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In this paper the theory of chemical equilibrium is applied to a mixture of paraffins C n H 2 n +2 , and it is shown that the equilibrium composition of the vapour and liquid phases can be approximately calculated at any given tempera­ture and pressure. Such a mixture has two independent constituents so that according to the phase rule the composition of the phases, whenever there are two, will be determined by two independent variables such as the temperature and pressure. Consider the reaction C n -1 H 2( n -1)+2 + C n +1H 2( n -1)+2 = 2C n H 2 n +2 .

The velocity ( v ) of an electron in a gas, due to an electric field of strength X, is given approximately by theoretical formula v = 0·815 X e λ/ m V. where e denotes the charge on the electron, λ its mean free path, m its mass, and V its mean velocity of thermal agitation. Townsend has made many determinations of this velocity v , and also of V, in several gases at different pressures ( p ) and finds that v is a function of X/ p , and that the values of λ given by the above equation are of the same order, in most cases, as those deduced from the viscosity by means of the kinetic theory of gases. The equation v = 0·815X e λ/ m V is obtained by assuming that there is no persistence of velocities when electrons collide with gas molecules.

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Thermodynamical theory of electron emission from metals.---By means of a reversible cycle similar to that first used by O. W. Richardson, an accurate expression for the thermionic emission is obtained and it is shown that the constant in the equation for the vapor pressure of the electrons is equal to the chemical constant for electron gas. It is shown that if all the internal heat of evaporation of the electrons is due to electrical forces then Richardson's original equation $I=A{\ensuremath{\theta}}^{\frac{1}{2}}{\ensuremath{\epsilon}}^{\frac{\ensuremath{-}b}{\ensuremath{\theta}}}$ must be correct and the specific heat of the negative electricity in the metal must be the same as for a monatomic gas at constant volume, but that if this specific heat is small, as is known to be the case, then all the internal heat of evaporation cannot be due to electrical forces and Richardson's second equation $I=A{\ensuremath{\theta}}^{2}{\ensuremath{\epsilon}}^{\frac{\ensuremath{-}b}{\ensuremath{\theta}}}$ is a better first approximation to the exact relation. It is shown that the equation $L=\frac{R{\ensuremath{\theta}}_{2}d(logp)}{d\ensuremath{\theta}}$ where $L$ is the heat of evaporation of a liquid at pressure $p$ and temperature $\ensuremath{\theta}$ is not exactly true for the evaporation of electrons. It is pointed out that the thermodynamical theory of evaporation was applied to electron emission by the writer in 1903 and that O. W. Richardson in 1912, M. V. Laue in 1918, R. C. Tolman in 1921 and S. Dushman in 1923 have made further applications of it to the same question.Quantum theory of the chemical constant.---A simple way of calculating the size of the region element in the state space for a monatomic gas is given which makes it equal to $N{h}^{3}$ where $N$ is the number of molecules in the gas and $h$ Planck's constant. This gives the same expression for the chemical constant as that found by Sackur.

In a previous paper the atomic weights of several light elements were calculated from nuclear reaction energies using the known values of the atomic weights of He 4 and H 1 . In the present paper it is shown that the atomic weights can be obtained from the reaction energies without making any use of atomic weights determined by other methods. Any atom may be supposed formed by the combination of neutrons and hydrogen atoms according to the reaction equation z 1 H 1 + ( w - z ) 0 n 1 = z A w + z E w , where z E w denotes the energy of formation of the atom z A w . If we consider N different elements including 1 H 1 and 0 n 1 then we have N — 2 energies of formation. If the energies of formation are known then the energy of any nuclear reaction may be calculated.

(1903). XLII. A determination of the charge on the ions produced in air by Rontgen rays. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 5, No. 28, pp. 429-441.

The effect of hydrogen on the discharge of negative electricity from hot platinum was examined by the writer in 1903 (‘Phil. Trans.,’ A, 352, vol. 202, 1903); it was found to produce a very large increase in the current carried by the discharge. At pressures below 0·1 millim. of mercury the leak was found to increase with the pressure and to fall when the pressure was reduced. The experiments in the paper just referred to were all done with nearly new platinum wires which had not been heated in the gas for any great length of time, because it was known that long continued heating caused the wire to disintegrate, its surface becoming covered with a network of cracks. The present paper contains an account of a series of experiments in which wires were heated for long periods in hydrogen, so that any gradual changes in the effect of the hydrogen could be observed. It appears that continued heating in hydrogen alters the character of the effects observed, so that the behaviour of an old wire may be very different from that of a new one. In the previous paper I suggested that the effect of hydrogen was due to the presence of hydrogen in the surface layer of the platinum, and this view appeared to be supported by the facts. Professor O. W. Richardson (‘Phil. Trans.,’ A, 413, vol. 207, 1906) puts forward a different theory, viz., that the hydrogen alters the state of the platinum, so that the effect may remain even after the removal of all the hydrogen.

It has been suggested that the writer should discuss the need for the atomic energy levels which he has recently proposed and their relation to previous work more fully. The summary way in which the theory was presented was partly due to the first papers on the subject having been returned, so that a later paper, intended to appear after the earlier papers, was rather unexpectedly published first. A brief preliminary account had been published in the ‘Physical Review,’ so when the earlier papers were rewritten much of the earlier work, showing how the theory arose, was omitted. According to Gamow’s theory, the gamma ray energies are equal to differences between the energy levels of an alpha particle in the nucleus, and these alpha particle levels are equal to the differences between the higher disintegration energies and the lowest or normal disintegration energy. Thus on Gamow’s theory the gamma and alpha energies depend only on the nucleus and are in no way related to the electronic energy levels. There are, however, several reasons for believing that the gamma and alpha energies, contrary to Gamow’s view, involve electronic energies. These reasons have been mentioned in previous papers, but it seems to be worth while to bring them together here.

In a previous paper on "Chemical Equilibrium in a Mixture of Paraffins" the composition of the mixture in equilibrium at any temperature and pressure was calculated on the assumption that only paraffins C n H 2n+2 were present. The condition for equilibrium among the members of any homologous series in the vapour was shown to be p n = p 1 f n-1 , where p n denotes the partial pressure of the n th member of the series and f is a quantity less than unity which is approximately independent of n . In the present paper unsaturated hydrocarbons containing one or more double bonds as well as paraffins will be supposed present in the mixture. The homologous series to be considered are therefore the paraffins C n H 2n+2 , the olefines C n H 2n with one double bond, the diolefines C n H 2n-2 with two double bonds, and other series C n H 2n-4 , C n H 2n-6 , C n H 2n-8 , ..., containing 3, 4, 5,... double bonds.

An Electromagnetic Theory of Gravitation.---An electric system in a medium whose specific inductive capacity $k$ varies from point to point tends to move in the direction of increasing $k$. It is suggested that if we assume the specific inductive capacity of the ether to vary near matter, gravitation may be explained as a result of this tendency. In a medium in which at a distance $r$ from a mass $m$, $k=\mathrm{I}+\frac{m}{r}$, it is shown that a rigid electrostatic system would be acted on by a force directed toward $m$ and equal to $\frac{m{m}^{\ensuremath{'}}}{{r}^{2}}$, where ${m}^{\ensuremath{'}}$ in the electromagnetic mass of the system. But in order to explain the observed deflection of light by the sun we must have $k=\mathrm{I}+\frac{2m}{r}$; and this will not give the force $\frac{m{m}^{\ensuremath{'}}}{{r}^{2}}$ unless the system contracts in the ratio of $\mathrm{I}:\mathrm{I}\ensuremath{-}\frac{m}{r}$. A physical explanation of this assumed contraction is suggested. If the system with the mass ${m}^{\ensuremath{'}}$ is also supposed to modify $k$, it is necessary to take into account the energy changes in $m$ and in the ether. The effect of gravitation on the frequency of the light emitted by an atom, which was predicted by Einstein, can be easily deduced from the present theory.

It is found that the spherical shell nuclear model has new energy levels due to the interaction of the vibrations and the rotation. Each vibration level has a series of equally spaced levels belonging to it. The levels of aluminium 28 and silicon 28 are compared with the values predicted by the theory and good agreement is found.

Of the many suggestions which have been made as to the origin of the earth’s magnetic field, perhaps the most promising is that it may be due to a slight modification of the laws of electrodynamics from the commonly accepted form. Electrically neutral matter is believed to consist of an intimate mixture of enormous amounts of positive and negative electricities, the electric and magnetic effects of which are usually supposed to balance each other. If the balance were not quite exact then small residual effects would be expected, among which gravitation and the earth’s magnetic field might be included. On such an hypothesis we might expect moving matter to produce a magnetic field similar to the field due to moving electricity, and we should expect some relation between the magnetic field due to moving matter and its gravitational action.

The following paper contains an account of a series of experiments on the perception of direction of sound which were undertaken with the object of investigating the nature of the influence of phase differences between the vibrations at the two ears. Lord Rayleigh has shown that such differences help to determine the apparent direction of the sound, the sound appearing to be on the side at which the phase is the more advanced. Professor More arrived at a similar conclusion to Lord Rayleigh by experiments of a different character. The following paper also contains a theory of the influence of phase differences which appears to offer a possible explanation of the observed effects. Most of our experiments have been done with an apparatus similar in principle to Professor More’s, but permitting of a continuous variation of the difference of phase. The apparatus consisted of a brass tube, AB (fig. 1), about 250 cm. long and 2∙5 cm. in diameter, with a short T-piece soldered on to it at its middle point. This tube could slide freely in two slightly larger brass tubes, CD and EF, which were supported horizontally a definite distance apart. From the ends of CD and EF wide tubes were led to caps fitting on to the ears of the observer. The tubes were made up of lengths of glass tubing joined together by pieces of wide indiarubber tubing, and the two sides of the apparatus were made as symmetrical as possible. The ear caps consisted of wooden discs with annular soft pads round them which could be pressed against the head. The caps were supported on retort stands clamped to a table, and were adjusted as symmetrically as possible.

The scattering of β -rays by thin sheets of matter has been the subject of a number of experimental and theoretical investigations in recent years. J. A. Crowther and B. F. Schonland give a good summary of the principal results so far obtained, together with an account of a new series of measurements. Crowther and Schonland regard their experiments as decisively in favour of the theory of “single scattering,” which was shown by Rutherford to account for the scattering of α -rays by thin plates in a thoroughly satisfactory way. In the case of α -rays the fraction of the rays scattered through considerable angles is very small, and it is on this that the success of the theory depends. In the case of β -rays the fraction scattered is very much larger, and it is difficult to believe that “multiple scattering” can be neglected.

It was shown by A. A. Noyes and the writer that the equilibrium constants for the reactions M = M + + e , where M denotes an atom of an alkali metal and e an electron, can be deduced from measurements of the electrical conductivity of flames, at 2000° K., containing the metal, and that the values so obtained agree approximately with those calculated by means of Saha’s well-known theory. This conclusion has since been fully confirmed by B. T. Barnes and by J. A. J. Bennett. Bennett found that the equilibrium constants deduced from his measurements agreed with Saha’s theory at temperatures near 2000° K., but that at lower temperatures the theoretical values were smaller than those given by the experiments.

The colour imparted to flames by the salts of an alkali metal is generally considered to be due to the metal existing in the state of incandescent vapour, but there does not appear to be any settled opinion as to the process by which the metal is set free from its salts. It is frequently assumed that the high temperature reigning in the flame dissociates the salt. There is, however, little, if any, independent evidence in favour of this view. Another explanation ascribes the liberation of metal to chemical decomposition. Thus, in the case of sodium chloride introduced into the flame of a Bunsen burner consuming coal-gas, it would be supposed that in the first instance the water vapour present would act in accordance with the following equation :— NaCl + H 2 O = NaHO + HC1. The sodium hydrate (or possibly oxide) so produced would then be deprived of its oxygen by reducing gases (hydrogen, hydrocarbon, carbon monoxide) existing in the flame. A somewhat similar explanation would have to be applied to the flames of hydrogen, carbon monoxide, and cyanogen, though, in the case of the last two gases, the steps of the processes are still more hypothetical.

It has been shown in previous papers that the nuclei of the radioactive atoms probably have equally spaced energy levels so that the energies of the rays emitted by the nucleus are equal to multiples of a constant q = 3·85 × 10 5 electron volts. Several light elements also appear to have nuclear levels with differences equal to q within the rather large limits of error. We should therefore expect the energies set free in nuclear reactions to be equal to multiples of q . The electronic energies of the light elements are small compared with q , so that the observed energies should be multiples of q . The energies of considerable number of nuclear reactions have been measured, but only a few with sufficient accuracy to show whether they are or are not equal to multiples of q . The energies of the 17 nuclear reactions given in a recent paper by Oliphant, Kempton, and Rutherford are given in Table I. The energies are in atomic weight units equal to 9·315 ×10 8 electron volts. Some of the values have been increased slightly since they were not quite accurately calculated from the energies in electron volts.

In previous papers the writer has considered chemical equilibrium in mixtures of paraffins and unsaturated hydrocarbons. The theoretical equilibrium compositions at different pressures and temperatures were compared with results obtained in commercial cracking operations and it was concluded that the theory represented the main features of such cracking. The hypothetical oils considered were supposed to contain only paraffins and unsaturated hydrocarbons and so differed from real oils which also contain naphthenes or cycloparaffins and aromatic hydrocarbons. The hypothetical oils therefore contained a higher percentage of hydrogen than real oils. For example a hypothetical oil of composition CH 2·1 was found to correspond with heavy crude or fuel oil. The percentage of hydrogen in an oil of composition CH 2·1 is 14·9 while heavy crude oils usually do not contain more than 12 or 13 per cent. of hydrogen. The percentage of hydrogen in naphthenes C n H 2n is 14·3 so that hypothetical oils containing naphthenes will contain less hydrogen than paraffins but will still contain more hydrogen than actual oils.

In cracking petroleum the oil is kept at nearly constant temperature and pressure for a certain time and is then separated by fractional distillation into gas, gasoline and heavier fractions. Usually the oil is passed, through a long pipe heated in a furnace, into a reaction chamber from which the cracked oil is withdrawn continuously. The fraction of the oil converted into gasoline depends mainly on the pressure and the temperature in the reaction chamber, the time taken to pass through the chamber and on the nature of the oil.

In a recent paper on the electrical conductivity and luminosity of flames containing salt vapours, by Professor A. Smithells, Mr. H. M. Dawson, and the writer, the similarity between the conductivity of flames and that of gases exposed to Rontgen rays was pointed out, and it was shown that the relation of the current between two electrodes in the flame to the potential difference between them could be represented by the formulae I - i = k 2 i 2/E2, C = i + k 1 E, where C = the current, E = the P. D. between the electrodes. I, k 1, k 2 are constants, and i is defined by the second equation. When E is large, these equations become C = I + k 1 E, and if k 1 = 0, then they reduce to I - C = k 2 C 2/E2, which represents the relation between the current and P. D. for the conductivity of Rontgenised gases. (See a paper by J. J. Thomson and E. Rutherford, 'Phil. Mag.,' Nov., 1896.) The experiments described in the present paper were undertaken with the object of following up the analogy between the conductivity of salt vapours and that of Rontgenised gases, and especially of getting some information about the velocities of the ions in the flame itself.

The following paper contains an account of a series of experiments on the motion of an electric discharge in a magnetic field perpendicular to the direction of the discharge current. The fact that the discharge moves in a magnetic field like a flexible conductor carrying a current was discovered long ago, and De La Rive showed that it could be made to rotate continuously round one pole of a magnet placed inside the vacuum tube. The apparatus used in the present experiments was similar in principle to De La Rive’s, but was arranged so that fairly exact measurements of the various quantities concerned could be obtained. Fig. 1 shows a vertical section of the vacuum tube and magnet used. The tube consisted of two concentric glass tubes cemented with sealing wax into aluminium discs. The discs had grooves turned in them to fit the glass tubes, and the part of the discs between the tubes projected a few millimetres, so that there was no danger of the discharge passing through the sealing wax. Polished platinum rings were fixed on to the aluminium discs between the glass tubes, and these formed the electrodes between which the discharge was passed. The ends of the tubes were carefully ground truly perpendicular to their axes, and the two platinum rings were accurately parallel. To keep the electrodes cool, a ring of narrow brass tubing was soldered on to the back of each disc and a stream of water was kept flowing through these whenever a discharge was passed. This arrangement enabled comparatively large currents to be used without softening the sealing wax. A narrow copper tube was soldered into one of the discs and communicated with the interior of the vacuum tube through a fine hole. The tube was connected by a mercury sealed joint with a glass tube leading to a bulb containing pure phosphorus pentoxide, a Töpler pump, and a McLeod gauge.

When the vapour of an alkali salt is present in a Bunsen flame the vapour becomes luminous and also increases the electrical conductivity of the flame. The fraction of the salt molecules which are luminous is probably very small, and unless the concentration of the salt vapour is very small the fraction of the salt molecules which are charged electrically, or are ionised, is also very small. Any particular salt molecule enters the flame at the bottom and moves up the flame with the velocity of the flame gases which is of the order of 200 cm. per second. The molecule is therefore in the flame for only a small fraction of a second, but this time interval is probably long enough for a state of equilibrium to be established between the several states in which the molecules can exist. For example, in the case of sodium chloride there is probably an equilibrium between NaCl, NaOH, Na 2 O, Na, H 2 O, HCL, and possibly other bodies such as CO, CO 2 , and Na 2 CO 3 .

In a previous paper by one of us it was shown that when an insulator of specific inductive capacity K rotates in a magnetic field there is an electro­motive force induced in it equal to that in a conductor multiplied by 1 — K -1 . The object of the experiments described below was to measure the induced electromotive force in a magnetic insulator rotating in a magnetic field parallel to the axis of rotation. According to the theory based on the “principle of relativity” this induced electromotive force should be equal to that in a conductor multiplied by 1 — ( μ K) -1 , where μ is the magnetic permeability of the insulator, whereas on the theory of H. A. Lorentz and Larmor the appropriate multiplier appears to be 1 — K -1 , as for a non-magnetic insulator.

The view adopted in the following paper is that the radiation from a black body is an irregular disturbance subject to statistical laws. This view is, I believe, that now generally held. It is shown that these laws can be deduced from the observed distribution of energy in the spectrum and that they enable the general character of the disturbance to be described. At any point in an actual spectrum of the radiation we have a large number of simple harmonic vibrations of arbitrary phases and various amplitudes. The radiation may be regarded as the sum of all the simple vibrations in the spectrum. The component vibrations may be regarded as continually varying, but the distribution of energy in the spectrum, when averaged over a short interval, remains constant.

The following paper contains an account of some measurements of the change in the conductivity of a Bunsen flame produced by a magnetic field the direction of which was perpendicular to the current through the flame and to the motion of the flame gases. The velocity of the negative ions in the flame has been calculated from the results, and the value of the velocity obtained agrees approximately with that found by other methods. The flame used consisted of a row of 12 small Bunsen flames burning from quartz tubes. The centres of the tubes were 1 cm. apart, and each tube had an internal diameter of 0.5 cm. Each flame was about 6 cm. high, and the adjacent flames touched each other, so that a flame about 14 cm. long, 6 cm. high, and about 2 cm. thick was obtained.

Conductivity of salted flames for high frequency currents.---Theory. Expressions are developed for the capacity and series resistance of a parallel plate condenser in a flame, which enable certain constants to be computed from the measurements of Bryan given in the preceding paper. Calculated density of positive ions increases from.03 e.s.u. in the unsalted flame to 1.5 e.s.u. for the flame sprayed with a solution of 10 gm/liter ${\mathrm{K}}_{2}$C${\mathrm{O}}_{3}$. For the smaller concentration, it varies about as the square root of the potassium present, as was to be expected. The variation with frequency and electric field is slight. Calculated mobility of electrons is found to diminish from 200 to 60 m/sec. per volt/cm as r.m.s. field increases from 9 to 64 volts/cm, in good agreement with values found by Loeb for electrons in pure nitrogen at room temperatures. It decreases markedly as the concentration of potassium increases.

In a recent paper on the electrical conductivity and luminosity of flames containing salt vapours, by Professor A. Smithells, Mr. H. M. Dawson, and the writer, the similarity between the conductivity of flames and that of gases exposed to Röntgen rays was pointed out, and it was shown that the relation of the current between two electrodes in the flame to the potential difference between them could be represented by the formulæ I - i = k 2 i 2 /E 2 , C = i + k 1 E, where C = the current, E = the P. D. between the electrodes. I, k 1 , k 2 are constants, and i is defined by the second equation. When E is large, these equations become C = I + k 1 E, and if k 1 = 0, then they reduce to I - C = k 2 C 2 /E 2 , which represents the relation between the current and P. D. for the conductivity of Röntgenised gases. (See a paper by J. J. Thomson and E. Rutherford, 'Phil. Mag.,' Nov., 1896.) The experiments described in the present paper were undertaken with the object of following up the analogy between the conductivity of salt vapours and that of Röntgenised gases, and especially of getting some information about the velocities of the ions in the flame itself.

The experiments described in this paper were undertaken with the object of obtaining information on the variation of the conductivity of air and of salt vapours with change of temperature, and on the maximum current which a definite amount of salt in the form of vapour can carry. They are a continuation of the two researches on the same subject published in 1899. In the paper “On the Electrical Conductivity and Luminosity of Flames” some observations on the variation of the conductivity with the temperature at different heights in the flame are given. They indicate a rapid increase in the conductivity with rise of temperature.

In a previous paper it was shown that the energies of nuclear reactions are multiples of q = 0·000415 in atomic weight units and that the atomic weights of the light elements may be supposed equal to N (1 + b ) sq , where N and s are integer and b is a small quantity the same for all elements. In the reaction equations the terms N (1 + b ) cancel out so that the reaction energies are given by nq = Σ sq . Thus the equation 4 Be 9 + 1 H 1 = 4 Be 8 + 1 H 2 + nq gives 9 (1 + b ) + 33 q + 1 + b + 19 q = 8 (1 + b ) + 17 q + 2 (1 + b ) + 34 q + nq , so that 33 q + 19 q = 17 q + 34 q + nq which gives 52 = 51 + n , or n = 1. The number of independent reaction equations is two less than the number of elements involved so that two of the values of the energy integer s can be elected. In the previous paper the values of s for 2 He 4 1 H 1 were taken to be 8 and 19 respectively and the values of s for the other elements were calculated by means of the reaction equations.

No general consensus of opinion appears to exist as to the mode by which the metal of an alkali salt is liberated when the salt is vaporised in a flame. By some the liberation is supposed to be effected thermally by chemical dissociation; others suppose that the salt is converted into hydrate or oxide, and then reduced by the flame gases.

It was shown by Faraday in 1831 that an electromotive force is induced in a conductor moving in a magnetic field so as to cut the lines of magnetic force. The object of the experiments described in the present paper was to see if a similar effect exists in a dielectric when it moves in a magnetic field, and to measure the amount of the effect if it were found to exist. According to Maxwell’s electrodynamic theory, as developed by H. A. Lorentz and by Larmor, such an electromotive force should be produced in a dielectric, and should be equal to the electromotive force in a conductor multiplied by the factor 1 — K -1 , where K is the specific inductive capacity of the dielectric.

The following paper contains an account of a series of experiments on the variation of the capacity of condensers having solid dielectrics with the potential difference and the time. The influence of temperature on the results has also been investigated. It is not proposed to give any detailed account of previous work on this subject here. A very full list of papers is given in a paper by Schweidler entitled “Studien liber die Anomalien im Yerhalten der Dielektrika,” ‘Ann. der Physik,’ No. 14, 1907, p. 711. Let A and B be two guard ring parallel plate condensers, the dielectric in A being air and in B any insulator. Let the two guard rings be permanently connected to earth, and the two small plates permanently connected together. Suppose initially the large plates and small plates are connected to earth, the small plates then disconnected, and then the large plate of the condenser B raised to a potential + V and that of A to a potential — V. After a time t , measured from the instant at which the plates were charged, the total charge on the small plates will be given by the equation (V + e ) C -(V - e ) C' + e C" = q, where C is the capacity of the condenser A, C' that of B, C" the capacity of the backs of the small plates and their connecting wire, and e the potential of the small plates. The charge q will be very small if the dielectric in B is a good insulator, and we may put it equal to k Vc' t , where k is a constant approximately.

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According to the electron theory of the electrical and thermal properties of metals, these bodies contain a large number of negative electrons, which move about between the metallic atoms like the molecules of a gas. This theory explains satisfactorily several of the fundamental facts, such as the emission of electrons from hot metals, Ohm’s law, and Wiedemann and Franz’s law, but fails in its simple form to account for the different values of the Hall effect and other phenomena. More elaborate forms of the electron theory, based on the quantum hypothesis, enable some of these difficulties to be removed.

The following paper contains an account of the results obtained in a series of experiments on the loss of electricity from hot platinum in several gases at various pressures. I shall begin by giving a brief account of some of the results obtained by previous workers on this subject, confining myself to those results which appear to bear more or less directly on the present investigation. Further information on the results of the earlier investigations may be found in Wiedemann’s ‘Elektrizität,’ vol. 4, in J. J. Thomson’s ‘Recent Researches,’ in Stark’s ‘Die Elektrizitat in Gasen,’ and in the papers referred to. Elster and Geitel (‘Wied. Ann.,’ vol 37, p. 315, 1889) found that hot platinum, in air and oxygen, produces positive electrification of the surrounding gas and bodies immersed in it, except at low pressures, when negative electrification is obtained. In hydrogen they found the electrification is always negative.

Theory of Reflection of X-rays from a Point Source, by a Perfect Crystal.\char22{}The derivation of the expression for the total reflected energy as obtained by other physicists, is given in simpler form. It is shown that the reflected rays are parallel in the plane of incidence but diverge in the perpendicular plane. Making the simplifying assumption that no ray is reflected more than once from any plane of atoms and that the absorption by the crystal is negligible, expressions for the intensity at any point in the reflected beam are derived. It is shown that interference fringes are to be expected whose distance apart under ordinary circumstances may be of the order of 4 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$ cm. The error due to the above mentioned simplifying assumptions can be corrected by multiplying by the appropriate exponential factor.

The light from Bunsen flames containing sodium and other metals was investigated by Gouy in 1879. He found that the intensity of the light is a function of the amount of sodium per square centimetre in the flame and that this function is approximately proportional to the square root of the amount of sodium per square centimetre when this is not extremely small. If d denotes the thickness of the flame, ρ the amount of sodium per unit volume in it and I the light intensity emitted in a direction perpendicular to the flame surface then Gouy’s results show that I = Aρ d /√ ρ d + B where A and B are constants. When ρ d is not very small the constant B can be neglected and І = A√ρ d . The following values of I and ρ d for a sodium flame, both in arbitrary units, were given by Gouy.

The following paper contains a description of some experiments made with the object of detecting possible effects due to electric and magnetic fields and moving matter on the velocity of propagation of light in glass. The results obtained were negative, but it seems worth while to publish a short account of the experiments. The optical part of the apparatus is a simple form of interferometer which proved very easy and convenient to work with. It consists of a square glass frame made up of glass bars of square cross-section cemented together with canada balsam. Three of the corners are cut off at 45°, as shown in the figure, and the fourth corner contains a half silvered surface FF. Light entering in the direction of the arrow A is divided into two beams by the silver film, which pass round the frame in opposite directions, being totally reflected at the cut-off corners. Half of each beam emerges in the direction of the arrow B, and the two beams at B are in a condition to interfere with each other.

The experiments described in this paper were undertaken with the object of obtaining information on the variation of the conductivity of air and of salt vapours with change of temperature, and on the maximum current which a definite amount of salt in the form of vapour can carry. They are a continuation of the two researches on the same subject published in 1899. In the paper on the Electrical Conductivity and Luminosity of Flames ( loc. cit .) some observations on the variation of the conductivity with the temperature at different heights in the flame are given. They indicate a rapid increase in the conductivity with rise of temperature.

It was shown by Faraday in 1831 that an electromotive force is induced in a conductor moving in a magnetic field so as to cut the lines of magnetic force. The object of the experiments described in the present paper was to see if a similar effect exists in a dielectric when it moves in a magnetic field, and to measure the amount of the effect if it were found to exist. According to Maxwell’s electrodynamic theory, as developed by H. A. Lorentz and by Larmor, such an electromotive force should be produced in a dielectric, and should be equal to the electromotive force in a conductor multiplied by the factor 1 — K-1, where K is the specific inductive capacity of the dielectric.

(1) THE property of matter which has always been regarded as most fundamental is “inertia.” This property is adopted as the measure of quantity of matter in dynamics, and the nearest approach to a complete explanation of a physical phenomenon is generally supposed to have been reached when the phenomenon has been shown to be due to the motion of particles possessing inertia. We may say, in fact, that the tendency of nineteenth century physics was to give a purely dynamical explanation of everything. A striking example of this tendency is Maxwell's dynamical theory of the electromagnetic field. (1) Mathematische Einfuhrung in die Elektronentheorie. By Dr. A. H. Bucherer. Pp. 148. (Leipzig and Berlin: Teubner, 1904.) Price 3.20 marks. (2) Experimentelle Elektrizitatslehre. By Dr. H. Starke. Pp. xiv + 422. (Leipzig and Berlin: Teubner, 1904.) Price 6 marks. (3) Leitfaden det Physik fur die oberen Klassen der Realanstalten. By Dr. F. Bremer. Pp. viii + 294. (Leipzig and Berlin: Teubner, 1904.) Price 3.20 marks.

IN February, 1896, M. Henri Becquerel found that uranium salts emit rays capable of affecting a photographic plate and of penetrating black paper and other bodies opaque to ordinary light. In the eight years which have elapsed since, a startling series of discoveries of extraordinary interest to the physicist and chemist has rewarded those experimental investigators who followed up the clue given by Becquerel's observation just mentioned. As the result of their labours, a new branch of physical chemistry has been created which already possesses a bulky literature, growing with ever-increasing velocity. The following are approximately the number of papers on radio-activity published in scientific journals for each year since Becquerel's original discovery:—1896, 7; 1897, 6; 1898, 7; 1899, 18; 1900, 39; 1901, 36; 1902, 41; 1903, 90. Thus at present the literature of the subject comprises several hundred papers, and new papers are appearing at the rate of several per week. Radio-activity. By Prof. E. Rutherford Pp. viii + 399. (Cambridge: University Press, 1904.) Price 10s. 6d. net. Radio-activity. By F. Soddy (The Electrician Printing and Publishing Co., 1904.) Radium. By L. A. Levy H. G. Willis. (London: Percival Marshall and Co., 1904.)

In a recent paperjon “The Effect of Hydrogen on the Discharge of Negative Electricity from Hot Platinum,” I gave a calculation of the thickness of the double layer on the surface and of the number of free electrons inside the platinum. Professor 0. W. Richardson has pointed out to me that two terms in one of the equations, one of which I discarded as being small compared with the other, are really of the same order of magnitude. The results of the calculation are consequently wrong, and the estimate of the number of free electrons is considerably too high. The difficulty mentioned in the paper, that the energy required to raise the temperature of the electrons is apparently greater than that required to raise the temperature of the platinum, consequently disappears. V = – β log (1 + 4 π σ 2 / p 0 β e – 4 π σ t / β + p 0 β /16 π σ 2 e + 4 π σ t / β + + β log (1 + 4 π σ 2 / p 0 β + p 0 β /16 π σ 2

THE α rays emitted by radium and other radio-active substances have been shown by Rutherford (“Radioactivity,” pp. 115–141) to consist of positively charged particles for which e/m=6×103. They are rapidly absorbed by gases and solids, the absorption coefficient being approximately proportional to the density of the absorbing medium. The value of the absorption coefficient in air divided by the density varies between 350 and 1300 for different types of α rays. The velocity of these rays is about 1/10th to 1/20th that of light.