Showing papers in "Physical Review in 1924"

On the Resistance Experienced by Spheres in their Motion through Gases

Abstract: Kinetic theory of the resistance to a sphere moving through a gas.— (1) Droplets small in comparison with the mean free path. The high degree of accuracy achieved in the experimental determination of the law of motions of droplets through gases, makes a careful theoretical examination of the problem desirable. Assuming the usual Maxwellian distribution of velocities in the gas, the force exerted by the impinging molecules is found to be M where M=(4π/3) Nma2cmV, N, m, a, and cm being the number per unit volume, mass, radius, and mean speed of the molecules and V the speed of the droplet. The force exerted by the molecules leaving the surface depends on how they leave. (1) For uniform evaporation from the whole surface, the force is -M; (2) for specular reflection of all the impinging molecules, -M; (3) for diffuse reflection with unchanged distribution of velocities, -(13/9)M; (4) for diffuse reflection with the Maxwell distribution corresponding to the effective temperature of the part of the surface they come from, -(1+9π/64)M, for a non-conducting droplet (4a), and -(1+π/8)M, for a perfectly conducting droplet (4b). Cases (1) and (2) can not be distinguished experimentally, but (2) is more probable physically. The experimental values agree with 1/10 specular reflection, case (2), and 9/10 diffuse reflection, case (4a) or (4b). For large values of l/a, the droplet behaves like a perfect conductor, case (4b). (2) Comparatively large spheres. The distribution of velocities is no longer Maxwellian because of the hydrodynamic stresses which can not now be neglected. The new law is derived (Eq. 47). The conditions at the surface of the sphere are discussed and it is shown that the diffusely reflected molecules have a Maxwellian distribution corresponding to the temperature and density of the gas, just as though they were reflected with conservation of velocity (specularly). The assumptions of Bassett are theoretically justified and a complete confirmation is obtained for the correction factor for Stokes' law [1+0.7004 (2/s-1) (l/a)] on which Millikan's conclusions are based, especially as to the percentage of specular reflection. (3) Rotating spheres are also considered in an appendix, and the values of the resistance are derived for various cases.

A Mathematical Treatment of the Electric Conductivity and Capacity of Disperse Systems I. The Electric Conductivity of a Suspension of Homogeneous Spheroids

Abstract: Conductivity measurements may give values for (1) the specific conductivity, (2) the concentration or (3) eccentricity of form of the suspended particles of suspensions such as biological tissues, blood and cream. Mathematical theory. The following relation is derived: $\frac{(\frac{k}{{k}_{1}\ensuremath{-}1})}{(\frac{k}{{k}_{1}+x})}=\frac{\ensuremath{\rho}(\frac{{k}_{2}}{{k}_{1}\ensuremath{-}1})}{(\frac{{k}_{2}}{{k}_{1}+x})}$, where $k$, ${k}_{1}$ and ${k}_{2}$ are the specific conductivities of the suspension, the suspending medium and the suspended spheroids, $\ensuremath{\rho}$ is the volume concentration of the suspended spheroids, and $x$ is a function of the ratio $\frac{{k}_{2}}{{k}_{1}}$ and the ratio $\frac{a}{b}$ of the axis of symmetry of the spheroids to the other axis. For the case of spheres, $x=2$ and the formula reduces to that of Lorentz-Lorentz and Clausius-Mossotti. Curves are given showing the variation of $x$ with $\frac{{k}_{2}}{{k}_{1}}$ for various values of $\frac{a}{b}$. Comparison with experimental data of Stewart for the conductivity of the blood of a dog (${k}_{2}=0$, $\frac{a}{b}=\frac{1}{4.25}$, $x=1.05$) shows excellent agreement for concentration from 10 to 90 per cent. Also the observations of Oker-Blom for two suspensions of sand in salted gelatine, give in each case constant values of $x$ for various concentrations.

Currents Limited by Space Charge between Concentric Spheres

Abstract: Limiting current between concentric spheres; calculation of the function $\ensuremath{\alpha}=f(\frac{r}{{r}_{0}})$ in the space charge equation $i=(\frac{4\sqrt{2}}{9})\frac{\sqrt{(\frac{e}{m})}{V}^{\frac{3}{2}}}{{\ensuremath{\alpha}}^{2}}$.---The coefficients of the first six terms of a series for $\ensuremath{\alpha}$ were determined, and ${\ensuremath{\alpha}}^{2}$ calculated from this series. The results were checked by an integration method which was also used to calculate values in the region where the series failed. For an emitter of radius ${r}_{0}$ inside a collector of radius $r$, values of ${\ensuremath{\alpha}}^{2}$ when $log(\frac{r}{{r}_{0}})g6.4$ are given by the equation $\frac{1}{2}{\ensuremath{\alpha}}^{2}=0.112 log (\frac{logr}{{r}_{0}})+\frac{1}{3}log (\frac{r}{{r}_{0}})+0.152.$ Where the collector is the inside sphere, values of ${\ensuremath{\alpha}}^{2}$ for $\frac{{r}_{0}}{r}g9$ are given by the equation ${(\frac{1}{2}{\ensuremath{\alpha}}^{2})}^{\frac{2}{3}}=1.11 (\frac{{r}_{0}}{r})\ensuremath{-}1.64$. It is shown that when the collector is the inside sphere the potential distribution near the collector is unaltered if the emitter is replaced by a non-emitting sphere with a diameter.677 times the original diameter.Limiting current between coaxial cylinders and between concentric spheres.---Equations are derived for the current in terms of the radius of curvature of the emitter. It is shown that at a surface in space four-fifths of the distance from the emitter to the collector the current density is independent of the radius of curvature when $\frac{r}{{r}_{0}} or \frac{{r}_{0}}{r}l2$; and in the case of coaxial cylinders with the emitter inside this holds true even when $\frac{r}{{r}_{0}}=20$.

A Method of Drawing Metallic Filaments and a Discussion of their Properties and Uses

Abstract: If a glass tube filled with a molten metal is placed in a tubular furnace or in a transverse hole through a heated copper rod and drawn out at the proper rate, metal filaments of almost any degree of fineness may be obtained down to a diameter of ${10}^{\ensuremath{-}5}$ cm, or even less. The glass or quartz used must soften at a temperature between the melting and the boiling point of the particular metal. Filaments of Pb, Sb, Bi, Au, Ag, Cu, Fe, Sn, Tl, Cd, Co, Ga, and In have been made by this method. The glass envelop may serve as insulation or may be removed, if desired, with HF. The filaments are very pliable and have greater tensile strength than wires of ordinary size. The temperature coefficients of resistance were not found to differ markedly from those of the metals in bulk, and to be more constant. Metallic filaments made in this way have been used for resistance thermometers, thermocouples, galvanometer suspensions, and hair lines for the eye pieces of telescopes. Their use in micropiles, bolometers and the moving coil of both direct and alternating current galvanometers is suggested. Conducting quartz threads were made by drawing down a tube with a silver core.

The Settling of Small Particles in a Fluid

Abstract: Settling of small particles in a fluid; mathematical theory.---Small particles immersed in a liquid experience a motion which is the combination of a steady gravitational drift and a Brownian movement. If there are space variations in the density of distribution of particles, the Brownian movement produces a diffusion which tends to equalize the density. In the steady state the density $n$ of particles is an exponential function of $x$, the distance below the surface of the liquid. This paper investigates the manner in which the steady state is established. A consideration of the combined effect of fall and diffusion leads to a partial differential equation for the number density of particles as a function of depth and time. A set of special solutions is obtained in terms of which a solution satisfying initial and boundary conditions can be expressed. (1) Liquid of finite depth. The solution is obtained for a liquid of finite depth with an arbitrary initial distribution ${n}_{0}=f(x)$. For the case of uniform initial distribution a reduced form of the solution is obtained which contains a single parameter. This one parameter family of curves is plotted, and from these curves, either directly or by interpolation, may be obtained the density distribution at any time for a solution of any depth, density, and viscosity, and for particles of any size and density. For small values of $t$, since the solution obtained converges slowly, an image method is used to obtain an integral formula for the density. (2) Liquid of semi-infinite or infinite depth. In the case of a liquid of infinite depth the solution for an arbitrary initial distribution is expressed by the Fourier integral identity. The case of zero initial density for negative $x$, and constant initial density for positive $x$ is calculated, as is also the case of particles initially uniformly distributed over a layer of depth $h$. In the case of a liquid extending from $x=0$ to $x=\ensuremath{\infty}$, the boundary conditions are satisfied by assuming a suitable fictitious initial distribution over the range from $x=\ensuremath{-}\ensuremath{\infty}$ to $x=0$. The cases of uniform initial distribution, and initial distribution over a layer, are calculated. The latter case, while derived for a liquid of semi-infinite depth, gives approximately the distribution of density during the settling of a layer of particles initially distributed uniformly over a depth $h$ at the upper end of a very long column of liquid.

Electron Emission from Metals as a Function of Temperature

Abstract: The equation $i=A{T}^{2}{e}^{\ensuremath{-}\frac{{b}_{\mathrm{o}}}{T}}$ was first presented in 1911, and the fact that $A$ is a universal constant was stated in 1915. The proof involved nothing beyond the application of elementary thermodynamics to the equilibrium of the external electron atmospheres, hence the development owes nothing to Nernst's heat theorem or chemical constants. Contrary to Dushman's implication (Phys. Rev. 21, 623, 1923), the writer did not consider it probable that the work function is the same for all substances.

A New Precision X-ray Spectrometer

Abstract: Multiple-deep-slit x-ray spectrometer.---A Bragg spectrometer was provided with two collimators, each consisting of a number of thin parallel strips of lead, separated a distance 1/166 times their length so as to produce many deep parallel slits. By this construction, radiation from a considerable area of the target passes through one or other of the slits of the first collimator, a large area of the specimen is thus irradiated, and also reflected radiation passing through one or other of the deep slits of the collimator fastened to the ionization chamber reaches a large area of cross section of that chamber; therefore the intensity of the ionization is relatively much greater than for the ordinary spectrometer. Any type of flat specimen can be studied, since in the large area irradiated properly oriented crystals are sure to be present, for some angles at least. The intensity curves obtained show sharp peaks, therefore lines can be accurately measured even when only 2\ensuremath{'} of arc apart. Moreover, the large intensity available enables such peaks to be located for large angles between the axis of the collimators, increasing the accuracy. A test with a small sheet of steel gave accurate measurements of the $\mathrm{MoK}{\ensuremath{\alpha}}_{1}$ and $\mathrm{K}{\ensuremath{\alpha}}_{2}$ peaks, the wave-length ratio coming out 1.00604 in agreement with Duane's value 1.00605. Also the expansion of the steel to 475\ifmmode^\circ\else\textdegree\fi{}C was readily observed, the shift of 9\ensuremath{'} giving a coefficient of 12 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}6}$. The change in atomic distance produced by stretching a steel strip beyond its elastic limit was also measured, the contraction at an angle of 82\ifmmode^\circ\else\textdegree\fi{} to the stress being 0.265 per cent. This instrument should prove useful in studying the effect of any agency tending to change the interatomic distances.

Compressibility of the Alkali Halides

Abstract: Compressibility of eleven alkali halides and its variations with pressure and temperature have been determined by measurements by Bridgman's new method, up to 12,000 atm. for both 30\ifmmode^\circ\else\textdegree\fi{} C and 75\ifmmode^\circ\else\textdegree\fi{} C. The samples were all single simple cubic crystals each grown from the melt in a new way, described elsewhere. The error in the values of the compressibility at zero pressure, ${\ensuremath{\kappa}}_{0}$, is probably less than one per cent; in the values for variation with pressure, ${\ensuremath{\psi}}_{0}$, and temperature the error may be 5 and 20 per cent respectively. By extrapolation approximate values of ${\ensuremath{\kappa}}_{0}$ for absolute zero are found. Periodic relations. Both ${\ensuremath{\kappa}}_{0}$ and ${\ensuremath{\psi}}_{0}$ when plotted against the alkali ion for a series of salts of the same halogen ion, or vice-versa, show similar behavior. The curves break sharply at the ion similar to argon (K or Cl) the rate of increase suddenly decreasing. This behavior is also shown by the grating space as measured by Davey, and tends to corroborate Bohr's theory of atomic structure according to which there is a discontinuity in atomic formation at argon, additional electrons going into inner shells.Interatomic forces in cubic crystals.--- The crystal potential energy as a function of volume, at absolute zero is determined from the experimental results, and an empirical expression for it is developed which is extrapolated to a volume so large that the repulsive forces between the atoms are small. The remaining attractive force is found approximately equal to that given by the expression derived by Madelung assuming each ion is singly charged. Then assuming electrostatic cohesion, a series development is obtained for the repulsion betwe atoms. This is found not to vary as any single inverse power of the grating space, as demanded by the theory of Born for salts of Na, K and Rb; nor is there any discontinuity between Li and the other metals. Values for the energy of dissociation of the crystal into ions are given. As would be expected, the change of compressibility with temperature is related to the thermal expansion in such a way that an increase of temperature and decrease of pressure have the same effect on both volume and compressibility.

Duration of Molecules in Upper Quantum States

Abstract: Values of rate of decay and mean life of atoms and molecules in upper quantum states calculated from data on the intensity of absorption lines.—By combining Fuchtbauer's method of determining from the intensity of absorption lines the probability that a molecule will absorb a quantum of energy, with Einstein's views as to the mechanism of light absorption and emission, the following equation is derived for calculating the rate at which molecules jump from upper to lower quantum states: A21=8πν2/c2N1p1/p2∫0∞αdν where A21 is the chance per unit time that a molecule will jump spontaneously from quantum state 2 to quantum state 1, ν is the frequency of the light emitted in such a jump, p1 and p2 are the a priori probabilities of quantum states 1 and 2, and α is the absorption coefficient of the substance measured under conditions such that N1 is the number of molecules per unit volume in the lower quantum state 1. The integral ∫αdν is to be taken over the total effective width of the absorption line corresponding to the passage of molecules from quantum state 1 to quantum state 2. The mean life τ of molecules which decay from state 2 to state 1 is the reciprocal of A21. Values of A21 and τ are calculated from existing data for the mercury line λ2537, for a number of lines belonging to the alkali doublets, for the iodine line λ5461, and for a very considerable number of lines belonging to the rotation-oscillation spectra of the hydrogen halides. The values obtained agree with the meager data made available by other experimental methods. From these results the following conclusions are drawn. The mean life of molecules and atoms in upper quantum states may vary for different states at least over the range 1 to 10-8 seconds. The rate of decay is not a simple function of the frequency of the emitted light. The rate corresponding to the emission of a line of high frequency may be greater or less than that for a line of lower frequency. The data now available for the alkali doublets 1s-mp1 and 1s-mp2 indicate a higher rate of decay the smaller the change in total quantum number for the line under consideration. The rate of decay from a given mp1 state is m times as great as from the corresponding mp2 state (already stated in another form by Fuchtbauer and Hofmann). In the case of the rotation-oscillation spectra of the hydrogen halides the rate of decay is greater for quantum states with one unit of oscillation and many of rotation, than for those with one unit of oscillation and only a few of rotation; and in the case of different molecules but the same quantum numbers the rate of decay is greater for the molecule with the greater frequency of oscillation. Finally the possibility and method of calculating absolute values of A21 from the Bohr correspondence principle is indicated.

The Absorption of Radiation by Multiply Periodic Orbits, and its Relation to the Correspondence Principle and the Rayleigh-Jeans Law. Part I. Some Extensions of the Correspondence Principle

Abstract: This part deals with the quantum theory aspects of the problem. In the absence of external radiation fields the distortion in the shape of the orbit is essentially the same in both the classical and quantum theories provided in the former we retain only one particular term ${\ensuremath{\tau}}_{1}$, ${\ensuremath{\tau}}_{2}$, ${\ensuremath{\tau}}_{3}$ in the multiple Fourier expansion of the force $\frac{2{e}^{2}\stackrel{\ifmmode\ddot\else\textasciidieresis\fi{}}{v}}{3{c}^{3}}$ on the electron due to its own radiation. The term to be retained is, of course, the combination overtone asymptotically connected to the particular quantum transition under consideration. Then the changes $\ensuremath{\Delta}{J}_{1}$, $\ensuremath{\Delta}{J}_{2}$, $\ensuremath{\Delta}{J}_{3}$ in the momenta ${J}_{k}$ which fix the orbits and which in the stationary states satisfy the relations ${J}_{k}={n}_{k}h$, are in the ratios of the integers ${\ensuremath{\tau}}_{1}$, ${\ensuremath{\tau}}_{2}$, ${\ensuremath{\tau}}_{3}$ in both the classical and quantum theories, making the character of the distortion the same in both even though the speed of the alterations may differ. One particular term in the classical radiation force is thus competent to bring an orbit from one stationary state to another.

The Magnetic Susceptibility of Oxygen, Hydrogen and Helium

Abstract: The method used was that of balancing the gas magnetically against an aqueous solution of nickel chloride. By varying the concentration of the solution it could be given a susceptibility approximately the same as that of the gas; then by varying the pressure of the gas or the temperature of the gas and solution, both could be given the same susceptibility. A manometric balance of great sensitivity enabled the observer to tell when the susceptibilities of the gas and the solution were the same. For both paramagnetic and diamagnetic gases, formulas are derived from which the susceptibility may be calculated from pressure and temperature observations on the gas when it is magnetically neutral against the solution. The volume susceptibility under a pressure of one atmosphere at the temperature 20\ifmmode^\circ\else\textdegree\fi{}C was found to be +0.1447\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ for oxygen; -1.64\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}10}$ for hydrogen, and -0.81\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}10}$ for helium. The result found for helium is about 25 times less than T\"anzler's value, but when substituted in the formula derived by W. Pauli Jr. for the diamagnetic susceptibility of a monatomic gas, it yields a result bearing on the dimensions of the atom which is compatible with our knowledge obtained from other sources.

Polarized Resonance Radiation in Weak Magnetic Fields

Abstract: Effect of a magnetic field on the polarization of resonance radiation of mercury and of sodium.---(1) Mercury $\ensuremath{\lambda}2536$. A beam of plane polarized monochromatic light was focussed on the bulb containing the vapor at low pressure (0\ifmmode^\circ\else\textdegree\fi{}C), and the polarization of the resonance radiation was determined photographically with the aid of a quartz wedge and a double image quartz prism. If the exciting beam is going east with the electric vector vertical, when the earth's field is carefully neutralized the polarization is 90 per cent in any horizontal direction and zero vertically; a field of only 2 gauss directed north reduces the polarization in its direction to nearly zero (the decrease with increasing field being exponential), changes the polarization east and also up to 60 percent, and increases the intensity directed upwards threefold. Similar effects are produced by fields in other directions. The polarization with zero field does not approach 100 per cent at low pressures, since 90 per cent was found also with the vapor at -50\ifmmode^\circ\else\textdegree\fi{}C, when the radiation first appeared. It was thought that the high value might be due to an orientation of the resonating atom by the field of the exciting light, but a beam of concentrated sunlight produced no effect. As found by Malinowski, a strong field of 10,000 gauss merely increased the intensity of the radiation about 10 per cent. This added light was found to be unpolarized. (2) Sodium $D$ line. In the case of sodium vapor the tube was heated to 185\ifmmode^\circ\else\textdegree\fi{}C, the observations were visual, and as a source of unreversed light, the glow on the surface of a sodium glass vacuum tube carrying a discharge, was used. The effects observed are similar to those for mercury, but differ for some directions; fields forty times stronger were required, and the polarization in zero field was only 6 per cent, probably due to traces of hydrogen. This was increased by the field in some directions to 30 per cent.Effect of magnetic field on fluorescent light of iodine vapor and on white scattered light from mercury and ether vapors.---The polarization was found not to be affected.

The Metastable State in Mercury Vapor

Abstract: Metastable state produced in mercury vapor at low pressures by electron impacts of 4.9 volts.---The persistence of the "radiation" produced by 4.9 volt impacts in mercury vapor was measured in a four electrode tube of the type usually employed in resonance potential measurements, consisting of an equipotential cathode of simple design, an inner grid $G$ for controlling the velocity of the impacting electrons, an outer photo-electric grid $H$ and a photo-electric plate $P$. A.c. and d.c. voltages were applied to the two grids in such a way that the electrons had sufficient velocity to excite the radiation only in alternate half-cycles and that the photo-electric current to the electrometer alternated in direction simultaneously. As a result of the persistence of the radiation there resulted a decrease in the current with increasing frequency, reaching a minimum at 1800 cycles for a distance between grids of 17 mm and at 3800 cycles for a distance of 8.5 mm. These results did not vary much with pressure,.003 to.032 mm. They show a lapse of time between the excitation and the arrival of the first radiation at the plate $P$ of about 1/3600 and 1/7600 sec. respectively. A mathematical discussion shows that the diffusion of the radiation by repeated emission and re-absorption (the "imprisonment" of radiation theory) cannot account for these results. A calculation, based on the assumption that the excited atoms remain in a metastable state and carry the energy of excitation to the photo-electric surfaces and there give it up, gives results in very close agreement with the observations. The conclusion is that a metastable state is formed by the atoms excited by the 4.9 volt electron impacts and that these are the effective ones in producing the photo-electric response in the tubes. In these experiments the $2{p}_{2}$ state is the only one excited by the impacts in appreciable amount. How these results can be reconciled with the Bohr theory, according to which the $2{p}_{2}$ state is not metastable, is not clear.

Theory and Experiments Relating to the Striated Glow Discharge in Mercury Vapor

Abstract: Theory of the glow discharge in a monatomic gas.---For the case of parallel plane electrodes with a hot cathode as source of electrons, the potential distribution and ion concentration in the Crookes dark space, negative glow, Faraday dark space and positive column are shown to be predictable from considerations of space charge and of ionization and excitation of the gas. While with weak currents there is a negative space charge throughout, sufficiently intense ionization is shown to lead to a cathode drop, followed by a region of reversed electric field in which positive ions and electrons both move toward the anode by diffusion, owing to their large concentration gradient. Still farther from the cathode the field changes to its normal direction and increases up to the positive column. In the positive column the field and concentration are uniform unless atoms excited by electron impacts in certain layers are prevented from diffusing between the layers, when striations may be obtained with periodic changes of field and of concentration. The cathode edge of each striation has a positive space charge. The theory of the arc discharge is essentially the same, the arc being simply the negative glow of the longer glow discharge.Glow discharge in mercury vapor.---Various predictions of the above theory were verified by experiments with Hg vapor in vacuum tubes provided with hot cathodes. (1) Potential distribution and ion concentration were investigated by Langmuir's modified probe method and found to agree with the theoretical deductions, except that the concentration of positive ions in the positive column comes out too large. This result indicates the presence of negative mercury ions. (2) The distribution of velocities of electrons is Maxwellian except between striations. (3) The emission of light seems associated more with excitation by electron collision than with ionization and recombination. (4) Conditions for existence of striations. Striations are not found in pure Hg vapor unless the current is small or some substance like ${\mathrm{H}}_{2}$ is introduced to remove excited atoms. (5) The presence of atomic hydrogen which should be produced in the process of removing excited Hg atoms was proved by use of tungsten oxide. (6) Introduction of He, which cannot remove excited atoms, does not tend to produce striations. (7) The relative concentrations of excited atoms was determined from the optical absorption of subordinate series Hg lines. It was found that excited atoms exist in striations but not in the regions between, and are more numerous if the amount of ${\mathrm{H}}_{2}$ impurity is reduced.Band spectrum of HgH seems associated with the action of excited Hg atoms on hydrogen, and is emitted as a result of inelastic collisions in striations.

Extreme ultra-violet spectra

Abstract: Extreme ultra-violet spectra, to 136 A, of twenty light elements, H to Cu.—Using the vacuum apparatus and explosive spark previously described, many plates have been made with a great variety of electrodes. By measuring and comparing thirty of these, over 800 lines between 136 A and 1862 A have been identified as belonging to one or other of the twenty elements studied. For H(1) only two lines, members of the Lyman series, were found; for He(2), and Li(3) none, though carefully looked for; for Be(4) one doubtful weak line; for Na(11) one strong line λ372.3 and one doubtful one λ376.6; for the other elements B(5), C(6), N(7), O(8), F(9), Mg(12), Al(13), Si(14), P(15), S(16), Cl(17), K(19), Ca(20), Cr(24) and Cu(29) from 9 to 160 lines each, all given in Tables. The strongest lines for each of the light elements are L series lines and form a progression like Moseley's for x-ray lines: Li (red), Be 3131.19, B 2066.2, C 1335.0, N 1085.2, O 834.0, F 656.4, Na 372.3, Mg 231.6, Al 162.4. These are mainly doublets, the separation increasing regularly with atomic number. M spectra also extend to shorter wave-lengths the higher the atomic number, reaching about 155 A for Cu, but on account of the complexity of the spectra only a few lines have been identified. Other series lines identified are: 2 diffuse series lines and 2 sharp series lines due to Mg+ or Mg(II), 5 lines due to Al+ and 9 due to Al++ or Al(III), 11 lines due to Si(IV) and probably the first terms of the principal series and of the diffuse series of P(V). Interpretation in terms of Bohr theory. By use of the Kossel equation in connection with available data it is shown that for Na, 372.3 A corresponds to an electron jump from the M shell to L(I); for Mg, 320.9, and 323.2 and 231.6 correspond to M(I)→L(II), M(I)→L(III) and M(III)→L(I); for Al, 162.4, 200.0, 230.8, 186.9 may correspond to jumps from shell 3 to the L shell; for Ca, 655.9 and 669.6 correspond to jumps N(I)→M(II) and N(I)→M(III). These interpretations give values of constants of the L and M levels of the atoms as follows: For Na, L(I), ν/R=2.826; for Mg, L(I) 4.298, L(II) 3.402, L(III) 3.381; for Al, L(I) 6.045, L(II) L(III) 5.008. The square roots of these values are linear functions of the atomic number. For Ca M(II), ν/R=1. 839, M(III) 1.810. From the difference L(II)—L(III) for Mg, the screening constant comes out 3.1; from the difference M(III)—M(II) for Ca, the constant is 7. These results are all in good agreement with other data. Ionization produced by explosive spark in vacuum.—The strongest spectrum lines are generally emitted by stripped atoms, that is atoms with no valence electrons left, Na(I), Mg(II), Al(III), Si(IV), P(V), etc.

Ionizing Potentials of Multiatomic Gases

Abstract: Ionizing potentials for helium and fifteen compound inorganic gases were measured by accelerating photo-electrons through a gauze into a chamber where the positive ions produced were drawn to a fine Pt electrode, made small so as to eliminate effects due to radiation. The current-voltage curves obtained consist of straight lines except at the breaks. Corrections for initial velocity, etc., were made by obtaining on the same curve both a break for the unknown gas and one for mercury (10.4 volts). The values found are, in volts: helium, 24.5; hydrogen, 15.8; nitrogen, 16.3; oxygen, 12.5, 16.1; $\mathrm{HCl}$, 13.8; $\mathrm{HBr}$, 13.2; $\mathrm{HI}$, 12.8; water, 13.2; ${\mathrm{NH}}_{3}$, 11.1; ${\mathrm{Cl}}_{2}$, 13.2; ${\mathrm{Br}}_{2}$, 12.8; ${I}_{2}$, 10.0; $\mathrm{NO}$, 9.4; ${\mathrm{CO}}_{2}$, 14.3; $\mathrm{CO}$, 14.1, 15.6; ${H}_{2}S$, 10.4. Comparison is made with results of other observers. Theoretical interpretation. An attempt is made to test the thermochemical method of estimating ionizing potentials in those cases (${\mathrm{H}}_{2}$S, N${\mathrm{H}}_{3}$, ${\mathrm{H}}_{2}$O) where data are available. No process of ionization involving molecular dissociation seems consistent with the experimental results. This and other evidence suggests that in those cases (HCl, HBr, HI) in which the thermochemical calculations yield accurate results, the agreement may be fortuitous, and that the lowest ionization potentials in each case corresponds to ionization without dissociation.

Direction of Ejection of Photo-Electrons by Polarized X-rays

Abstract: Direction of ejection of photo-electrons by polarized x-rays.---Stereoscopic photographs were obtained, by Wilson's cloud expansion method, which show the ionized tracks of photo-electrons ejected by plane polarized x-rays. The polarized x-rays, scattered by a paraffin block at 90\ifmmode^\circ\else\textdegree\fi{} to an unpolarized primary beam of hard x-rays, were directed horizontally through the expansion chamber of a Wilson cloud apparatus in which they produced the photo-electrons. Exploded tungsten wires furnished the instantaneous illumination of the droplets. The photographs, taken with the plate at 90\ifmmode^\circ\else\textdegree\fi{} to the polarized beam, show two types of asymmetry in the direction of ejection of the photo-electrons. Lateral asymmetry. There is a strong concentration of photo-electrons ejected nearly in the direction of the electric vector of the plane polarized radiation performing the ejection. Longitudinal asymmetry. Stereoscopic examination of the photographs shows one-sixth of the photo-electrons ejected with a component opposite to the beam, one-third ejected approximately at right angles to the beam, and one-half ejected with a component along the beam. Theoretical interpretation according to the classical and quantum theories. The results are in accord with the classical theory. To explain them on the quantum theory we must assume that the quantum is a vector bundle of energy, for it explodes, so to speak, at right angles to its direction of motion.

The Barkhausen Effect

Abstract: Barkhausen effect for silicon steel.---In a typical experiment a strip of silicon (4.2%) steel, after having been carried through several hysteresis cycles and brought to a steep part of the $B\ensuremath{-}H$ curve, was subjected to a magnetic field which was increased in a continuous manner by 0.13 gauss in 2 sec. To obtain a record of the discontinuities in magnetization, the specimen was surrounded by a small search coil connected through an amplifier to a moving coil oscillograph. The oscillograph records show many almost instantaneous deflections with a random distribution both as to time of occurrence and as to magnitude, each followed by an approximately exponential return to zero. The duration of an impulse depends probably on eddy currents in the specimen. A rough time constant of 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ sec. is computed for a 4% silicon steel wire, 1 mm in diameter. The apparatus was calibrated by means of artificial impulses of the same type. Assuming each impulse is due to a sudden saturation of a small portion of the material, the change in magnetic moment of this portion is found to vary from.001 to.008 e.m.u.; the average change.003 is sufficient to saturate a volume of 1.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ cc. This volume, while comparable with that of a crystal grain in the particular case described, was found not to depend upon grain size in any marked degree in other experiments. The results favor the suggestion of Barkhausen that magnetic materials magnetize discontinuously, but leave open the question as to what determines the size and shape of the portions which suddenly change.

Dielectric Anomalies in Rochelle Salt Crystals

Abstract: Residual charge and fatigue effects for Rochelle salt condenser.---The throw of a ballistic galvanometer connected to a condenser with Rochelle salt crystal as dielectric depends on the time of charging and the time of discharging. It increases to a maximum as the charging time is increased to 2 sec. (for crystal plates.15 cm. thick) and then decreases slowly, reaching for a time of 24 hours a value about half the original. The decrease of the throw for.03 sec. charging, due to fatiguing for 24 hours at 100 volts, was found to be nearly independent of the temperature from -15\ifmmode^\circ\else\textdegree\fi{}C to +20\ifmmode^\circ\else\textdegree\fi{}C. The first increase is probably due to residual charges which are easily displaced to a more or less definite limit and which account for the high dielectric constant in this temperature range. The subsequent decrease is due to a fatigue effect which may be likened to an electrolytic polarization of the internal displacement current. These effects are associated with the water of crystallization, since dessication decreases them while previous soaking in alcohol accelerates them. To explain the limited temperature range of the effects it is supposed that at -20\ifmmode^\circ\else\textdegree\fi{}C there is a loosening of the water ions enough to permit a slight motion of about ${10}^{\ensuremath{-}9}$ cm with reference to the Rochelle salt molecules, while at temperatures above +25\ifmmode^\circ\else\textdegree\fi{}C further loosening allows electrolytic conduction to increase greatly.Thermal changes in Rochelle salt.---There is apparently an evolution of heat starting at 24\ifmmode^\circ\else\textdegree\fi{}C and persisting to 54\ifmmode^\circ\else\textdegree\fi{}C where a very strong absorption of heat takes place.

Ionization of Gases as a Function of the Energy of Electron Impacts

Abstract: Ionization of various gases by electrons of energy up to 300 volts.---Electrons were accelerated from a tungsten wire to a plane perforated electrode $G$, through which a small fraction passed into a space where they were all stopped by a retarding field between the perforated electrode and a plane parallel plate $P$ connected to an electrometer, which collected all the positive ions formed on collision between the electrons and the gas molecules. The fraction of the collisions resulting in ionization as a function of the energy of impact is shown to be $f({V}^{\ensuremath{'}})=(\frac{1}{2apD})[\frac{d(\frac{{V}_{0}P}{E})}{d{V}_{0}}]$, where $\frac{P}{E}$ is the ratio of positive ions produced to the number of electrons passing through the perforated electrode $G$, ${V}_{0}$ is the retarding potential between $P$ and $G$ and is somewhat greater than ${V}^{\ensuremath{'}}$ the maximum energy of impact, $p$ is the pressure, $D$ the distance apart of $P$ and $G$, and $a$ is the chance of collision per cm for 1 mm pressure which is assumed to have the Kinetic Theory value. For helium, neon, argon, hydrogen, nitrogen, and methane, $f({V}^{\ensuremath{'}})$ was found to increase very rapidly to a maximum value, after which there was a less rapid, though marked, decrease. The maxima occur at 147, 157, 80, 74, 101, and 80 volts for the gases in the order named, the maximum values being respectively.11,.14,.35,.21,.32, and.28. Even for the most favorable velocities, then, less than half of the collisions result in ionization.Radiation potentials of argon and carbon. A break in the argon curve suggests $L$ radiation for argon at 250 volts impact energy, while a break in methane curve indicates a possible $K$ radiation for carbon at 248 volts.