# Showing papers in "Physical Review in 1935"

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TL;DR: Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that one is led to conclude that the description of reality as given by a wave function is not complete.

Abstract: In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false. One is thus led to conclude that the description of reality as given by a wave function is not complete.

12,554 citations

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TL;DR: In this article, it is shown that a certain "criterion of physical reality" formulated in a recent article with the above title by A. Einstein, B. Podolsky and N. Rosen contains an essential ambiguity when it is applied to quantum phenomena.

Abstract: It is shown that a certain "criterion of physical reality" formulated in a recent article with the above title by A. Einstein, B. Podolsky and N. Rosen contains an essential ambiguity when it is applied to quantum phenomena. In this connection a viewpoint termed "complementarity" is explained from which quantum-mechanical description of physical phenomena would seem to fulfill, within its scope, all rational demands of completeness.

2,576 citations

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TL;DR: In this article, the authors investigate the possibility of an atomistic theory of matter and electricity which, while excluding singularities of the field, makes use of no other variables than the general relativity theory and the Maxwell theory.

Abstract: The writers investigate the possibility of an atomistic theory of matter and electricity which, while excluding singularities of the field, makes use of no other variables than the ${g}_{\ensuremath{\mu}\ensuremath{
u}}$ of the general relativity theory and the ${\ensuremath{\phi}}_{\ensuremath{\mu}}$ of the Maxwell theory. By the consideration of a simple example they are led to modify slightly the gravitational equations which then admit regular solutions for the static spherically symmetric case. These solutions involve the mathematical representation of physical space by a space of two identical sheets, a particle being represented by a "bridge" connecting these sheets. One is able to understand why no neutral particles of negative mass are to be found. The combined system of gravitational and electromagnetic equations are treated similarly and lead to a similar interpretation. The most natural elementary charged particle is found to be one of zero mass. The many-particle system is expected to be represented by a regular solution of the field equations corresponding to a space of two identical sheets joined by many bridges. In this case, because of the absence of singularities, the field equations determine both the field and the motion of the particles. The many-particle problem, which would decide the value of the theory, has not yet been treated.

921 citations

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TL;DR: In this article, the Brester-Wigner theory of small vibrations when the potential energy is invariant under the rotation displacement group is developed, and it is shown that the use of these coordinates implies the use a particular (normal) system of rotating axes whose construction is given.

Abstract: The theory of small vibrations when the potential energy is invariant under the rotation-displacement group is developed. The results are compared with the Brester-Wigner theory of the normal coordinates, and it is shown that the use of these coordinates implies the use of a particular (normal) system of rotating axes whose construction is given. It is shown that when the motion of a normal molecule is referred to these axes, those terms of the Hamiltonian which are linear in the angular momenta will be especially small and of the same order of magnitude as the quadratic terms (Casimir's condition). When the amplitude of one or more of the normal vibrations becomes large, this is no longer true of the normal axes; this will always be the case when one of the normal frequencies is small compared to the others, as has been noted by other writers. The normal axes are not the principal axes of inertia of the instantaneous configuration of the system, and certain conclusions recently published by the author are wrong for that reason.

860 citations

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TL;DR: In this article, the effects of shearing stress at the plastic flow point were investigated and it was found that many substances normally stable become unstable and may detonate, and conversely combinations of substances normally inert to each other may be made to combine explosively.

Abstract: Mean hydrostatic pressures up to 50,000 kg/${\mathrm{cm}}^{2}$ combined with shearing stresses up to the plastic flow point are produced in thin disks confined between hardened steel parts so mounted that they may be subjected to normal pressure and torque simultaneously Qualitative and quantitative studies are made of the effects of such stresses Among the qualitative effects it is found that many substances normally stable become unstable and may detonate, and conversely combinations of substances normally inert to each other may be made to combine explosively Quantitatively, the shearing stress at the plastic flow point may be measured as a function of pressure The shearing stress at plastic flow may rise to the order of 10 or more times greater at 50,000 kg/${\mathrm{cm}}^{2}$ than it is normally at atmospheric pressure; this is contrary to the usually accepted results in a narrower range of pressure If the substance undergoes a polymorphic transition under these conditions of stress, there may be a break in the curve of shearing stress vs pressure This gives a very convenient tool for the detection of transitions 57 elements have been explored in this way, and a number of new polymorphic transitions found

471 citations

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TL;DR: In this paper, the positron theory for the special case of impressed electrostatic fields is investigated and the existence of an induced charge corresponds to a polarization of the vacuum, and as a consequence, to deviations from Coulomb's law for the mutual potential energy of point charges.

Abstract: Some of the consequences of the positron theory for the special case of impressed electrostatic fields are investigated. By imposing a restriction only on the maximum value of the field intensity, which must always be assumed much smaller than a certain critical value, but with no restrictions on the variation of this intensity, a formula for the charge induced by a charge distribution is obtained. The existence of an induced charge corresponds to a polarization of the vacuum, and as a consequence, to deviations from Coulomb's law for the mutual potential energy of point charges. Consequences of these deviations which are investigated are the departures from the Coulombian scattering law for heavy particles and the displacement in the energy levels for atomic electrons moving in the field of the nucleus.

416 citations

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399 citations

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TL;DR: In this paper, it was shown that the mass defect of a proton can be made arbitrarily large by taking $a$ small enough, and that the interaction between two neutrons can be regarded as arising from a singularity in configuration space.

Abstract: Suppose that the interaction between a neutron and a proton depends on their distance apart so as to be negligible above a certain small distance $a$, and yet is responsible for the mass defect of ${\mathrm{H}}^{2}$. Suppose further that the interaction between two neutrons and a proton may be compounded in the usual way from that between a neutron and a proton, the interaction between two neutrons being neglected, while there is no prohibition of a wave function symmetrical in the positions of two neutrons. Then it is shown that the mass defect of ${\mathrm{H}}^{3}$ is made arbitrarily large by taking $a$ small enough. The observed mass defect of ${\mathrm{H}}^{3}$ thus provides, on the above assumptions, a lower limit for $a$; and in particular rules out the possibility that the interaction may be regarded as arising from a singularity in configuration space. We conclude, in effect, that: either two neutrons repel one another by an amount not negligible compared with the attraction between a neutron and a proton; or that the wave function cannot be symmetrical in their positions; or else that the interaction between a neutron and a proton is not confined within a relative distance very small compared with ${10}^{\ensuremath{-}13}$ ${\mathrm{cm}}^{1}$.

377 citations

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313 citations

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TL;DR: In this paper, the probability of simultaneous emission of two electrons and two neutrinos has been calculated from the Fermi theory of ''ensuremath{\beta}$-disintegration''.

Abstract: From the Fermi theory of $\ensuremath{\beta}$-disintegration the probability of simultaneous emission of two electrons (and two neutrinos) has been calculated. The result is that this process occurs sufficiently rarely to allow a half-life of over ${10}^{17}$ years for a nucleus, even if its isobar of atomic number different by 2 were more stable by 20 times the electron mass.

276 citations

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TL;DR: In this article, a new type of expansion of the function of the spherical coordinates of a vector function is developed which can be used to find the vector potential due to a steady current distribution.

Abstract: A new type of expansion of $\frac{\mathrm{i}(1){{e}^{\mathrm{ikr}}}_{12}}{{r}_{12}}$ is developed. Here i is a vector function of the spherical coordinates denoted by 1 and ${r}_{12}$ is the distance between two points denoted by 1 and 2. This expansion is used in the solution of Maxwell's equations and a simple general expression is found for the energy radiated from a known current distribution. A brief application to Dirac's theory of radiation is given. An expansion for $\frac{\mathrm{i}(1)}{{r}_{12}}$ is developed which can be used to find the vector potential due to a steady current distribution.

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TL;DR: In this paper, the authors put Zwaan's scheme for deriving the Kramers connection formulas on a rigorous basis, differential equations are set up governing the variation in the coefficients used to fit a linear combination of the B. W. K. type approximation functions to an exact solution of Schrodinger's equation in one dimension.

Abstract: In order to put Zwaan's scheme for deriving the Kramers connection formulas on a rigorous basis, differential equations are set up governing the variation in the coefficients used to fit a linear combination of the B. W. K. type approximation functions to an exact solution of Schr\"odinger's equation in one dimension. Approximate solutions of the differential equations are worked out which lend themselves to the setting up of the connection formulas and give definite upper bounds to the errors involved in their use. The method is also used to set up the Sommerfeld phase integral quantum condition independently of the connection formulas. An upper limit to the error in the energy is worked out. A similar treatment of the problem of the transmission of matter waves through rounded potential barriers is formulated.

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General Electric

^{1}TL;DR: In this paper, an approximate mathematical theory of the rupture of a plane liquid surface in a uniform electric field has been developed, and the relation between initial distortion, rupture time, and field strength has been calculated for fields large compared to that which just renders the surface unstable.

Abstract: Surface distortion and rupture permits field emission from liquid surfaces at field strengths less than those effective for equally smooth solid surfaces. An approximate mathematical theory of the rupture of a plane liquid surface in a uniform electric field has been developed. The relation between initial distortion, rupture time, and field strength has been calculated for fields large compared to that which just renders the surface unstable. This critical field is ${E}_{m}=2{\ensuremath{\pi}}^{\frac{1}{2}}{(\ensuremath{\rho}gT)}^{\frac{1}{4}}=53$ kv ${\mathrm{cm}}^{\ensuremath{-}1}$ for mercury, where $\ensuremath{\rho}$ is density and $T$ is surface tension. Typically, the theory shows that a hump initially 4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ cm high and of diameter 9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ cm will lead to rupture in 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ sec. in a field of ${10}^{6}$ v ${\mathrm{cm}}^{\ensuremath{-}1}$. Relative to initial humps in the surface whose linear dimensions vary inversely as the square of the field, the time to rupture varies inversely as the cube of the field strength. This calculation shows that a lowered sparking potential to liquid mercury can be ascribed to surface rupture and shows that it is possible that surface rupture plays a part in Beams' low field emission from liquid mercury. Possible application of the theory to the high field condition at the cathode spot of the Hg arc is not clear.

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TL;DR: In this paper, a table has been constructed so that wave functions and energies, for any atomic state having $1s, $2s$ and $2p$ electrons, can be computed by variational means.

Abstract: Tables have been constructed so that wave functions and energies, for any atomic state having $1s$, $2s$ and $2p$ electrons, can be computed by variational means Exchange terms are included, so that singlet and triplet states can be minimized separately By using the tables a state can be calculated in a few hours A few of the possible states have been worked out The best parameters, the total energies and the term values are given for the states $(1{s}^{2})^{1}S,(1s,2s)^{1}S,^{3}S;(1,2p)^{1}P,^{3}P; (1{s}^{2},2s)^{2}S; (1{s}^{2},2p)^{2}P; (1{s}^{2},2{s}^{2})^{1}S; (1{s}^{2},2s,2p)^{1}P,^{3}P; (1{s}^{2},2{p}^{2})^{1}S,^{1}D,^{3}P; (1{s}^{2},2{s}^{2},2p)^{2}P; (1{s}^{2},2{s}^{2},2{p}^{6})^{1}S$; of the atoms He, Li, Be, B, C, N, O, F, Ne, Na and Mg The intramultiplet separations have been computed, including the spin-spin interaction when necessary: the check with experiment being fairly satisfactory By the use of an empirical correction rule, term values can be predicted to within a few hundred wave numbers

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TL;DR: In this article, a new technique is described by which pressures of 50,000 kg/${cm}€ and more may be applied to solids, and the parameters of any transitions measured.

Abstract: A new technique is described by which pressures of 50,000 kg/${\mathrm{cm}}^{2}$ and more may be applied to solids, and the parameters of any transitions measured. A systematic examination has been made for polymorphism of many of the elements in the new pressure range. New modifications are found for Bi, Hg, Tl, Te, Ga, and ${\mathrm{I}}_{2}$, and the transition parameters measured. A beginning has been made of a systematic study of polymorphism of compounds, and results obtained for KCl, KBr, and KI, which assume at about 20,000 kg/${\mathrm{cm}}^{2}$ presumably the CsCl type of structure.

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TL;DR: In this article, the work function of a metal is defined as the difference in energy between a lattice with an equal number of ions and electrons, and the lattice of the same number of ion and electron, but with one electron removed.

Abstract: The factors which determine the work function of a metal are described in a qualitative way The work function is defined as the difference in energy between a lattice with an equal number of ions and electrons, and the lattice with the same number of ions, but with one electron removed The work function is then found by first calculating the energy of a lattice with n i ions and n e electrons The final formula gives the work functions of monovalent metals in terms of the heats of sublimation This formula is approximate, and can claim validity only in a qualitative way, as one of the important factors, the electric double layer on the surface, is omitted entirely, and it is assumed that the Fermi energy is as great as if the electrons were entirely free The values obtained from this formula check very closely with the experimental values for the alkalis, so that it can be concluded that the double layer is probably small for these metals Finally, the deviations to be expected for other than monovalent metals are considered A more exact calculation of the work function of one substance (Na) will be given by one of us in an ensuing paper

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TL;DR: In this paper, the Thomas-Fermi method is applied to metals, by replacing each atom by a sphere, assuming the potential to be spherically symmetrical within it, and solving the Thomas Fermi equation subject to the boundary condition that the electronic charge within the sphere shall balance the nuclear charge, rendering it electrically neutral.

Abstract: The Thomas-Fermi method is applied to metals, by replacing each atom by a sphere, assuming the potential to be spherically symmetrical within it, and solving the Thomas-Fermi equation subject to the boundary condition that the electronic charge within the sphere shall balance the nuclear charge, rendering it electrically neutral. Calculations are presented giving potential field, charge density, and kinetic, potential, and total energy of the metal, as function of lattice spacing. The virial theorem is verified for the energy. The total energy shows no minimum, the pressure being always positive. Calculations are also made using the Dirac method of correcting for exchange, for three atoms, Li, Na and Cu. The exchange lowers the energy, but still not quite enough to produce a minimum of energy and an equilibrium at zero pressure. The result should be useful as a first approximation in self-consistent field approximations for the structure of metals, and could be adapted to give approximate treatment for matter under very high pressure, as in stars.

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TL;DR: In this article, the formation of negative ions by electron capture in gases in which a dissociation process does not occur is explained by a unimolecular process involving the excitation of molecular vibrational levels and subsequent loss of energy by collision or resonance.

Abstract: The formation of negative ions by electron capture in gases in which a dissociation process does not occur is explained by a unimolecular process involving the excitation of molecular vibrational levels and subsequent loss of energy by collision or resonance. In order to obtain a proper order of magnitude to agree with experimental observations, one must assume a change of only one vibrational quantum number. This sets an upper limit on the electron affinity. For the case of ${\mathrm{O}}_{2}$, this limit is 0.17 volt consistent with other observations. The theory also yields a dependence of the phenomenon on the average energy of the electrons which is in agreement with experiment.

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TL;DR: In this article, the far ultraviolet absorption spectrum of oxygen has been photographed under high dispersion in the region 1300-650A and the results strongly support Mulliken's assignment of the visible O 2 O 2, 2, 1.1 and 18.2 volts, respectively, with possible errors of about a tenth of a volt.

Abstract: The far ultraviolet absorption spectrum of oxygen has been photographed under high dispersion in the region 1300-650A. The bands are explained as going to the various excited states of $\mathrm{O}_{2}^{}{}_{}{}^{+}$ as limits and are attributed to the removal of $v\ensuremath{\pi}$, $\ensuremath{\omega}\ensuremath{\pi}$ and $x\ensuremath{\sigma}$ electrons, respectively, from the normal state of ${\mathrm{O}}_{2}$. The results strongly support Mulliken's assignment of the visible $\mathrm{O}_{2}^{}{}_{}{}^{+}$ bands to the transition $^{4}{\ensuremath{\Sigma}}_{g}^{\ensuremath{-}}\ensuremath{\rightarrow}^{4}\ensuremath{\Pi}_{u}$. The distances of the $^{4}\ensuremath{\Pi}_{u}$ and $^{4}{\ensuremath{\Sigma}}_{g}^{\ensuremath{-}}$ states of $\mathrm{O}_{2}^{}{}_{}{}^{+}$ from the ground state of ${\mathrm{O}}_{2}$ are given as 16.1 and 18.2 volts, respectively, with possible errors of about a tenth of a volt. The appearance and nonappearance of strong electronic series going to known ionization potentials are also discussed.

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TL;DR: In this article, a method is given for determining the forms of potential function which permit an exact solution of the one-dimensional Schr\"odinger equation in terms of series whose coefficients are related by either two or three term recursion formulas.

Abstract: In classical mechanics the problem of determining the forms of potential function which permit solution in terms of known functions received considerable attention. The present paper is a partial study of the same problem in quantum mechanics. A method is given for determining the forms of potential function which permit an exact solution of the one-dimensional Schr\"odinger equation in terms of series whose coefficients are related by either two or three term recursion formulas. The more interesting expressions for the potential energy have been tabulated. A correspondence is found between these solutions and the solutions of the corresponding Hamilton-Jacobi equation. It is shown that whenever the Hamilton-Jacobi equation is soluble in terms of circular or exponential functions, the corresponding Schr\"odinger equation is soluble in terms of a series whose coefficients are related by a two-term recursion formula. Whenever the Hamilton-Jacobi equation is soluble in terms of elliptic functions, the corresponding Schr\"odinger equation is soluble in terms of a series whose coefficients are related by a three-term recursion formula. For the first case the quantized values of the energy are found by restricting the series to a polynomial and in the second by finding the roots of a continued fraction. A brief discussion of the technique of solution of continued fractions is given.

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TL;DR: In this paper, the effect of the finite size and ready polarizability of the deuteron on the probability of transmutations involving the capture of the neutron was considered, and it was shown that the Coulomb repulsion of the nucleus is less effective than for alpha-particles or protons.

Abstract: We consider the effect of the finite size and ready polarizability of the deuteron on the probability of transmutations involving the capture of the neutron. These have as a consequence that the Coulomb repulsion of the nucleus is less effective than for alpha-particles or protons, and that the corresponding transmutation functions increase less rapidly with deuteron energy. We treat the collision by the adiabatic approximation and obtain quantitative results for this energy dependence which are in good agreement with experiment.

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TL;DR: In this article, the charge and current densities were obtained for the positron theory induced in vacuum by an electromagnetic field, accurate to the first order in ${e}^{2}$, and the corresponding correction terms in the Maxwell field equations involve integral operators.

Abstract: Expressions, accurate to the first order in ${e}^{2}$, are obtained for the charge and current densities which, according to positron theory, are induced in vacuum by an electromagnetic field. Because the corresponding correction terms in the Maxwell field equations involve integral operators, it does not seem possible to treat the modified field equations by Hamiltonian methods.

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TL;DR: The large probability of nuclear disintegration byslow neutrons as well as the large cross section for the elastic scattering of slow neutrons can be explained without any new assumption.

Abstract: The large probability of nuclear disintegration by slow neutrons as well as the large cross section for the elastic scattering of slow neutrons can be explained without any new assumption. Interaction between neutron and nucleus is assumed to be only present when the neutron is inside the nucleus or very near its boundary. The rate of change of the potential energy of the neutron at the boundary of the nucleus is important for the quantitative, but not for the qualitative results; in agreement with other data, it has been assumed that the potential drops to $\frac{1}{e}$ in a distance 1.5.${10}^{\ensuremath{-}13}$ cm (range of the forces between neutron and nucleus).

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TL;DR: In this article, the van der Waals interaction energy of two hydrogen atoms at large internuclear distances is discussed by the use of a linear variation function, in which 26 terms for the dipole-dipole interaction, 17 for the quadrupole-quadrupole interaction and 6 terms for quadrupoles-quadrrupoles interaction are included in the variation function.

Abstract: The van der Waals interaction energy of two hydrogen atoms at large internuclear distances is discussed by the use of a linear variation function. By including in the variation function, in addition to the unperturbed wave function, 26 terms for the dipole-dipole interaction, 17 for the dipole-quadrupole interaction, and 26 for the quadrupole-quadrupole interaction, the interaction energy is evaluated as ${W}^{\ensuremath{'}\ensuremath{'}}=\ensuremath{-}\frac{6.49903{e}^{2}}{{a}_{0}{\ensuremath{\rho}}^{6}}\ensuremath{-}\frac{124.399{e}^{2}}{{a}_{0}{\ensuremath{\rho}}^{8}}\ensuremath{-}\frac{1135.21{e}^{2}}{{a}_{0}{\ensuremath{\rho}}^{10}}\ensuremath{-}\ensuremath{\cdots},$ in which $\ensuremath{\rho}=\frac{R}{{a}_{0}}$, with $R$ the internuclear distance. Some properties of the functions ${F}_{\ensuremath{
u}\ensuremath{\lambda}\ensuremath{\mu}}(\ensuremath{\xi},\ensuremath{\vartheta},\ensuremath{\phi})$, which are orthogonal for the volume element $\ensuremath{\xi}d\ensuremath{\xi}sin\ensuremath{\theta}d\ensuremath{\theta}d\ensuremath{\phi}$, are discussed, and their usefulness in atomic problems is pointed out.

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TL;DR: In this article, an absorption spectrum of acetylene in the region 1520A to 1050A has been found, where the small isotopic shifts of many bands revealed them to be vibrationless electronic transitions.

Abstract: An absorption spectrum of acetylene in the region 1520A to 1050A has been found. It appears at very low pressures. The analysis was made by obtaining the spectrum of acetylene made from about 50 percent heavy water. The small isotopic shifts of many bands revealed them to be vibrationless electronic transitions. These are arranged into two Rydberg series going to the same limit which corresponds to an ionization potential of 11.35 volts. The upper levels of the two series are designated as $\mathrm{np}\ensuremath{\Sigma}$ and $\mathrm{np}\ensuremath{\Pi}$ levels. The excitation and ionization are from the CC bond and only vibrations affecting this bond appear. The character of the vibrations present is deduced from the magnitude of the isotopic shifts. Strong predissociation occurs around 1520A. This yields a value of about 187 Cal/mole for the strength of the triple CC bond. A similar set of bands appears in ethylene in the region 1750A to 1200A. The bands are more diffuse than those in acetylene, and only one strong Rydberg series was discovered. The limit of the series corresponds to an ionization potential of 10.41 volts. The vibrational analysis is similar to that in acetylene. The spectrum of ethane is extremely diffuse and no analysis of it could be made. It is concluded that, as in methane, all the upper states are unstable.