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This paper presents a computationally efficient constitutive model for magnetostrictive materials. High computational efficiency is achieved through the use of local linearization (about easy axes) and discrete energy-averaging techniques. The model is applied to iron-gallium alloys (Galfenol) and tested for different magnetic field orientations relative to the easy axes. It is observed that the model accurately predicts both sensing and actuation characteristics while reducing the computation time by a large factor ( >1000 times) when compared to the nonlinear energy minimization models. Furthermore, the average error observed in λ– H and B– H curves is less than 3.5% with the error increasing at magnetic field orientations farther from easy axes, particularly at large magnetic field values. Finally, the model is integrated with a finite element framework to predict the response of a Galfenol rod transducer system, and parametric studies are performed for different current and prestress conditions to optimize the device performance.

This paper reports on the observation of substantial rotation and reflection enhancements with thin magnetic films evaporated on the base of high index prisms with films of suitable index on only the air side of the magnetic thin film. Angles of incidence at the prism‐magnetic thin‐film interface were near the critical angle for total internal reflection. The magnetic film thickness and the thicknesses and indices of the dielectrics were obtained with the help of a computer program which calculated the reflection coefficients as well as the Kerr rotations and energy mode transfer. Enhancements of rsp up to a factor of 20 were obtained.

Laminated material is often used as insulation in an electrical device in such a way that a large component of the dielectric field passes through it parallel to its laminations. In present test methods dielectric loss measurements are made on such material with the dielectric field passing through it perpendicular to its lamination. It is evident that the two conditions are different and the dielectric losses as measured by test are not the same as exist when in use. This paper presents a test method by which power factor, dielectric constant and dielectric loss factor of laminated insulating materials can be measured with the dielectric field parallel to the laminations. Results of measurements made with the dielectric field parallel to laminations of both unconditioned and conditioned specimens are compared, respectively, with results obtained with the field perpendicular to laminations.

This paper describes a theoretical and experimental study of heat effects in viscous liquids up to rates of shear of the order of a million reciprocal seconds, corresponding to the rates experienced in lubrication practice. Even at much lower rates the effect of heat generated by viscous resistance in a capillary tube is sufficient to produce an appreciable drop in the apparent viscosity. This drop cannot be fully corrected for by laboratory observations of the mean efflux temperature, since the temperature rise will not be uniform over the cross section. Detailed calculations are necessary in order to distinguish between heat effects and non‐Newtonian behavior. The theory is illustrated by experimental data on lubricating oils.

Considerable time has been spent by the author in studying, by experimental methods, the behavior of a bow while the arrow is being discharged. Some of the results of these investigations have been published in the magazine previously mentioned and in The Journal of the Franklin Institute (October, 1929). He has also had high speed pictures (one to three thousand frames per second) taken by Electric Research Products which, in addition to putting an end to all controversies regarding the “archers paradox” furnish an excellent means of studying the motions of the arrow and bow limbs. While these experimental methods are interesting and valuable, they are necessarily slow and expensive. An analytical method was therefore developed for determining the dynamical forces, the velocities and accelerations of the arrow and bow limbs. This method has been useful in improving the design and cast of bows. The method is briefly set forth in this paper. Since the dynamical treatment depends on the static conditions, a few of the static equations will first be given. Let us assume that the bow is made up of a short rigid middle section and two limbs, which, for all positions of the draw, bend in arcs of circles. This assumption is reasonable because

In this paper equations are set up which describe the behavior of a solid under the action of combined stresses when a steady state of creep is assumed to exist. A material is said to be in a steady state of creep if it yields with a constant speed under a given constant stress. In an ordinary creep test the steady state exists when the deformation has reached the point where the ``creep curve'' becomes a straight line. In mathematical language this can be expressed by saying that the stress is a function of the rate of strain and is independent of the amount of strain. Cases are worked out in which this stress vs. strain rate relation is a simple power function. Various types of flow including purely plastic flow and viscous flow can be discussed by changing the value of the exponent in the power function relation. Several specific examples which include the case of the thick walled cylinder with closed ends loaded by internal pressure and the case of a disk having a circular hole and loaded in its plane are worked out. Equations are developed which show the steady state stresses in such cases. Expressions for the stress concentration factors in creep are also obtained.

In this paper the principal results of experiments on the viscosity of lubricating oils under high pressure, other than mineral oils, have been reduced to the same units and collected for comparison. The investigations reviewed are those of the American Society of Mechanical Engineers; J. H. Hyde at the National Physical Laboratory of Great Britain; S. Kiesskalt at the Technische Hochschule, Karlsruhe, Germany; and Y. Suge at the Institute of Physical and Chemical Research, Tokyo, Japan. Viscosity‐pressure‐temperature data are given for eleven different oils.

This paper gives the results of an investigation of the voltage characteristic of the copper arc in air during the process of arc formation. A pair of copper electrodes, initially in contact and carrying current, were separated and the voltage arising across the arc gap was studied. Cathode‐ray oscillograms indicate that at the instant of contact separation there develops across the gap a voltage of about 12.2 volts. This voltage was attained in less than 10−5 seconds. This rapidly developed voltage was found to be independent of arc current for current values up to 100 amperes, which suggests that the rapidly developed initial voltage corresponds to the cathode fall of the arc.

Curves are presented from which it is possible to obtain the adiabatic compressibility of a petroleum oil in the range of 40°–200°F and up to 5000 pounds per square inch when only the specific gravity at 60°F and the kinematic viscosity at 100°F are known. A chart is given for obtaining the velocity of a pressure wave in an oil in which both the viscous drag and expansion of the containing tube are neglected. A table showing compressibilities and wave velocities for a number of Diesel fuel oils at 120°F and 1750 pounds per square inch pressure is given. The effects of viscosity and tube wall expansion on wave velocity are discussed and a chart is presented to aid in determining the wave velocity in steel tubes. The paper is concluded with a discussion of the effect of wave velocity on the point of injection of the fuel in the Diesel cycle.

This paper presents a new theory of failure for materials subjected to a combined state of stress. The theory is developed for brittle materials, such as concrete, in which the compressive and tensile strengths are of different magnitudes. It is a semi‐empirical theory which has some experimental support. Based on it working stresses are defined for various loading conditions. The use of these proposed working stresses in some cases makes considerable difference in design as compared to the present specifications requirements. These working stress values are conveniently represented by a diagram to facilitate the computations in design. The application of this information can be made simply in most cases where there are stresses acting in two right‐angled directions—such as slabs in buildings, roads and bridges, retaining walls, dams and other hydraulic structures of concrete and reinforced concrete.

It is shown that the invariant field equations of Maxwell for stationary bodies are also valid for accelerated bodies, if all ordinary differentiations are replaced by absolute differentiation. The affine connection Γγαβ appearing in the absolute derivatives refers to a general non‐Riemannian metric space, with a holonomic or nonholonomic reference frame. The field equations are in a more general form than those used in the five‐dimensional unified field theory and reduce to the latter as a special case. However, the presence of an electrostatic field is not assumed in this paper. The motion of an accelerated body possessing mass, electric current and magnetic flux is given by an extended form of the dynamical equations of Lagrange containing the same general affine connection as the field equations. The material terms of the dynamical equations are expressed by a mechanical impulse‐energy tensor and the resultant motion of the material body under the influence of an electromagnetic field and a mechanical...

This paper considers in detail numerical methods of solving Laplace's equation in an arbitrary two‐dimensional region with given boundary values. The methods involve the solution of approximating difference equations by iterative procedures. Modifications of the standard Liebmann procedure are developed which lead to a great increase in the convenience and rapidity of obtaining such a numerical solution. These modifications involve the use of formulas which simultaneously improve a block of points in place of a single point; methods of operating on the differences of trial functions in place of the functions themselves; and also a method of extrapolating to the final solution of the difference equations. The theory underlying these procedures is considered in detail by a new method which involves the expansion of the error and difference functions in terms of eigenfunctions. This permits definite comparison of rates of convergence of various procedures. The techniques of handling practical problems are considered in detail.

This paper describes a method for determining the dynamic current voltage characteristic curves of glow discharge tubes. The technique differs from that previously used for the oscillographic study of glow tubes in that the manner in which the current varies with time is under control. This is accomplished by the use of a vacuum tube to limit the current passed by the glow tube. The rate at which the current rises and falls, the current amplitude, the frequency of repetition of the current cycle, and the interval between cycles can be varied at will by changing the wave form of the voltage applied to the grid of the control tube, and the grid bias of the control tube. A number of oscillograms obtained by this method are shown, and the form of the characteristics is explained on the basis of time taken for ionization and deionization of the gas.

This paper describes a new method of precalculating the performance of a power tube from its static characteristic curves. The 60‐cycle test method is also briefly outlined and the results of the two methods compared and discussed. An appendix discusses the effect of secondary emission from the plate and grid and primary emission from the grid on the performance of the tube.

This paper describes an electron diffraction study of copper oxides formed from evaporated copper by exposing it in an oxygen atmosphere at various temperatures for various lengths of time. It also discusses several of the orientations which were observed in the evaporated copper.

The extremely finely detailed drawing in Lichtenberg figures offers an unusually clear record of the early stages of discharge phenomena. The interpretation of these records in terms of electronic ionization, space charge, plasma formation, and neutralization of charges is presented in this paper. After giving a short summary of our present knowledge about gas breakdown, the ``normal'' history of a Lichtenberg discharge is established by a study in nitrogen between five millimeters of mercury and thirty atmospheres of pressure. It progresses in three stages—the primary figure, spark development, and the discharge of negative surface charges. (The ``back figure.'') Admixture of carbon tetrachloride and experiments in ``Freon'' up to six atmospheres show the decisive influence of electro‐negative components on the development of the phenomena, and reveal the reasons why these new gases are so effective in suppressing corona discharges. Deviations from Paschen's law, recently observed by several workers, can be interpreted in terms of the photographic evidence gained.

This paper describes experiments on the birefringence of a strip of plastic material, first when the stretched strip is maintained at constant length and second when it carries a constant load. The results indicate that in neither case is the birefringence proportional to the tension. The data are further examined, and the argument is presented to show that in the constant length experiment the ratio of tension T at any time after the initial tension, T1, is established should be the same function of the time as is the expression [1−2μlogeLL1] for the constant load experiment. Finally it is shown that the tension ratio data can be represented by a curve of the type, T′T1=Ae−at+Be−bt+Ce−ct.

This paper considers numerical methods for the solution of Poisson's equation in an arbitrary two‐dimensional region with given boundary values. The methods are similar to those discussed by Shortley and Weller for Laplace's equation. It is shown that the entire theory of networks may be applied to Poisson's equation without change. Formulas for the treatment of irregular points and for blocks of points are developed. In addition to the mathematical considerations, the application of the methods to the case of torsion in shafts of any cross section is described. Additional formulas are derived for the determination of the maximum shear at any point in a shaft as well as the torsional stiffness of such a shaft.

International audience; From the viewpoint of torsional oscillations an internal combustion engine with a long crankshaft is generally considered to be equivalent to a uniform shaft carrying equidistant identical disks. It is here shown that advantage can be taken of the regularity of such a system to simplify the calculation of torsional oscillations. This is done by applying a mathematical method known as the calculus of finite differences. The procedure leads to a frequency equation (2.7) of remarkable symmetry in which appear as parameter the number n of cylinders in line and two simple functions K 1 and K 2 of the frequency which characterize the dynamical properties of the machines coupled at both ends of the crankshaft. These characteristic functions are of the nature of mechanical impedances, but due to their physical interpretation as a spring modulus (or spring constant) generalized to dynamic phenomena, the appellation dynamic modulus is being preferably used in the present paper. The concept of dynamic modulus is briefly introduced in the first section, while the second deals with the establishment of the frequency equation and an artifice for its rapid graphical solution avoiding the necessity of plotting an oscillatory function. Numerical applications to Diesel engines are treated in the last section. An example is also given of an extreme case where the fundamental frequency has a very low value and a special method is used for the calculation of this frequency.

The anomalous flow of certain suspensions through narrow tubes, known as the ``sigma'' phenomena, for which no fully satisfactory explanation has yet been given, is discussed. If it be assumed that the streamlining layers are not infinitely thin, so that a summation treatment takes the place of an integration, a series of equations can be derived depending on the relation assumed to exist between velocity gradient and shearing stress and on the nature of the friction between the layers. These equations reduce, in the limiting case of infinitely thin layers to the well‐known forms of Poiseuille, Buckingham‐Reiner, etc., and the general equation of Schofield‐Scott Blair can also be derived. For finite thicknesses of layer, the equation derived adequately explains the sigma‐phenomenon, and this is shown quantitatively by applying it to the data given in the original paper.

This paper is a report on an experimental investigation of the resistance to the uniform motion of a solid through a viscous liquid, the results of which appear to indicate that the liquid slipped on the surface of the solid. The apparatus was a straight, closed, glass tube containing a steel ball and the liquid being studied. The tube was arranged so that it could be inclined at various angles with the horizontal, and the only motion of the ball that was considered in working up the observations was one of pure rolling. The liquids employed were mixtures of glycerine and methyl alcohol. The analysis of the data is based upon Stokes' and Oseen's forms of Rayleigh's law of resistance, and the results of the investigation are interpreted in the light of theories due to A. B. Basset and to H. Brillie.

The problem of dynamics of liquid columns, particularly in Diesel engine injection systems, requires a knowledge of the velocity of propagation of compressional waves in the system. Approximate values are generally used in the solution of such problems. In an effort to correlate the physical properties of petroleum oils with the velocity of wave propagation and to relate the characteristics determined at atmospheric pressure with those at higher pressures, tests were conducted in the Physical Laboratories of the Standard Oil Company of California on thirty‐seven hydrocarbon oils at atmospheric pressure. Five hydrocarbon oils were investigated in the Mechanical Engineering Laboratories at the University of California at four temperatures ranging from 57°F to 210°F, and pressures ranging from 500 lb. per square inch to 6000 lb. per square inch. In this paper the experimental methods are described and results presented.

This paper describes the results of an investigation and extension of the various proposed procedures and methods of analysis for the photoelastic determination of three‐dimensional states of stress. Two important limitations of the previous developments are removed. A true extension to three dimensions is given by the determination of the effect on retardation of appreciable variation in the orientation of the secondary principal stresses in planes perpendicular to the wave normal (such variation being the rule rather than the exception for general states of stress). Also, methods for the analysis of whole planes are presented, thus avoiding the cumbersome and tedious point by point procedures that have been advanced. In the particular case of plane stress, these methods reduce to a purely optical technique for determining the principal stresses themselves, or more easily their sum, for the entire model.

The general survey which has been presented here shows that, while a number of the optical properties of rubber have been investigated, the measurements of most of them have been more or less preliminary or exploratory in nature and often directed towards some immediately practical application. There appears to be ample opportunity for extended, systematic research on the optical properties for their own sake. The results to be expected from such study may lead in two directions, each of them illustrated in a very preliminary fashion, by examples given in the present paper. The one direction is that of more fundamental knowledge of the constitution of rubber, especially when optical methods are used in conjunction with other types of measurement. An illustration already mentioned is the use of molecular refractivity to confirm the existence of a C5H8 unit containing one double bond as the unit group in rubber. Such work might well be extended as assistance in elucidating the constitution of vulcanized rubber. Another illustration is the use of infrared spectra or Raman spectra to determine the types of chemical bonds present in rubber. The other direction in which a study of the optical properties of rubber may lead is toward the direct solution of practical problems without regard for the theoretical significance of the measurements. Problems of control or analysis might be approached in this manner, since optical methods usually require only small amounts of material, and are often easily adaptable to rapid and precise measurements. Such applications have already been illustrated in preliminary form by the use of refractive index to determine amounts of combined or dissolved sulfur. The solution of practical problems by optical methods is also illustrated by the use of the photoelastic method for the analysis of stresses in rubber. Optical measurements in the past have been restricted in most cases to samples having fairly high light transmission. On this account the work has included only unvulcanized rubber and vulcanized compounds of the “pure gum” type. By the use of very thin sections or by employing methods which are based on the reflection of light rather than its transmission, it should be possible to extend the measurements to many practical rubber compounds which appear to be opaque, but which in reality are dispersions of filler particles in a matrix of transparent rubber.

An experimental investigation has been made of the initial focusing of ions from capillary sources of the diffusion type described in the previous paper. The lens system used consisted of a 90‐degree cone at the ion source followed by three coaxial cylinders which were arranged at various potentials up to 25 kilovolts. Since the beams are rendered slightly luminous by traces of gas in the high vacuum region, they have been studied by a photographic method. The beams have also been studied by an electrical scanning method. Both types of investigation were made as functions of the electrode potentials and arc variables and are in good agreement. Based on these observations a focusing and canal arrangement suitable for differential pumping has been tested. This arrangement has been embodied in a design for a projected ion gun assembly.

International audience; The settlement of soils under load is caused by a phenomenon called consolidation, whose mechanism is known to be in many cases identical with the process of squeezing water out of an elasticporous medium. The mathematical physical consequences of this viewpoint are established in the present paper. The number of physical constants necessary to determine the properties of the soil is derived along with the general equations for the prediction of settlements and stresses in three‐dimensional problems. Simple applications are treated as examples. The operational calculus is shown to be a powerful method of solution of consolidation problems.

Carefully prepared test bars of 17S‐T aluminum alloy have been fatigued; x‐ray diffraction patterns of each specimen were taken at intervals as fatiguing progressed. Approximately thirty different test bars have been studied. Seven series of diffraction patterns, corresponding to seven different specimens, are reproduced and discussed in this paper. This study shows that (1) fatigue failure of 17S‐T aluminum is always preceded by fatigue damage which is detectable by the use of x‐ray diffraction patterns; (2) nearly all of the detectable changes occur in the last stages of fatiguing and consist of rotation of grains, introduction of strains in some of the crystallites, and fragmentation of some of the crystallites; (3) these changes do not occur when the specimen is fatigued below its endurance limit, but always occur prior to failure when it is fatigued above the endurance limit; (4) failure is probably intercrystalline rather than intracrystalline in character.

A fast moving electron strikes a target—an x‐ray is born. This paper leads one from this simple fact to the most advanced sealed‐off tubes with air or liquid cooling, rotating targets, as well as demountable tubes of both vacuum and gas‐filled types.

The reaction of hydrogen selenide and pigment zinc oxide at room temperature has been investigated, using electron and x‐ray diffraction as a means of examining the reaction product. It was found that hydrogen selenide reacts with zinc oxide to form zinc selenide as a coating around the zinc oxide particles. After approximately one‐tenth of the zinc oxide is converted to zinc selenide by this surface reaction, the resulting coating of zinc selenide prevents the continuance of the reaction. Since the effective depth of penetration of electrons under the conditions of electron diffraction is much less than the average diameter of the pigment particles used in this investigation, the electron diffraction photograms necessarily arise largely from the particle surfaces. For this reason electron diffraction was successfully used to demonstrate that the reaction proceeded in the manner described. The paper illustrates the applicability of electron diffraction to the general problem of the examination of the surfaces of pigment particles.

There are two fundamentally different methods of correcting calorimetric data for heat losses to surroundings. The first method, applicable only to experiments in which the supply of heat to the calorimeter can be neglected after a certain time, uses the afterperiod cooling curve, together with a similar curve from data taken before the heat supply started, to evaluate appropriate correction terms. This problem is discussed from a general point of view and correction formulas previously reported by Regnault and Pfaundler, Schultes and Nubel, Roth, and others are shown to be variations of a general scheme. A second method is needed in such experiments as the measurement of specific heat when it is not safe to neglect the heat supplied by the hot body even after a very long time. In this case, there is no afterperiod cooling curve and additional assumptions concerning the heat exchange between the calorimeter and the hot body within it must afford the needed information. The assumptions originally suggested by Rowland are re‐examined. It is shown that previous investigators (Rowland and Hoare) deduced inadequate correction methods from these assumptions. A better method is developed and a simple approximation of it is suggested. Application of the new method to a set of data gives results different from those obtained by the Rowland‐Hoare methods, from those obtained by the Regnault‐Pfaundler method (which, despite previous use, should not be applied to such data), and from those obtained by the method of Dickinson (which is recommended by the ASTM standards). The differences are significant in precision work. A brief critical review of graphical methods of obtaining the temperature correction concludes the paper. This review includes a graphical analog of the new method mentioned above.

Buildings such as churches and auditoriums that are not continuously heated need larger heating plants than continuously heated buildings because of the large transient heat currents that must be supplied to the cold walls while the temperature of the building is being raised. The present unsatisfactory practice is to estimate the magnitude of these currents by various unreliable empirical methods. The purpose of this paper is twofold. First, for simple exterior walls, an equation is derived by means of which tables can be computed that will make rapid and reliable determinations possible. Second, the equation is put into such a form that the actual calculation of the tables can be carried out by N. Y. A. boys whose services can be obtained without cost. The unidirectional heat flow equation is solved for the boundary conditions that the outdoor temperature remains constant, the temperature of the wall is constant previous to time t=0, and after that time a constant heat current is applied to the wall. Th...

This paper does for simple interior walls and furniture what the previous paper did for simple exterior walls. Unidirectional heat flow is assumed and the boundary conditions are simpler than for the simple exterior wall so that the solution is easily expressed in the form of a formula. The treatment of the interior surface resistance as a constant quantity is justified.

Starting with the set of linear equations that determine the complex currents of a general n‐mesh circuit, a method is presented for the numerical solution of the equations to determine the various mesh currents of the system.The method presented has computational advantages over the conventional methods usually used in that only real numbers are involved in the various numerical operations and only the evaluation of second‐order determinants is involved. The operations required are those of matrix multiplication and are most conveniently performed with a calculating machine. The paper is concluded by the solution of a general Y‐Y circuit with a neutral return as an example of the method presented.

This is a continuation of the work reported in 1934. The greater part of the paper is devoted to a discussion of the properties of iron‐nickel‐cobalt alloys, especially the composition Fe 54 percent, Ni 31 percent, Co 15 percent—called fernico—including sensitiveness to impurities and polymorphism. Three new glass‐metal combinations are described, the metals being 42 percent nickel‐iron, 26 percent chromium‐iron, and pure iron, respectively. The strength of the glass‐metal bond is discussed briefly.

This paper describes the electrical characteristics of gas‐filled discharge tubes when flashed by a condenser discharge. The object of the experiments was to determine the effects of tube dimensions, pressure, voltage, and capacity upon the performance. The results are of an experimental nature and cover a limited range of values of tubes and circuit constants. An empirical constant called tube resistance is defined and evaluated. This constant is useful in predicting the performance of tubes in electrical circuits.

It has been proposed by P. Boning that the curve of the rise of continuous voltage due to the residual charge of a capacitor may be used for computation of the dielectric loss under alternating potential. The proposal has been examined in experiments on two types of capacitor, one with impregnated paper and the other with glass as dielectric. A reasonable agreement between measured and computed values was found for the glass capacitor. A wide divergence was found for each of the two impregnated paper capacitors and grounds are offered for the conclusion that the Boning proposal is not sufficient for certain types of dielectrics.

The problem of correcting calorimetric data for thermal leakage has been discussed by King and Grover in a recent paper in this Journal. From their analysis of the problem these authors have concluded that large errors are involved in the usual methods of correcting the data of bomb‐calorimetric measurements, and of experiments by the method of mixtures. In the present note it is shown, in agreement with W. P. White's treatment of calorimetric lag, that in the case of bomb‐calorimetric measurements the errors in question are practically completely eliminated by calibrating the calorimeter experimentally. Since experimental calibration of the calorimeter is the usual practice in modern bomb‐calorimetric measurements, the results of such measurements are not affected by the errors discussed by King and Grover. In the case of measurements by the method of mixtures these errors can be avoided by so conducting the experiment that the final temperature of the calorimeter will be very near the convergence temperature.

Straight analytic determination of the heat exchange by radiation in a device is possible only if the emitting and absorbing surfaces are very simple in shape and configuration. In most practical cases, and particularly if the radiation is partly absorbed on its way by gases, approximative calculations and graphical methods have been used in order to evade the mathematical difficulties. In the present paper an experimental model method with the following characteristic features is described. A model, similar to the device under investigation, is constructed. Light is used instead of the long wave heat radiation, and its absorption by photographic films which cover the surfaces of the model, is measured by the methods of photometry. The case of gases which absorb heat radiation is imitated by using liquids which absorb light rays. The application of the method to radiation through a non‐absorbing medium is shown by experiments on a tube bank model. The adaption of the method to heat radiation through absorbing gases is demonstrated by photos of the spectrum of a special combination of light filter, absorbing liquid, and photographic film which are in tune in a narrow wave‐length range.

The view is now generally held that in bars containing circular holes or other discontinuities the state of stress ceases to be two‐dimensional when the ratio of the radius of the hole r to the thickness of the bar t is less than unity. It is further believed that the factor of stress concentration in thick bars is materially smaller than in thin bars. This view also forms the basis for the doubts which have arisen regarding the reliability of certain theoretical work on stress concentrations produced by very small holes. In this paper results are reported from a photoelastic investigation using both elastic and frozen (see reference 4, Chapter 10) stress patterns and showing that the present point of view is erroneous. Experimental results show that no deviation from a state of plane stress can be found in bars with central circular holes when r/t is of the order of magnitude of about ¼ instead of unity. Experiments further show that the factors of stress concentration remain essentially the same in thick as in thin bars. The present work may also be taken as experimental corroboration of the theoretical value for the factor of stress concentration obtained by Neuber for a very small hole in a bar in tension or compression.

This paper covers the general methods employed in mass spectrometry, machine design, and possible sources of error in relative‐abundance measurements which are inherently associated with instrument design. Also included are graphs for determining the critical constants of the usual types of instruments.

THE formula for the inductance per unit length of two parallel conductors of rectangular cross section, obtained by using the formal expressions for the geometric mean distance of a rectangle to itself and the geometric mean distance between two rectangles with sides parallel, is exceedingly cumbersome. More than a score of logarithms and arc tangents must be evaluated when computing the inductance for a given conductor spacing and cross section. To circumvent such lengthy calculations when computing the reactance of like parallel rectangular strap conductors, Dwight1,2 has published curves, each plotted for a certain conductor spacing and cross section, from which the reactance can be obtained. Unless, however, the conductor spacing and the ratio of conductor thickness to breadth coincides with those values for which the curves are plotted, interpolation is necessary. Recently Roth3 has expressed the inductance of such lines in the form of a rapidly converging series, the parameters of which are the spacing and dimensions of the conductors. Usually, a few terms of this series suffice to yield a value of inductance sufficiently accurate for all design purposes. As regards rectangular tubular conductors, the only analytical literature is a paper by Dwight and Wang4 giving formulas for thin square tubular conductors. These are derived on the assumption that the conductor walls are so thin that the sides can be considered as but line segments. The geometric mean distances for such segments are then used to calculate the inductance. Such a procedure is equivalent to asserting that the current flows solely on the surface of the conductors. It follows, then, that the values of inductance computed on this basis will be less than the actual values. Consequently, while these formulas suffice for many calculations on square tubular conductors, if accuracy is a desideratum of design this minimization of thickness restricts the range of application of these formulas to very thin square tubular conductors. Recognizing this restriction and noting, further, that commercial conductors have rounded corners, Dwight and Wang give formulas, empirically deduced, from which corrections for thickness and for rounded corners can be calculated.

The paper gives a description of some tests carried out in preparation for the construction and development of an apparatus for artificial atomic disintegrations. The problems involved are (i) the focusing of a beam of 10–30 kv hydrogen ions from a canal‐ray ion source (glow discharge type) and (ii) the behavior of a cascade acceleration tube of the Coolidge type. In particular it was necessary to know the efficiency of the latter, i.e., the ratio of output to input currents. The general properties of electrostatic focusing systems are first treated briefly, and adequate references are given to enable those interested in the problem to pursue the matter further. It is pointed out that in view of the aberrations present, the constants of our lenses cannot be accurately calculated and we have therefore concentrated our attention on presenting the results in a concise form. Several lens systems were used to focus the canal‐ray beams and details are given in tables. It was found possible to focus at least 50 ...

This paper, consisting of three parts, describes investigations made with the objective of developing a simplified, practical microscope of the type which yields magnified images of transparent specimens with a resolving power superior to that of the best light microscopes. The first part deals with the general problem of design, including the electron gun and the imaging lenses. A later part will describe a completed instrument embodying many of the results of the investigations.

The rate of removal of mechanical strain should follow Maxwell's first‐order law, but for glasses it has been found that the rate is proportional to the square of the birefringence. The present paper explains this in terms of the structural picture of glass. During annealing the stress optical constant of the glass, as well as its viscosity, undergoes a continuous change. Birefringence, therefore, is not a correct measure of the stress, and the Adams‐Williamson findings are only apparently in contradiction to the classical derivation of Maxwell.

A solution of the problem of Dirichlet for a two‐dimensional region that can be mapped conformally on a circle is given by the formula of Schwarz. This formula is specialized to yield a complete solution of the torsion problem of St. Venant, and it is demonstrated that the results obtained formally by R. M. Morris are deducible rigorously from the general results of N. Muschelisvili. It is shown that the solution of the torsion problem for a prism whose cross section is the inverse of an ellipse, offered by T. J. Higgins, can be obtained more easily by utilizing the method outlined in this paper rather than by following the procedure of R. M. Morris.

A review of the literature has shown that there was no reliable method of measuring the flow properties of fluids in the range of viscosity 106 to 1012 poises where the flow is ``generally viscous.'' The theory of the penetrometer has been developed in this paper to a point where absolute viscosities may be determined both for viscous flow (viscosity independent of rate of shear) and generally viscous flow (viscosity dependent on rate of shear). The new penetrometer method was checked (1) with the capillary viscometer for viscous flow using coal tar pitch, and (2) with the revised axially moving cylinder method for generally viscous flow using a high melting blown asphalt. For any one temperature, the flow properties of a generally viscous material are defined by the straight line relationship between log shearing stress and log rate of shear. From this relationship viscosity may be calculated at any desired rate of shear. The slope n of this line is required in the calculation of rate of shear both for t...

This paper describes a method for determining Fourier series coefficients from area measureurements on photographs of the function to be analyzed with the graph sheet formed into a series of semi‐cyclinders.

The cyclotron is in process of a metamorphosis from an academic luxury for nuclear physicists to an indispensable tool for applied science and industry. Tracer experiments with induced radioactivities have become invaluable for basic studies in other sciences and as a guide to engineering development in many industries. The radioactivities and neutron radiations themselves are being put to use in industry and in medicine on an ever increasing scale. The time is near when the use of the cyclotron as a production unit may even outweigh its further scientific usefulness. Cyclotron physicists, well aware of this trend, are eager to push the development of the instrument to engineering perfection. To further this effort, this paper evaluates available information which may aid in improving the efficiency, reliability, and output and in determining most economical sizes and designs of cyclotrons for large scale applications.