Pi -Po) <>' - v) = - (n'/V*)f(n/V)v.

Now, it is known that when a salt is dissolved in water, the vapour-pressure is lowered in proportion to the concentration of the salt — at any rate when the concentration is small : in

from Faraday to J . J. Thomson. 383

fact, by the law of Kaoult, (p0-pi)/po is approximately equal to nv/ V ; so that the previous equation becomes

p. V(v' -f.) -*/(»/ F).

Neglecting v in comparison with v', and making use of the equation of state of perfect gases (namely,

pjt = ST.

where T denotes the absolute temperature, and R denotes the constant of the equation of state), we have

and therefore

Thus in the available energy of one gramme-molecule of a dissolved salt, the term which depends on the concentration is proportional to the logarithm of the concentration ; and hence, if in a concentration-cell one gramme-molecule of the salt passes from a high concentration c2 at one electrode to a low concentration GI at the other electrode, its available energy is thereby diminished by an amount proportional to log (c2/c,). The energy which thus disappears is given up by the system in the form of electrical work; and therefore the electromotive force of the concentration-cell must be proportional to log (Cz/cJ.. The theory of solutions and their vapour-pressure was not at the time sufficiently developed to enable Helmholtz to determine precisely the coefficient of log (c2/Ci) in the expression.*

An important advance in the theory of solutions was effected in 1887, by a young Swedish physicist, Svante Arrhenius.f

• The formula given by Helmholtz was that the electromotive force of the cell is equal to b(l - ri) v log (czjc), where ci and c\ denote the concentrations of the solu- tion at the electrodes, v denotes the volume of one gramme of vapour in equilibrium with the water at the temperature in question, n denotes the transport number for the cation (Hittorfs 1/w), and b denotes q x the lowering of vapour- pressure when one gramme-equivalent of salt is dissolved in q grammes of water, where q denotes a large number.

t Zeitschrift fur phys. Chem. i (1887), p. 631. Previous investigations, in which the theory was to some extent foreshadowed, were published in Bihang till Svenska Vet. Ak. Forh. viii (1884), Nos. 13 and 14.

384 Conduction in Solutions and Gases,

Interpreting the properties discovered by Kohlrausch* in the light of the ideas of Williamson and Clausius regarding the spontaneous dissociation of electrolytes, Arrhenius inferred that in very dilute solutions the electrolyte is completely dissociated into ions, but that in more concentrated solutions the salt is less completely dissociated; and that as in all solutions the transport of electricity in the solution is effected solely by the movement of ions, the equivalent conductivityf must be pro- portional to the fraction which expresses the degree of ionization. By aid of these conceptions it became possible to estimate the dissociation quantitatively, and to construct a general theory of electrolytes.

Contemporary physicists and chemists found it difficult at first to believe that a salt exists in dilute solution only in the form of ions, e.g. that the sodium and chlorine exist separately and independently in a solution of common salt. But there is a certain amount of chemical evidence in favour of Arrhenius' conception. For instance, the tests in chemical analysis are really tests for the ions ; iron in the form of a fer- rocyanide, and chlorine in the form of a chlorate, do not respond to the characteristic tests for iron and chlorine respectively, which are really the tests for the iron and chlorine ions.

The general acceptance of Arrhenius' views was hastened by the advocacy of Ostwald, who brought to light further evidence in their favour. For instance, all permanganates in dilute solution show the same purple colour; and Ostwald considered their absorption-spectra to be identical ;J this identity is easily accounted for on Arrhenius' theory, by supposing that the spectrum in question is that of the anion which corresponds to the acid radicle. The blue colour which is observed in dilute solutions of copper salts, even when the strong solution is not blue, may in the same way be

• Cf. p. 374.

t I.e. the ohmic specific conductivity of the solution divided by the number of gramme-equivalents of salt per unit volume.

J Examination of the spectra with higher dispersion does not altogether confirm this conclusion.

from Faraday to J .J. Thomson. 385

ascribed to a blue copper cation. A striking instance of the same kind is afforded by ferric sulphocyanide ; here the strong solution shows a deep red colour, due to the salt itself ; but on dilution the colour disappears, the ions being colourless.

If it be granted that ions can have any kind of permanent existence in a salt solution, it may be shown from thermo- dynamical considerations that the degree of dissociation must increase as the dilution increases, and that at infinite dilution there must be complete dissociation. For the available energy of a dilute solution of volume V, containing «j gramme-molecules of one substance, >/2 gramme-molecules of another, and so on, is (as may be shown by an obvious extension of the reasoning already employed in connexion with concentration-cells)*

r (T) + RT^nr log (UT! V) + the available energy

possessed by the solvent before the introduction of the solutes, where 0r (T) depends on T and on the nature of the rth solute, but not on V, and R denotes the constant which occurs in the equation of state of perfect gases. When the system is in equilibrium, the proportions of the reacting substances will be so adjusted that the available energy has a stationary value for small virtual alterations Swj, &^, ...... of the

proportions ; and therefore

0 - SSnr .<t>r(T) + RT2$nr.log (nrjV)

Applying this to the case of an electrolyte in which the disappearance of one molecule of salt (indicated by the suffix ,) gives rise to one cation (indicated by the suffix 2) and one anion (indicated by the suffix 3), we have B^ = - £7^ = - Sn* ; so the equation becomes

0 = 0, (T) - 02 (T) - 03 (T) + RT log (n, V/n.n,) - RT,

or

= a function of T only.

• Cf. pp. 382-383. 2 C

386 Conduction in Solutions and Gases,

Since in a neutral solution the number of anions is equal to the number of cations, this equation may be written

nf = Fw-i x a function of T only ;

it shows that when V is very large (so that the solution is very dilute), n2 is very large compared with n^ ; that is to say, the salt tends towards a state of complete dissociation.

The ideas of Arrhenius contributed to the success of Walther Nernst* in perfecting Helmholtz' theory of concentration-cells, and representing their mechanism in a much more definite fashion than had been done heretofore.

In an electrolytic solution let the drift-velocity of the cations under unit electric force be u, and that of the anions be vt so that the fraction uj(u + v} of the current is transported by the cations, and the fraction v/(u + v) by the anions. If the concentration of the solution be Cj at one electrode, and c2 at the other, it follows from the formula previously found for the available energy that one gramme - ion of cations, in moving from one electrode to the other, is capable of yielding up an amountf RT log (c2/c,) of energy; while one gramme - ion of anions going in the opposite direction must absorb the same amount of energy. The total quantity of work furnished when one gramme-molecule of salt is transferred from concentration ct to concentration c{ is therefore

u + v

The quantity of electric charge which passes in the circuit when one gramme-molecule of the salt is transferred is pro- portional to the valency v of the ions, and the work furnished is proportional to the product of this charge and the electro-

*Zeitschr. fur phys. Chem. ii (1888), p. 613; iv (1889), p. 129; Berlin Sitzungsberichte, 1889, p. 83 ; Ann. d. Phys. xlv (1892), p. 360. Cf. also Max Planck, Ann. d. Phys. xxxix (1890), p. 161 ; xl (1890), p. 561.

t The correct law of dependence of the available energy on the temperature was by this time known.

from Faraday to J . J . Thomson. 387

motive force E of the cell ; so that in suitable units we have

-, RTu-v. c, E = -- - log -.

v u + v Ci

A typical concentration-cell to which this formula may be applied may be constituted in the following way : — Let a quantity of zinc amalgam, in which the concentration of zinc is d, be in contact with a dilute solution of zinc sulphate, and let this in turn be in contact with a quantity of zinc amalgam of concentration cz. When the two masses of amalgam are con- nected by a conducting wire outside the cell, an electric current flows in the wire from the weak to the strong amalgam,* while zinc cations pass through the solution from the strong amalgam to the weak. The electromotive force of such a cell, in which the current may be supposed to be carried solely by cations, is

RT. c,

— lo-

V °

Not content with the derivation of the electromotive force from considerations of energy, Nernst proceeded to supply a definite mechanical conception of the process of conduction in electrolytes. The ions are impelled by the electric force asso- ciated with the gradient of potential in the electrolyte. But this is not the only force which acts on them ; for, since their available energy decreases as the concentration decreases, there must be a force assisting every process by which the concentra- tion is decreased. The matter may be illustrated by the analogy of a gas compressed in a cylinder fitted with a piston; the available energy of the gas decreases as its degree of compression decreases; and therefore that movement of the piston which tends to decrease the compression is assisted by a force — the "pressure" of the gas on the piston. Similarly, if a solution were contained within a cylinder fitted with a piston which is permeable to the pure solvent but not to the solute, and if the whole were immersed in pure solvent, the available energy of

• It will hardly be necessary to remark that this supposed direction of the .current is purely conventional.

2 C 2

388 Conduction in Solutions and Gases,

the system would be decreased if the piston were to move outwards so as to admit more solvent into the solution; and therefore this movement of the piston would be assisted by a force — the "osmotic pressure of the solution," as it is called.*

Consider, then, the case of a single electrolyte supposed to be perfectly dissociated ; its state will be supposed to be the same at all points of any plane at right angles to the axis of x. Let v denote the valency of the ions, and V the electric potential at any point. Sincef the available energy of a given quantity of a substance in very dilute solution depends on the concentration in exactly the same way as the available energy of a given quantity of a perfect gas depends on its density, it follows that the osmotic pressure p for each ion is determined in terms of the concentration and temperature by the equation of state of perfect gases

Mp = ETc,

where M denotes the molecular weight of the salt, and c the mass of salt per unit volume.

Consider the cations contained in a parallelepiped at the place x, whose cross-section is of unit area and whose length is dx. The mechanical force acting on them due to the electric field is - (vc/M) d Vfdx . dx, and the mechanical force on them due to the osmotic pressure is - dp/dx . dx. If u denote the velocity of drift of the cations in a field of unit electric force, the total amount of charge which would be transferred by cations across unit area in unit time under the influence of the electric forces alone would be - (uvc/M) d V/dx ; so, under the influence of both forces, it is

uvcidV ET dc\ M\dx cv dx)

Similarly, if v denote the velocity of drift of the anions in a

• Cf . van't Hoff, Svenska Vet.-Ak. Handlingar xxi (1886), No. 17; Zeitschrift fiir Phys. Chem. i (1887), p. 481.

t As follows from the expression obtained, supra, p. 383.

from Faraday to jf . J . Thomson. 389

unit electric field, the charge transferred across unit area in unit time by the anions is

vvcfdV^ RT dc\ M\dx cv dx)

We have therefore, if the total current be denoted by i, . vc dV RT do

-u+M^-u-v>^Tdx>

or

dV 7 Mdx u-v RT dc ,

• -T- dx = - -— ^ + -- — dx. dx (u + v)vc u + v vc dx

The first term on the right evidently represents the product of the current into the ohmic resistance of the parallelepiped dx, while the second term represents the internal electromotive force of the parallelepiped. It follows that if r denote the specific resistance, we must have

u + v = Mjrvc,

in agreement with Kohlrausch's equation ;* while by integrating the expression for the internal electromotive force of the parallelepiped dx, we obtain for the electromotive force of a cell whose activity depends on the transference of electrolyte between the concentrations c, and cz, the value

u-v RT fl dc .

-- - T- <te> u + v v c dx

u-v RT , c,

or — log-,

u + v v GI

in agreement with the result already obtained.

It may be remarked that although the current arising from a concentration cell which is kept at a constant temperature is capable of performing work, yet this work is provided, not by any diminution in the total internal energy of the cell, but by the abstraction of thermal energy from neighbouring bodies. This indeed (as may be seen by reference to W. Thomson's general

• Cf. P. 374.

390 Conduction in Solutions and Gases,

equation of available energy)* must be the case with any system whose available energy is exactly proportional to the absolute temperature.

The advances which were effected in the last quarter of the nineteenth century in regard to the conduction of electricity through liquids, considerable though these advances were, may be regarded as the natural development of a theory which had long been before the world. It was otherwise with the kindred problem of the conduction of electricity through gases : for although many generations of philosophers had studied the remarkable effects which are presented by the passage of a current through a rarefied gas, it was not until recent times that a satisfactory theory of the phenomena was discovered.

Some of the electricians of the earlier part of the eighteenth century performed experiments in vacuous spaces ; in particular, Hauksbeef in 1705 observed a luminosity when glass is rubbed in rarefied air. But the first investigator of the continuous discharge through a Tarefied gas seems to have been Watson,! who, by means of an electrical machine, sent a current through an exhausted glass tube three feet long and three inches in diameter. " It was," he wrote, " a most delightful spectacle, when the room was darkened, to see the electricity in its passage : to be able to observe not, as in the open air, its brushes or pencils of rays an inch or two in length, but here the coruscations were of the whole length of the tube between the plates, that is to say, thirty-two inches." Its appearance he described as being on different occasions " of a bright silver hue," " resembling very much the most lively coruscations of the aurora borealis," and " forming a continued arch of lambent flame." His theoretical explanation was that the electricity " is seen, without any preternatural force, pushing itself on through the vacuum by its own elasticity, in order to maintain the

• Cf. p. 241.

t Phil. Trans, xxiv (1705), p. 2165. Fra. Hauksbee, Physico- Mechanical Experiments, London, 1709.

I Phil. Trans, xlv (1748), p. 93, xlvii (1752), p. 362.

from Faraday to J . J . Thomson. 391

equilibrium in the machine " — a conception which follows naturally from the combination of Watson's one-fluid theory with the prevalent doctrine of electrical atmospheres.*

A different explanation was put forward by Nollet, who performed electrical experiments in rarefied air at about the same time as Watson,f and saw in them a striking confirmation of his own hypothesis of efflux and afflux of electric matter.J According to Nollet, the particles of the effluent stream collide with those of the affluent stream which is moving in the opposite direction ; and being thus violently shaken, are excited to the point of emitting light.

Almost a century elapsed before anything more was dis- covered regarding the discharge in vacuous spaces. But in 1838 Faraday, § while passing a current from the electrical machine between two brass rods in rarefied air, noticed that the purple haze or stream of light which proceeded from the positive pole stopped short before it arrived at the negative rod. The negative rod, which was itself covered with a con- tinuous glow, was thus separated from the purple column by a narrow dark space: to this, in honour of its discoverer, the name Faraday's dark space has generally been given by subsequent writers.

That vitreous and resinous electricity give rise to different types of discharge had long been known; and indeed, as we have seen,) | it was the study of these differences that led Franklin to identify the electricity of glass with the superfluity of fluid, and the electricity of amber with the deficiency of it. But phenomena of this class are in general much more complex than might be supposed from the appearance which they present at a first examination ; and the value of Faraday's discovery of the negative glow and dark space lay chiefly in the simple and definite character of these features of the discharge, which indicated them as promising subjects for further research. Faraday himself felt the importance of

• Cf. ch. ii. f Nollet, Recherches sur FElectricite, 1749, troisiemediscours. t Cf. p. 40. § Phil. Trans., 1838 ; Exper. Res. i, § 1526. || Cf. p. 44.

392 Conduction in Solutions and Gases,

investigations in this direction. " The results connected with the different conditions of positive and negative discharge," he wrote,* " will have a far greater influence on the philosophy of electrical science than we at present imagine."

Twenty more years, however, passed before another notable advance was made. That a subject so full of promise should progress so slowly may appear strange ; but one reason at any rate is to be found in the incapacity of the air-pumps then in use to rarefy gases to the degree required for effective study of the negative glow. The invention of Geissler's mercurial air-pump in 1855 did much to remove this difficulty; and it was in Geissler's exhausted tubes that Julius Plticker,t of Bonn, studied the discharge three years later.

It had been shown by Sir Humphrey Davy in 1821 J that one form of electric discharge — namely, the arc between carbon poles — is deflected when a magnet is brought near to it. Pliicker now performed a similar experiment with the vacuum discharge, and observed a similar deflexion. But the most interesting of his results were obtained by examining the behaviour of the negative glow in the magnetic field ; when the negative electrode was reduced to a single point, the whole of the negative light became concentrated along the line of magnetic force passing through this point. In other words, the negative glow disposed itself as if it were constituted of flexible chains of iron filings attached at one end to the cathode.

Pliicker noticed that when the cathode was of platinum, small particles were torn off it and deposited on the walls of the glass bulb. " It is most natural," he wrote, " to imagine that the magnetic light is formed by the incandescence of these platinum particles as they are torn from the negative electrode." He likewise observed that during the discharge the walls of

• Exper. Res., § 1523.

| Ann. d. Phys. ciii (1858), pp. 88, 151 ; civ (1858), pp. 113, 622 ; cv (1858), p. 67; cvii (1859), p. 77. Phil. Mag. xvi (1858), pp. 119, 408; xviii (1859), pp. 1, 7.

J Phil. Trans., 1821, p. 425.

from Faraday to J . J. Thomson. 393

the tube, near the cathode, glowed with a phosphorescent light, and remarked that the position of this light was altered when the magnetic field was changed. This led to another discovery ; for in 1869 Plucker's pupil, W. Hittorf,* having placed a solid body between a point-cathode and the phosphorescent light, was surprised to find that a shadow was cast. He rightly inferred from this that the negative glow is formed of rays which proceed from the cathode in straight lines, and which cause the phosphorescence when they strike the walls of the tube.

Hittorf's observation was amplified in 1876 by Eugen Goldstein,f who found that distinct shadows were cast, not only when the cathode was a single point, but also when it formed an extended surface, provided the shadow-throwing object was placed close to it. This clearly showed that the cathode rays (a term now for the first time introduced) are not emitted indiscriminately in all directions, but that each portion of the cathode surface emits rays which are practically confined to a single direction ; and Goldstein found this direction to be normal to the surface. In this respect his discovery established an important distinction between the manner in which cathode rays are emitted from an electrode and that in which light is emitted from an incandescent surface.

The question as to the nature of the cathode rays attracted much attention during the next two decades. In the year following Hittorf's investigation, Cromwell VarleyJ put forward the hypothesis that the rays are composed of " attenuated par- ticles of matter, projected from the negative pole by electricity" ; and that it is in virtue of their negative charges that these particles are influenced by a magnetic field. §

During some years following this, the properties of highly

• Ann. <1. Phys. cxxxvi (1869), pp. 1, 197; translated, Annales de Cbimie, xvi (1869), p. 487.

t Berlin Monatsberichte, 1876, p. 279.

J Proc. Roy. Soc. xix (1871), p. 236.

§ Priestley in 1766 had shown that a current of electri6ed air flows from the points of hodies which are electrified either vitreously or resinously : cf. Priestley's History of Electricity, p. 591.

394 Conduction in Solutions and Gases,

rarefied gases were investigated by Sir William Crookes. Influenced, doubtless, by the ideas which were developed in connexion with his discovery of the radiometer, Crookes,* like Varley, proposed to regard the cathode rays as a molecular torrent : he supposed the molecules of the residual gas, coming into contact with the cathode, to acquire from it a resinous charge, and immediately to fly off normally to the surface, by reason of the mutual repulsion exerted by similarly electrified bodies. Carrying the exhaustion to a higher degree, Crookes was enabled to study a dark space which under such circumstances appears between the cathode and the cathode glow ; and to show that at the highest rarefactions this dark space (which has since been gene- rally known by his name) enlarges until the whole tube is occupied by it. He suggested that the thickness of the dark space may be a measure of the mean length of free path of the molecules. " The extra velocity," he wrote, " with which the molecules rebound from the excited negative pole keeps back the more slowly moving molecules which are advancing towards that pole. The conflict occurs at the boundary of the dark space, where the luminous margin bears witness to the energy of the collisions."f Thus according to Crookes the dark space is dark and the glow bright because there are collisions in the latter and not in the former. The fluorescence or phosphorescence on the walls of the tube he attributed to the impact of the particles on the glass.

Crookes spoke of the cathode rays as an " ultra-gaseous " or " fourth state " of matter. These expressions have led some later writers to ascribe to him the enunciation or prediction of a hypothesis regarding the nature of the particles projected from the cathode, which arose some years afterwards, and which we shall presently describe ; but it is clear from Crookes' memoirs that he conceived the particles of the cathode rays to be ordinary gaseous molecules, carrying electric charges ; and by

• Phil. Trans, clxx (1879), pp. 135, 641 ; Phil. Mag. vii (1879), p. 57. t Phil. Mag. vii (1879), p. 57.

from Faraday to J . J . 71wmson. 395

" a new state of matter " he understood simply a state in which the free path is so long that collisions may be disregarded.

Crookes found that two adjacent pencils of cathode rays appeared to repel each other. At the time this was regarded as a direct confirmation of the hypothesis that the rays are streams of electrically charged particles ; but it was shown later that the deflexion of the rays must be assigned to causes other than mutual repulsion.

How admirably the molecular- torrent theory accounts for the deviation of the cathode rays by a magnetic field was shown by the calculations of Eduard Riecke in 1881.* If the axis of z be taken parallel to the magnetic force Ht the equations of motion of a particle of mass ra, charge e, and velocity (u, v, w)

are

mdu/dt = evH, mdvjdt = - euH, mdw/dt = 0.

The last equation shows that the component of velocity of the particle parallel to the magnetic force is constant; the other equations give

u = A sin (eHt/m), v = A cos (eHi/m),

showing that the projection of the path on a plane at right angles to the magnetic force is a circle. Thus, in a magnetic field the particles of the molecular torrent describe spiral paths whose axes are the lines of magnetic force.