bluuebunny/crossref_metadata_2025 huggingface dataset:
The Accuracy of Lumping in an Electric Circuit Representing Heat Flow in Cylindrical and Spherical Bodies
Authors: Paschkis Victor , Heisler Michael P.
Published: January 2005

In using lumped resistance-capacitance circuits for studying heat conduction problems the influence of number and size of lumps is important. Several methods of lumping are conceivable for representation of cylindrical or spherical bodies and results of comparative tests show that equal geometrical size of lumps is most accurate. In the various lumps resistance and capacitance have to be in certain definite relationships, which are established in the paper. The influence of number of lumps is also investigated.
A Computer for Solving Linear Simultaneous Equations
Authors: Berry Clifford E. , Wilcox Doyle E. , Rock Sibyl M. , Washburn H. W.
Published: January 2005

The mathematical principles of the classical iterative method of solving linear simultaneous equations are discussed. Basic electrical circuits for setting up an analog of the mathematical relations are given, and a commercial model of a 12-equation computer is briefly described. The results of solving a number of problems on the computer are given to illustrate its accuracy and speed of operation. It is found that solving sets of 12 equations requires only 1/4 to 1/7 the time required by conventional methods.
The Thin Cylindrical Antenna: A Comparison of Theories
Authors: Middleton David , King Ronold
Published: January 2005

The solutions of Hallén's integral equation for the cylindrical antenna given by Hallén, Bouwkamp, Gray, King and Middleton are compared. Comparison is also made with the transmission-line theory of Schelkunoff and with experiment.
Preparation of Electron Microscope Specimens for Determination of Particle Size Distribution in Aqueous Suspensions
Authors: Cravath A. M. , Smith A. E. , Vinograd J. R. , Wilson J. N.
Published: January 2005

Small droplets of the suspension to be examined are deposited from a mist upon a specimen film whose surface has been treated to promote wetting by the droplets. This procedure makes the entire residue left by a whole droplet available for examination and promotes uniform dispersion of the deposit.
Elastic Properties of Cork. I. Stress Relaxation of Compressed Cork
Authors: Dart S. L. , Guth Eugene
Published: January 2005

The stress relaxation of corky materials is of theoretical significance for the understanding of such two-phase (corky material+air) systems, and is of great practical interest, since these materials are commonly used as gaskets, seals, etc. Stress relaxation was studied at various degrees of compression and at temperatures ranging from 30°C to 200°C. The experimental data were obtained from an automatic stress-relaxation machine which employed the principle of a chainomatic balance. It was found that the stress-time curves for various compressions could be obtained from each other by multiplication. This experimental fact is generalized by the statement that the stress is a product of two functions. The first factor is essentially identical with the S-shaped load-compression curve of cork and is independent of time. The second factor is shown to be a linear function of log t and is independent of compression. The linear stress-log time curve is found to persist over a wide range of times and to continue until the stress has decayed to zero at the higher temperatures. The decay time as obtained either by actual experiment or by extrapolation is shown as a function of temperature. This gives a fairly complete picture of the stress-time-temperature behavior of cork under compression.
The Formation of Ionized Water Films on Dielectrics under Conditions of High Humidity
Authors: Field Robert F.
Published: January 2005

When a dielectric is placed in an atmosphere of 100 percent relative humidity, an ionized film of water forms, whose conductivity at the end of one minute is within a factor of ten of its equilibrium value, which is usually attained within an hour. This equilibrium conductivity ranges from essentially zero for certain hydrocarbon waxes, silicone resins and silicone-treated glass to 100 micromhos for ordinary glass and quartz. The ionized water film also produces interfacial polarization at its interface with the dielectric, which produces a marked increase in both capacitance and dissipation factor at audiofrequencies. This polarization builds up in the same manner as the conductivity. Its relaxation frequency appears to be in the audio-range.
Thermal Polymerization of Drying Oils
Authors: Adams H. E. , Powers P. O.
Published: January 2005

A statistical analysis of the thermal polymerization of drying oils has been made, and equations have been derived which predict the amount of a specific polymer present as a function of the extent of reaction and the original composition of the oil. Several samples of oils have been heat bodied to test the validity of this analysis. Certain discrepancies are apparent. The presence of an intrapolymer is postulated to explain these discrepancies. Indirect evidence for the presence of such a compound is presented. Additional studies of the heat polymerization of drying oils have been made by conducting the polymerization in dilute solution. After the reaction has been carried out, the solvent is removed and the properties of the oils compared with oils similarly treated without solvent. It has been found that iodine values of the oils are substantially the same regardless of the concentration of oil, and depend only on the time and temperature of heating, but that the viscosity decreases with lower concentration of the oils. This behavior substantiates the formation of an intrapolymer. By using the values at various concentrations it may be possible to estimate the extent of intrapolymer formation in heat bodied oils.
Electrostatic and Tensile Properties of Rubber and GR-S at Elevated Temperatures
Authors: Havenhill R. S. , O'Brien H. C. , Rankin J. J.
Published: January 2005

This paper describes a new apparatus for measuring electrostatic contact potentials on various materials at elevated temperatures. In this apparatus, the electrostatic charge, acquired by rolling a steel ball down the surface of a rubber test specimen on a heated inclined plane, is measured when the ball drops into the cup of a suitable measuring device such as our electrostatic modulator. With this instrument the contact potentials of both rubber and GR-S was found to become highly negative at elevated temperatures. This apparent ``boiling off'' of electrons and resultant disruption of electrostatic attractive forces within the material is much greater for GR-S than for rubber and probably accounts for the much greater decrease in tensile of GR-S over rubber at elevated temperatures, and is further confirmation of the electrostatic contact potential theory of reinforcement. By the further application of this theory suitably dispersed compounding materials, which are in effect highly positive at elevated temperatures such as certain proteins, finely divided silica and sodium silicate, have been found to increase substantially the hot tensile strengths of GR-S compounds.
Significance of the Equation of State for Rubber
Authors: Guth Eugene , Wack Paul E. , Anthony Robert L.
Published: January 2005

The physical significance of stress-strain curves and of isometrics obtained by the relaxation method is discussed and clarified. Stress-strain curves taken at various temperatures give the correct dependence of stress upon temperature if they are taken sufficiently fast so that stress relaxation does not mask the temperature dependence. Isometrics obtained after previous relaxation of the sample are shown to depend upon duration and temperature of the relaxation by a numerical factor only. The basis for this behavior is the factorization of the stress into a factor depending upon extension and temperature only which corresponds to the equation of state and another factor depending upon the temperature T* and the duration of the relaxation process. For simple stress relaxation, the same factorization holds with T* equal to T. A general theory is formulated for time dependent elastic phenomena by generalizing Boltzmann's theory. The theory explains why factorization does not hold for creep, in agreement with experiment.
Crystallization of Unvulcanized Rubber at Different Temperatures
Authors: Wood Lawrence A. , Bekkedahl Norman
Published: January 2005

The crystallization and melting of unvulcanized natural rubber in the unstretched state have been investigated at different temperatures. Change of volume has been used as a quantitative measure of the extent of crystallization, and mercury-filled dilatometers containing the rubber have been used for the volume measurements. Crystallization was observed to occur at temperatures between −50° and +15°C and to be most rapid at about −25°C. The final decrease of volume on crystallization was usually found to lie between 2.0 and 2.7 percent. The melting of the crystalline rubber was found to occur over a range of temperature and to be strongly dependent on the temperature at which the crystals were formed. The temperature at which the beginning of melting occurs is from 4° to 7° above the temperature of crystallization. The range of melting is about 35° at the lowest temperatures and decreases to about 10° at the highest. The same range of temperature of melting is obtained regardless of the extent of the crystallization.
Tackiness of GR-S and Other Elastomers
Authors: Busse W. F. , Lambert J. M. , Verdery R. B.
Published: January 2005

The deficiency of GR-S in ``tackiness'' resulted in a great deal of work in the rubber industry to improve this complex property, but practically all the work had to be evaluated by qualitative ``hand tests'' because quantitative tests were not available. An analysis of the factors involved in the ``tackiness'' of various materials showed that different factors were critical in the so-called ``tackiness'' of rubber, paints, and varnishes, printing inks, adhesive tapes, etc. A quantitative test was developed to measure the effects of rate of removal on the adhesion or ``tackiness'' of pressure-sensitive adhesive tapes over a 106-fold range of rates. This showed why the results of standard ``adhesion tests'' of tapes do not predict the relative behavior of the tapes under small forces acting for long times. Another test was developed for the measurement of the ``tackiness'' of GR-S rubber which correlates well with the judgment of tackiness by hand tests and it even works reasonably well with rough samples taken from a laboratory mill. With this test, the effects of mastication conditions, aging, and of the addition of softeners and tackifiers on ``tackiness'' of GR-S (with and without carbon black) were studied. The German tackifier ``Koresin,'' which is now manufactured in this country, was found to be far more effective than rosin and similar materials formerly used, and gave a tackiness approaching that of natural rubber.
Applications of Infra-Red Methods in the Structural Examination of Synthetic Rubber
Authors: Field J. E. , Woodford D. E. , Gehman S. D.
Published: January 2005

The physical properties of a synthetic polymer are associated with variations in molecular structure which are dependent on the conditions of the polymerizing reaction and the monomers used. In some cases, structural differences of significance for physical properties cannot be detected by infra-red methods because the relative number of chemical linkages affected is too small. An important structural detail which can be followed by infra-red analysis is the relative amount of 1,2 and 1,4 polymerization occurring in polymerization reactions of butadiene. Absorption curves are reproduced to show the wide range in the relative amounts of these two structures. A description is given of an attempt to obtain a quantitative measure of this ratio by means of a calibration curve derived from known mixtures of pure octene 1 and octene 2. For polyisoprene, variations in the proportions of 1,4 and 1,2 or 3,4 structure also occur depending upon the type of polymerization. Comparison with Hevea rubber and Balata fails to disclose definite evidence of trans-isomerism in synthetic polyisoprene. Structural differences due to oxidation of polymers may be readily apparent in infra-red spectra, hydroxyl and carbonyl groups being especially prominent. The effectiveness of anti-oxidant in preventing structural changes caused by oxidation is shown in a series of absorption curves for samples of GR-S with and without anti-oxidant. When the samples were heat-treated in air, pronounced structural changes occurred for the sample without anti-oxidant, but no perceptible changes were evident for the sample with anti-oxidant. On the other hand, the anti-oxidant used (phenyl-β-naphthylamine) was ineffective for stabilizing the structure toward ultraviolet light.
A Photoelectric Instrument for Light Scattering Measurements and a Differential Refractometer
Authors: Debye P. P.
Published: January 2005

The method of determining particle sizes and molecular weights by light scattering measurements on solutions is finding increasing fields of application. In order to obtain the necessary data quickly and conveniently, an instrument has been developed which allows the required light scattering measurements to be taken on a routine basis. This apparatus is described. It measures transmission and the scattering of light at 90°; two different schemes can be employed to obtain the angular intensity distribution of the scattered light. A description is also given of a compensating refractometer which is used to determine the difference in refractive index of solvent and solution. The instrument, which is simple in design, gives a direct reading of the refractive index difference and has an accuracy of better than 10−5. The light scattering instrument has been tested using polystyrene of known molecular weight, and has been applied to study the change of apparent molecular weight (or particle size) of a series of polyvinyl ethers as a function of concentration in some cases, also a number of solvents. For a series of polyvinyl n-butyl ether samples which was studied, the relation between the intrinsic viscosity [ηi] of the benzene solutions and the weight average molecular weight M determined by light scattering is ηi = .365×10−7M1.45.
Thermal Expansion and Second-Order Transition Effects in High Polymers: III. Time Effects
Authors: Spencer R. S. , Boyer R. F.
Published: January 2005

It has been suggested that the so-called second-order transition in high polymers is not an equilibrium phenomenon, i.e., a true thermodynamic singularity, but rather a rate effect. Confirmation of this point of view has been obtained by determining the equilibrium volume-temperature curve of polystyrene. Such equilibrium curves exhibit no transition within the range of from 20° to 140°C, whereas the same material shows a transition at about 82°C for rates of heating usual in thermal expansion measurements. Two facts appear in agreement with the viscous flow interpretation of the thermal expansion process: First, two mechanis ms were found to operate, at markedly different rates. One gave almost instantaneous expansion, even at room temperature, whereas the other was quite temperature-dependent in this region, being extremely slow at room temperature. Second, the activation energy for the slower mechanism was found to be of the order of magnitude of that for viscous flow, considerably lower than the activation energy for rubber-like elasticity. Volume-temperature curves at finite rates of heating are discussed in light of these findings.
Parafocusing Properties of Microcrystalline Powder Layers in X-Ray Diffraction Applied to the Design of X-Ray Goniometers
Authors: Brentano J. C. M.
Published: January 2005

A distinction is drawn between the focusing properties of single crystals with regard to x-ray diffraction and the parafocusing properties of microcrystalline powder layers. A discussion of these parafocusing properties and of the absorption term, which arises in the diffraction of x-rays from powder layers, is followed by a discussion of various types of powder goniometers. Their characteristic properties are compared. The application of parafocusing conditions to the design of a goniometer for quantitative evaluations and of back reflection cameras is discussed in greater detail.
A Study of Oxide Cathodes by X-Ray Diffraction Methods: Part I. Methods, Conversion Studies, and Thermal Expansion Coefficients
Authors: Eisenstein A.
Published: January 2005

Two methods are described for obtaining x-ray diffraction patterns of oxide-coated cathodes. One method is used in the study of the conversion process in forming the oxide cathode while the other method is utilized in measuring the thermal expansion coefficients of barium, strontium, and thorium oxides. The conversion of an equal molar barium-strontium carbonate solid solution, (BaSr)CO3, involves (1) crystal growth in the carbonate, (2) decomposition to the mixed oxides, BaO and SrO, (3) formation of the oxide solid solution, (BaSr)O, and (4) crystal growth in the oxide. A similar sequence of events is observed in the conversion of a mixed carbonate, BaCO3+SrCO3. Crystal and particle size growth of carbonates and crystal growth of oxides are investigated and possible relationships are discussed.
Methods for Betatron or Synchrotron Beam Removal
Authors: Crittenden Eugene C. , Parkins William E.
Published: January 2005

Two methods for bringing out a partially collimated electron beam from a betatron or synchrotron are discussed. Both of the methods become easier as the size of the accelerator is increased. One method makes use of a perturbing magnetic field to focus the electrons as they are made to leave the field of the accelerator by means of orbit expansion. The other method makes use of a pulsed deflecting system where the deflecting field is applied during a time short compared to the period of revolution of the electrons.
A Graphical Method for Determining Particle Trajectories
Authors: Parkins William E. , Crittenden Eugene C.
Published: January 2005

A graphical ray tracing scheme is described which gives improved accuracy for tracing particle orbits of the type encountered in the cyclotron, betatron, and synchrotron. The method allows a large increase in scale factor by elimination of the necessity of a compass arm. The motion of the particle is deduced from the motion of a working point, related to the instantaneous center of curvature of the particle orbit.
Analyses of Mixtures of Light Gases by Infra-Red Absorption
Authors: Coggeshall Norman D. , Saier Eleanor L.
Published: January 2005

A discussion is given of the application of infra-red absorption methods of analysis for light gases which do not obey Beer's law of absorption due to pressure broadening. Some of these gases do not obey Beer's law in the pure state or when contaminated by foreign gases. The method of analysis depends upon the nature and intensity of the pressure broadening effect of the different components in the sample upon each other. Data are presented showing the nature of some of these effects and illustrating the accuracy obtainable for certain types of analyses. The instrumentation used in routine gas analyses by infra-red in this laboratory is described.
Methods of Minimizing Lead Loss in Emissivity and Resistivity Determinations
Authors: Malter L. , Langmuir D. B.
Published: January 2005

Two means are described for minimizing the effects of lead loss in determining the electrical properties of thin filaments as a function of temperature. In both cases the filaments are supported at the mid-points of filamentary U's. In one case the U's are made of finer wire than the main filament so that lead loss is reduced. In the other case, alternating current is passed through the U's so that the temperature of the main filament is maintained uniform down to its points of support.
Theory and Application of the Parallel Plate Plastometer
Authors: Dienes G. J. , Klemm H. F.
Published: January 2005

A method has been established for the measurement of the viscosity of high polymers at low rates of shear in the range 104 to 109 poises using a parallel plate plastometer. This is based on a mathematical criterion for separating the viscous portion of the deformation from the ``elastic'' and ``delayed elastic'' components. Experimentally, the plate separation is measured at a given temperature as a function of time. The theory furnishes a relation, which is also the criterion for predominantly viscous deformation, between viscosity, plate separation, applied load, and time. This relation, a modified form of Stefan's equation, is used for calculating the viscosity from the experimentally observed quantities. The method has been applied to polyethylene and vinyl chloride-acetate resin compounds. The viscosity-temperature behavior of these materials is shown to be simple over the temperature range studied; that is, log viscosity varies linearly with the reciprocal of the absolute temperature. Data are presented which show that polyethylene resins and polyethylene resin-paraffin wax mixtures follow Flory's relation; that is, log viscosity varies linearly with the square root of the weight average molecular weight. Accordingly, the parallel plate plastometer offers promising possibilities for the empirical determination of the weight average molecular weight of these materials. Data are also presented on plasticized vinyl chloride-acetate resin systems which point to a close parallel between the effects of increasing temperature and increasing plasticizer concentration.
Fatigue Failure of Rayon Tire Cord
Authors: Waller R. C. , Roseveare W. E.
Published: January 2005

Tire-cord fatigue tests are characterized and interpreted in terms of the following parameters: magnitude and frequency of the cyclic stroke, average load, minimum load, temperature, and humidity. By varying one test parameter at a time, it is shown that the effects of creep and degradation are minimized by using a high frequency and a high stroke. The relative rating of two samples of rayon depends on the parameters of the test and on the modulus and twist structure of the samples. Fatigue breakdown is interpreted in terms of progressive fracture under localized strains occurring at the peak stress of the cycle. A comparison of the fatigue behavior of rubbers, metals, and tire cord suggests they may all involve the same basic process of crack growth.
The Absorption of Microwaves by Gases
Authors: Hershberger W. D.
Published: January 2005

The absorption by ammonia of electromagnetic waves having a length in the one-centimeter range has been known for some years. An investigation has been made to determine whether other gases show similar absorption for microwaves and as a result fourteen additional gases have been found whose absorption is comparable to that of ammonia. Among these gases are dimethyl ether, a variety of amines and alkyl halides, and several others. Measurements on the absorption coefficient and dielectric constant of these gases taken at 1.25 cm at room temperature and a pressure of one atmosphere are given. The frequency at which the absorption coefficient attains its maximum value may be inferred from the curve: absorption coefficient vs. pressure. Data on the absorption of several gas mixtures are given. Possible molecular mechanisms adequate to account for the large absorptions observed are discussed together with the conclusions reached.
Pressure-Volume Relation for Cylindrical Tubes with Elastomeric Walls: The Human Aorta
Authors: King Allen L.
Published: January 2005

The general theory of the elasticity of elastomers as developed by James and Guth (reference 9) is extended and applied to cylindrical elastomeric tubes. Data obtained by Hallock and Benson (reference 4) on human aortas of several age groups are described rather well by the resulting equations. On the basis of this analysis an interpretation of the aging process for aortas is given.
Approximations to Planckian Distributions
Authors: Moon Parry , Spencer Domina Eberle
Published: January 2005

The use of Planck's equation in theoretical photometry and colorimetry has been hampered by the difficulty of integration. The following investigation attempts to eliminate this obstacle by replacing Planck's equation in the visible region by simpler expressions that are easily integrated. Two such approximations are employed—a three-term polynomial and the Wien function. Both allow analytic integrations to be performed with considerable ease and satisfactory accuracy. The method applies even in the weighted integrations of colorimetry: the standard weighting functions representing characteristics of the human eye are introduced in their analytic form and make possible the use of analytic methods in place of the unwieldy numerical approximations employed previously.
Approximate Calculation of the Range of a Winged Jet Projectile
Authors: Krzywoblocki M. Zbigmew
Published: January 2005

The purpose of this note is to discuss the possibility of launching winged jet bombs or mail-rockets on very long flights of perhaps 3000 miles, but the problem is considered from one standpoint only, i.e., that of mass ratio. There will be no discussion of the directional and stability instruments of a long distance winged jet projectile and the real mechanics of flight of such a unit, nor on various problems connected with winds, accuracy, etc. The problem will be treated in simplified form from the point of view of mass ratio at the beginning and at the end of flight. The simplified equations of 3 periods of flight are given: climbing, horizontal flight, and gliding. The simplifications introduced present a very rough approximation to the actual problem, but exact solution is not possible because of mathematical difficulties. A short example at the end of this note shows that the required mass ratio for a flight of 2000 or 3000 miles is high.
Design of Broad Band I.F. Amplifiers
Authors: Baum Richard F.
Published: January 2005

This paper deals with the design of broad band I.F. amplifiers with single tuned circuits in t stages. It is found that the figures of merit (Qn) of the individual circuits should be related to the Q of a reference circuit according to: Q/Qn=sin [(2m+1)π/2t]·ω0ω0n,  m=0,1,2,…(t−1). Then by proper tuning either an oscillatory or a monotonic response may be obtained. The relative band width BW/f0 and the gain tolerance d0 within the band determines the value of Q. The minimum number of stages for a given minimum attentuation in the cut-off region depends only on the gain tolerance and on the desired kind of response. Gain maxima (attenuation minima) appear at frequency deviations Δfnmin from middle band frequency f0 given by: 2Δfnmin/BW=cos [(2m+1)π/2t]. Their location depends only on the number of stages. The resonance deviations Δf0n of the tuned circuits are proportional to Δfnmin with a proportionality factor F dependent on t and d0. The circuit impedances are calculated from a prescribed gain or from the maximum attainable gain. A formula for the maximum gain band width product is derived. The result is extended to double tuned stages. A practical example is given.
The Relation between Nodal Positions and Standing Wave Ratio in a Composite Transmission System
Authors: Feenberg Eugene
Published: January 2005

Reflection generally occurs at a lossless transition region joining two uniform lossless lines. If the output line feeds into a matched load (no reflection) a standing wave ratio η0 different from unity exists on the input side of the transition region. If the output line is terminated by a movable short circuit, a relation exists between the nodal positions on opposite sides of the transition section. The relation can be used to determine η0 thus dispensing with the need for a calibrated detecting system to measure this quantity.
A Microwave Dielectric Loss Measuring Technique
Authors: MacLean William R.
Published: January 2005

Dielectric loss is measured by Q determinations of a resonator partially filled with the sample. Double sample technique is used to eliminate dominant spurious losses. Metal loss is reduced by confining field mostly to sample. Detuning for Q determination is accomplished by large movement of small rod. Detuning is calculated by action theorem.
Magnetically-Controlled Gas Discharge Tubes
Authors: Makinson R. E. B. , Somerville J. M. , Makinson K. Rachel , Thonemann P.
Published: January 2005

Discharge tubes are described in which a low pressure glow discharge is initiated by means of a magnetic field pulse. A tube has been developed in which a glow discharge so triggered leads to the formation of a cathode spot on a mercury pool; this tube will hold off 20 kv until fired and will then pass a current pulse of several hundred amperes. Its use in radar modulator circuits is envisaged.
Depreciation of Fluorescent Lamps without Passage of Current
Authors: Froelich H. C.
Published: January 2005

Fluorescent lamps with thin and with partial coatings of phosphor on bulbs of ultraviolet transmitting glass were irradiated with Hg 2537 radiation. Comparison with similar lamps which were burned showed a decline in lumen output which was of the same general character in all experiments, except for different time factors. This indicates that the process of lamp depreciation is fundamentally of photochemical nature, involving excited mercury, but not requiring either Hg ions or neutral atoms. It is assumed that superficial oxygen ions of the phosphor crystal react with Hg* to form links of the type-SiO-O-Hg-Hg..., thus tying mercury to the crystal with a resulting loss of phosphor brightness.
The Interpretation of Harker Syntheses
Authors: Buerger M. J.
Published: January 2005

An elegant way of studying the geometrical meaning of a Harker synthesis is to transform it into a diagram here termed the implication diagram. This is done by transformation of polar coordinates, the characteristics of the transformation depending on the number of operations in the cyclical group of the axial symmetry for which the Harker synthesis is prepared. The implication diagram has the important property that it is a map of the location of atoms in the crystal structure plus additional locations (ambiguities) which would give rise to the same Harker synthesis, plus satellitic locations. Fortunately the satellitic locations can be identified as such. Satellitic peaks are caused by powers of rotation operations and by reflections. Satellitic peaks occur in specialized locations which are discussed for the several cases. On the other hand, it is not generally possible to decide between ambiguities. An implication diagram which is a map of the crystal structure, with ambiguities, but without satellitic locations, exists for the following 18 of the 21 possible parallel-axial symmetries: P2, P21, C2, H3, H31, H32, R3, P4̄, I4̄, P41, P42, P43, I41, H61, H65, H62, H64, and H63. This is also true of certain axial symmetries combined with reflections, such as 2c and 3c. Only for the three axial symmetries P4, I4, and H6 do no implications exist without satellitic peaks. The implication diagrams of the Harker syntheses P(xy⅙) for the space groups H61, H65, H612, and H652 and for Harker synthesis P(xy0) for R3̄ lack both ambiguities and satellitic peaks. For these space groups the implication diagrams are true maps of the crystal structure. Harker syntheses greatly exaggerate the electron densities of atoms in the structure, and for this reason their greatest usefulness lies in the location of the more compact atoms. Diffuse atoms, and therefore especially anions, provide Harker peaks of such low magnitude as to be often lost in the background. Background due to non-Harker interactions is discussed. An important characteristic of Harker syntheses, which is independent of any interpretation of their meaning with regard to the location of atoms in the crystal structure, is that they provide criteria for distinguishing space groups which cannot be distinguished in ordinary qualitative x-ray crystallography. This is because the Harker synthesis provides definite criteria for identifying reflection planes and rotation axes. It fails only to distinguish pairs of space groups which differ by a group of inversions alone. Harker synthesis thus realizes the ultimate possibilities of x-ray crystallography because it is quantitative.
Dissociation Energies of Surface Films of Various Oxides as Determined by Emission Measurements of Oxide Coated Cathodes
Authors: Jacobs Harold
Published: January 2005

A mechanism of falling emission in vacuum tubes is discussed. It is demonstrated that when an electron achieves a critical kinetic energy in moving from the cathode to the anode, and if the anode is an oxide, the electrons will cause a dissociation of the oxide. The liberated oxygen will return to the cathode and falling emission will result. The critical energy of the electron starting the dissociation is found to be equivalent to the heats of formation of the oxides bombarded in the case of five different oxides. Using this equivalence principle, the heats of formation of two compounds are found which have not been recorded in the literature, Ta2O4 and ZrO. In addition, the contact potential between barium oxide cathodes and seven various oxides are determined and the work function of the seven oxides computed.
An Experimental Investigation of Forced Vibrations in a Mechanical System Having a Non-Linear Restoring Force
Authors: Ludeke Carl A.
Published: January 2005

This paper introduces a mechanical apparatus capable of generating and recording forced vibrations in a system having a non-linear restoring force. The experimental wave forms are then compared with the theoretical results given by three graphical methods. These are the methods of Martienssen, Hartog, and Rauscher. Provided a suitable first guess for the amplitude can be made, one application of Rauscher's method gives better results than the other methods. A graph is made of the experimental amplitude as a function of the disturbing frequency. These results are compared with the theoretical results of the above three methods. Again one application of Rauscher's method gives satisfactory results. In all experimental results it is noted that even though the restoring force is distinctly non-linear, the wave forms of the resulting motion are nearly sinusoidal as long as the frequency of the observed motion is the same as the frequency of the disturbing force. However, steady oscillations can be maintained for which the observed frequency is a sub-multiple of the disturbing frequency. Two such subharmonics were recorded and the experimental wave forms are shown.
A New Method for Measuring Dielectric Constant and Loss in the Range of Centimeter Waves
Authors: Roberts S. , Von Hippel A.
Published: January 2005

In 1940, dielectric measurements in the centimeter range were considered as difficult and not very accurate. The authors, therefore, developed a ``hollow-pipe'' method which overcame these objections and required only a weak oscillator and small amounts of the dielectric material. The theory and its practical applications, as perfected by March 1941, are presented in this paper.
Interpolation with the Aid of a Plot of First Differences
Authors: Fulcher Gordon S.
Published: January 2005

Given the values of y−1, y0, y1, and y2 corresponding to x−1, x0, x1, and x2, we first plot Δy/Δx, the ratio of first difference to abscissa interval, as a function of mean abscissa x̄, and then draw a smooth curve through the graph points which gives the values of a function S(x̄). To determine the value of yp for any value of xp between x0 and x1, we substitute values of S(x̄′) and S(x̄″), obtained from the curve, in the following equations: y′=y0+fΔx·S(x̄′); y″=y1−(1−f)Δx·S(x̄″);yp=y′+(y″−y′)(1+f)/3; where x̄′=12(x0+xp); x̄″=12(x1+xp) and f=(xp−x0)/Δx. With a carefully drawn smooth curve, the error in the result is only about one-sixth of the fourth difference term in the Newton-Bessel interpolation formula. In a simpler variation of the method, the function L(x̄), whose values are given by straight lines connecting the graph points, is substituted for S(x̄) in the equations; however, the accuracy of the result is only about one-sixth. It is shown that the accuracy obtainable in any case can be estimated from the sagittas σ1 and σ0 for x̄ equal to x1 and x0, respectively, where σ1 = L(x̄1) − S(x̄1) and σ0 = L(x̄0) − S(x̄0), since the error is proportional to (y″ − y′) times (σ1 − σ0) / (σ1 + σ0). This is true for unequal datum point intervals as well as for equal intervals. When the sagittas are equal or approximately so, the results may be as accurate if the rectilinear variation is used. Taking advantage of this fact, a diagram is given which enables the logarithm of any number to be determined to eight places by substituting values of L(x̄), obtained by linear interpolation between given figures, in certain equations. The method has been found useful when a number of interpolations are required in a single set of data. An important advantage is that it can be used as easily when the abscissa intervals between datum points are unequal as when they are equal.
The Use of Color and Fluorescence Indicators for Determining the Structure of Glasses
Authors: Weyl W. A.
Published: January 2005

The fact that light absorption and emission depend on the environment of the ions and molecules which absorb or emit light can be used to draw conclusions about the structure of liquids, glasses, and crystals. This method supplements, to a certain extent, information gained from other sources, such as x-ray diffraction data. The method is illustrated by several examples, like the influence of thermal history on the structure of glass and the constitution of the yellow fluorescing zinc orthosilicate.
The Pulsed Properties of Oxide Cathodes
Authors: Coomes Edward A.
Published: January 2005

A survey of the results obtained in an experimental study of the pulsed properties of oxide cathodes is presented. Pulsed measurements reveal that unusually large electron currents are available in microsecond pulses, and that several other phenomena are modifications of the d.c. properties, namely (a) sparking and (b) pulse temperature rise. Sparking may be either current limited or voltage limited, depending upon cathode materials and life. The pulse temperature rise also depends upon materials and life and is indicative of the nature of the cathode resistance. Evidence for a layer structure of the oxide cathode can be drawn from pulsed data.
A Study of Oxide Cathodes by X-Ray Diffraction Methods: Part II. Oxide Coating Composition
Authors: Eisenstein A.
Published: January 2005

X-ray diffraction methods were used to investigate time changes which occur in the composition of oxide cathode coatings, initially equal molar (BaSr)O. Changes which occur in the composition of the bulk of the coating were detected by means of lattice constant measurements. A new method of analysis was developed to permit a determination of the variation of composition with depth below the surface. The bulk loss of BaO is primarily a function of the base metal used and the surface loss from the oxide is effected to a lesser extent. Possible correlations with thermionic emission are discussed.
Studies of the Interface of Oxide Coated Cathodes
Authors: Fineman A. , Eisenstein A.
Published: January 2005

X-ray diffraction patterns are presented as evidence for the existence of a crystalline ``interface'' compound between the base metal and the coating of the oxide coated cathode. Measurements of the coating resistance to microsecond pulse currents, made with imbedded probes, indicate the presence of an anomalous ``interface'' resistance between the metal and coating. The relative magnitude of the coating and interface resistances are shown as a function of current for various operating temperatures.
A Method for Preparing Rubber Latex Specimens for the Electron Microscope
Authors: Kelsey R. H. , Hanson E. E.
Published: January 2005

A new method was developed for preparing natural and synthetic rubber specimens for examination with an electron microscope. The technique consisted of mixing latex with a water solution of polyvinyl alcohol and forming a film from the mixture. Electron micrographs of such specimens showed none of the flattening of particles characteristic of the collodion film method and the micrographs were suitable for direct particle-size measurements.
Perturbation Theory of the Normal Modes for an Exponential M-Curve in Non-Standard Propagation of Microwaves
Authors: Pekeris C. L.
Published: January 2005

In this paper a perturbation method is developed for treating non-standard propagation of microwaves beyond the horizon in the case when the deviation of the M-curve from the standard (≡ the M-anomaly) can be represented by a term αe−λz, where z denotes height in natural units. Here M denotes the modified index of refraction of the air. The method is also applicable to other forms of the M-anomaly which can be derived from an exponential term by differentiation with respect to λ; in fact, in its region of convergence it is formally applicable to the most general type of M-curve, including elevated ducts. The region of practical convergence of the method ranges from highly substandard conditions down to cases where the decrement is a fraction of the standard value. The procedure followed is to express the height-gain function Uk(z) of the kth mode in the non-standard case as a linear combination of the height-gain functions Um0(z) of all the modes in the standard case: Uk(z)= ∑ m=1∞AkmUm0(z). The execution of this plan hinges on the possibility of evaluating the quantities βnm(λ)= ∫ 0∞Un0(z)Um0(z)e−λzdz. It is shown that βnm(λ) satisfies the differential equation dβnmdλ=22λ+βnm(λ).[−12λ+12(Dm0+Dn0)+λ24+14λ2(Dm0−Dn0)2],whose solution is βnm(λ)=12√λexp[λ2(Dn0+Dm0)+λ312−14λ(Dm0−Dn0)2]· ∫ 0λdx√xexp[−x2(Dm0+Dn0)−x312+14x(Dn0−Dm0)2]·Here Dm0 denotes the characteristic value of the mth mode in the standard case. For large λ the following asymptotic formula holds βnm=−2[λ3+2λ(Dm0+Dn0)−2+1λ(Dm0−Dn0)2]+8[3λ3+2λ(Dm0+Dn0)−1λ(Dm0−Dn0)2][λ3+2λ(Dm0+Dn0)−2+1λ(Dm0−Dn0)2]3·Having determined the βnm(λ) from (d), or by a numerical solution of (c), the characteristic values Dk and the coefficients Akm are to be solved from the infinite system of equations ∑ m=1∞Akm[(Dk−Dm0)δnm+αβnm(λ)]=0, n=1,2,3,…,where δnm denotes the Kronecker symbol. For this purpose a simple iterative procedure has been developed, which has been found to be rapidly convergent. The Akm are normalized by the condition ∫ 0∞Uk2(z)dz=1= ∑ m=1∞Akm2.[The integral ∫0∞Uk2(z)dz diverges when taken along the real axis; it converges, however, and to the same limit, when the path is a radial line in the fourth quadrant of the z plane. In the sequel, whenever an integral is divergent, it will be understood that the path is suitably modified.] One can also expand Dk as a power series in α Dk=Dk(0)+αDk(1)+α2Dk(2)+…,Dk(1)=−βkk; Dk(2)=eiπ/3 mβmk2(τm−τk),m≠k.An alternative expression for Dk(2) is given in Eq. (58).
Particle Size Determination from X-Ray Line Broadening
Authors: Birks L. S. , Friedman H.
Published: January 2005

The x-ray line broadening method of determining particle size was compared with direct measurement on electron micrographs. By controlled heating of the carbonate, magnesium oxide particles were prepared from 50 to 1000A in diameter. Particle size calculated from x-ray data taken on a Geiger counter spectrometer agreed to ±10 percent with the microscope measurements. Mechanical mixtures of two different sizes were examined by the x-ray method, but the particle sizes could not be determined unless the two maxima of the distribution curve were completely resolved.
Hysteresis and Related Elastic Properties of Tire Cords
Authors: Wakeham Helmut , Honold Edith
Published: January 2005

A method of evaluating mechanical hysteresis, elastic modulus, elongation, and growth rate of a yarn or cord subjected to cyclic loads in a fatigue test is described. The test is applied to seven typical tire cords-one Nylon, two rayon, and four cotton cords including both high stretch and low stretch cords. Results are presented showing the effect of cycle number, moisture content, temperature, and load range on the elastic properties of each of the cords tested. The influence of cyclic loading on the stress-strain curve is also discussed. It is concluded that moisture content is the dominant factor influencing the elastic properties of tire cords and that the heat produced by mechanical hysteresis of the tire cord contributes appreciably to the heat build-up observed in tires during heavy duty service.
Design of Broad Band I. F. Amplifier. Part II
Authors: Baum Richard F.
Published: January 2005

This paper is a continuation of a previous article on the design of broad band I.F. amplifiers of the stagger-tuned type. The analysis is extended to unrestricted band width. It is shown that an exact solution is possible for either an oscillatory or a monotonic response, with this result: 1. The necessary number of stages (t) for a given minimum attenuation in the cut-off region depends again only on the gain tolerance and the desired response. 2. Attentuation minima and maxima again appear at frequencies within the band, easily located and dependent only on the number of stages. 3. The amplifier consists of a number of pairs of circuits, which have the same figure of merit Qn and tune at resonant frequencies f0n disposed in geometric symmetry around the middle band frequency f0 thus making f0n equal to δnf0 and f0/δn, respectively. Formulas for Qn and δn are derived. The circuit impedances are calculated from a prescribed gain or from the maximum obtainable gain. A formula for the maximum gain band width product is given. A comparison is made between the performance of amplifiers with monotonic and oscillatory response. A practical example is worked out.
The Numerical Solution of Laplace's Equation in Composite Rectangular Areas
Authors: Frocht Max M.
Published: January 2005

An analytical method is developed which yields key values of a harmonic function U in rectangular figures in terms of certain simple combinations of known boundary values, which we call Laplacian perimeters and denote by P. From the key values all the remaining interior values can be directly and rapidly calculated. The basic ideas consist of the introduction of four elementary figures of variable lengths: 3(2+δ), 3(3+δ), 4(2+δ), and 4(3+δ), where 0≤δ≤1, for which the key values are found algebraically, Eqs. (9.1) to (9.8) inclusive, and of combining analytically these elementary cases to obtain continuous solutions for rectangles (3×n′) and (4×n′) for any number n′ greater than 2. The general expression for any key value (ui)m×n′ in a rectangle (m×n′) is (ui)m×n′=C1P1+C2P2+…CiPi+…Ckpk,in which C1, C2…Ck are constant coefficients. Analytical relations are established between the coefficients for the last key value uk in a rectangle (m×n), where n is an integer, and the coefficients for the next key value uk+1 in the rectangle m(n+δ) or m(n+δ+1). Specific values of the coefficients are presented in tabular form for rectangles (3×n′) and (4×n′) with the aid of which all key values in such rectangles can be rapidly calculated. The tables also permit the calculation of any one interior key value by itself. A numerical example and further approximate formulas are given, and applications to composite rectangular areas such as angles, channels, etc., are discussed.
Oscillation Conditions in Single Tuned Amplifiers
Authors: Faust William R. , Beck Hugo M.
Published: January 2005

An application of the calculus of finite differences has been made in obtaining the complete expression for the voltage gain of an n-stage amplifier having identical grid-to-plate impedances and plate loads when driven by a generator of any given internal impedance. An application of these results was made in determining the conditions of oscillation in a multi-stage amplifier using single-tuned circuits. It was found that there is a certain minimum grid-to-plate capacitance required to cause oscillation. If the actual grid-to-plate capacitances are below this value, the system will not oscillate. There also exists a region of stable gain, zero to 21/n, wherein it is impossible to make the amplifier oscillate even with grid-to-plate capacitance arbitrarily large.