Volume 23, Issue 1, 01 January 1952

A Vertical Shaft for the Production of Thick Artificial Clouds and for the Study of Precipitation Mechanics
View Description Hide DescriptionProgress in cloud physics has been seriously limited because of the impossibility of conducting controlled cloud experiments on a sufficiently large scale. To meet the requirements, a laboratory has been built in which thick artificial expansion type clouds may be produced under controlled and measurable conditions.
A mine shaft 0.210 kilometer deep and 2.2×2.2 meters in cross section has been sealed and adapted to the production of thick artificial clouds. The shaft and its principal auxiliaries necessary for the study of some of the basic problems of clouds and precipitation are described. Dense, thick clouds completely filling the shaft are now being produced on a routine basis. Some preliminary illustrative data are presented.

Mass‐Spectrographic Study of Ionic Reactions in Hydrogen
View Description Hide DescriptionAn analysis of the ratios of the di‐ and tri‐atomic ions of hydrogen, deuterium, and H—D mixtures obtained from a hot‐cathode arc discharge in a magnetic field was used to examine the nature of ionic collision and displacement processes. Ion mobility, and consequently the rate of ion‐molecule collisions, at constant pressure, were controlled by varying the intensity of the magnetic field. Statistical treatment of mass spectrograph data indicates that the formation of H_{3} ^{+} is due to the reactionand that the ion rather than the molecule undergoes dissociation on collision.

An Experimental Investigation of the Dielectric Rod Antenna of Circular Cross Section Excited in Rotationally Symmetrical Modes
View Description Hide DescriptionThe radiation patterns were measured for three series of dielectric rod antennas of circular cross section excited in the TM _{01} mode at a frequency of 9275 mcps. Only one parameter was changed in each series of rods so that the effect of this parameter on the pattern could be studied. Dielectricantennas excited in the TM _{01} mode have a null in the radiation pattern in the forward direction. It was found that maximum attenuation of secondary lobes was obtained using large diameter rods but sharper and deeper central nulls were obtained with small diameter rods. It was also noted that the deepest central null was obtained using a rod of uniform cross section. For uniformly tapered rods of various lengths, the maximum secondary lobe attenuation as well as the sharpest and deepest central null was obtained using the longest rod. The radiation patterns of the antennas excited in the TE _{01} mode were of the same nature as those obtained using the TM _{01} mode. Measurements were made also of the electric field strength on the surfaces of the radiating rods and these measurements were correlated with the radiation patterns.

The Collapse and Rebound of a Gas Bubble
View Description Hide DescriptionThe velocity and pressure field in a slightly compressible liquid resulting from the collapse of a spherical bubble is computed as a function of the pressure at the bubble wall, using the acoustic approximation. The results are accurate as long as the liquid velocities are small compared to the sonic velocity in the liquid; they agree with the results previously obtained by C. Herring.
The following bubble model is then investigated. The bubble is supposed filled with inviscid perfect non‐conducting gas; special emphasis is given to the gas motion which involves a series of shock waves. A fraction of the energy of compression is thus degraded so that the radius of the bubble after the first rebound is somewhat less than the original radius. The pressure variation at the bubble wall is virtually the same as if the gas were compressed uniformly and isentropically.

On the Empirical Law of Adhesive Wear
View Description Hide DescriptionCareful measurements have been made of the wear of rubbing steel surfaces as a function of load, distance of travel, and hardness under controlled conditions which eliminated the effect of all factors except adhesion. At normal pressures averaged over the apparent contact area which are less than one third the hardness of the softer material the amount of wear was found to depend linearly on the distance of travel and on the load but was independent of the apparent area of contact. At average pressures greater than one third of the hardness, the depth of wear varied linearly with the distance of travel, was independent of the apparent area of contact for a given average normal stress, but increased many fold for small increases in stress. These findings rationalize the familiar observations on the running‐in of machine surfaces. The results are discussed in the light of the current adhesion theory of dry friction.

Electromagnetic Resonant Behavior of a Confocal Spheroidal Cavity System in the Microwave Region
View Description Hide DescriptionThe resonance of a small spheroidal object in a large spheroidal cavity is investigated. This approximates the case of a thin needle‐like antenna in a large cavity. It is shown that this needle, if thin enough, shows marked resonantproperties, in that when the cavity is tuned to a resonant frequency defined by the needle, the magnetic field on the surface of the needle is greatly enhanced. This property can be used in a practical way, in measuring surface impedance of the material of which the needle is composed: at resonance most of the loss in the cavity is located at the surface of the needle and depends on the material of which it is composed.

The Structure of Sputtered Silver Films
View Description Hide DescriptionThe electron microscope has been used to study the structure of sputteredsilverfilms. When compared with evaporated silverfilms which are prepared at the same rate, the sputteredfilms are observed to have a more continuous structure. When compared with evaporated silverfilms which are produced at much faster rates, the sputteredfilms exhibit a crossover phenomenon in which the thinner films are the more continuous and the thicker films less continuous than evaporated films of the same thickness. These properties are in agreement with resistivity measurements. A possible explanation for the results is proposed.

Simulation of Trajectories of Charged Particles in Magnetic Fields
View Description Hide DescriptionA ball rolling on a rotating surface is shown to simulate the motion of a charged particle in a magnetic field. The theory is given for the case of a warped surface undergoing arbitrary rotation about a fixed axis and translation perpendicular thereto, while the system from which the ball is observed partakes of similar but independent motion. With approximations based on not too large departure of the surface from flatness, the following cases can be simulated: (a) The magnetic field is homogeneous and constant. The electric field is perpendicular to the magnetic field, and irrotational, but otherwise arbitrarily spatially dependent, and arbitrarily time dependent within certain limits. (b) The magnetic field is homogeneous but arbitrarily time dependent. The electric field is perpendicular to the magnetic field and may have a variety of space and time dependences, including a part which encircles the axis and has just the right magnitude to produce acceleration in a circular orbit as in the betatron.
Results of rudimentary experiments are presented which indicate that the method is capable of good accuracy.

The Supersaturation of Nitrogen in a Hypersonic Wind Tunnel
View Description Hide DescriptionTests in a small hypersonic wind tunnel have determined critical temperature and pressure conditions for the condensation of pure dry nitrogen and have indicated that in the range of pressure (0.5–2.8 mm Hg) and temperature (52°–64°R) obtained in the tests, there is a supersaturation of about 30 Fahrenheit degrees.

Investigation of Stress‐Strain Relations of Metal Wires by Electrical Resistance Changes
View Description Hide DescriptionA method is described by which the stress‐strain curve of a wire tensile specimen can be derived from measurements of its changes of electrical resistance as a function of strain. The method can be applied only to a selected group of metals that have experimentally been shown to be suitable. A material is suitable when its resistance changes per unit of elastic and per unit of plastic strain are each constant and different from each other. The method assumes uniform strain throughout the length of the specimen, which limits conditions studied to those prior to necking. Examples are shown illustrating the linear resistance‐strain relations and the applications of the method for several suitable materials. The resistance‐straincharacteristics of several materials that are not suitable are given, together with a statement of some mechanisms responsible.

Glass Cracking Caused by High Explosives
View Description Hide DescriptionHigh‐speed photographs have been obtained of the fracture of glass produced by the detonation of a high explosive charge. Using photoelastic methods, the shock waves set up in the glass can also be photographed. In addition to providing a high intensity loading method, the explosive also serves as a convenient time base for determination of the rates of propagation of shock waves and cracking.
The results presented in this paper extend those obtained by other investigators who used low energy impacts to produce fracture.

The M.I.T. Linear Electron Accelerator
View Description Hide DescriptionThe M.I.T. linear electron accelerator consists of a circular wave guide fitted with uniformly spaced irises, and sustains a standing‐wave, transverse magnetic π‐mode oscillation at a resonant frequency of 2800 Mc/sec. The phase velocity is equal to the velocity of light. Electrons are injected into the accelerating tube at an energy of 2 Mev by a standard Van de Graaff generator. Acceleration up to an energy of at least 18 Mev has been obtained, using the 21‐foot length of the accelerator. Peak accelerated currents of the order of 10 ma, and average currents of the order of 1 μa, are obtained. The accelerator is fed by 21 tunable magnetrons (Raytheon RK5586), phased in synchronism. In this paper, the principles of design, constructional features, and operation are discussed. The accelerator is now being used for nuclear experimentation.

Particle Dynamics in the Linear Accelerator
View Description Hide DescriptionHamilton's equations for the motion of an electron in a linear accelerator are integrated to find the final kinetic energy and phase of an electron injected with arbitrary initial kinetic energy and phase, after traveling down a fixed length of accelerator. The results are expressed in the form of a map of the initial energy‐phase space onto a final energy‐phase space. This map proves in practice to be very convenient for discussing the actual operation of the accelerator. The curves presented are calculated for numerical values appropriate for the M.I.T. accelerator.

Field Strength Measurements in Resonant Cavities
View Description Hide DescriptionIt is shown that the frequency of a resonant electromagnetic cavity is perturbed by inserting a metallic sphere, needle, or disk of dimensions small compared to a wavelength by an amount depending upon the local electric and magnetic field at the position of the perturbing object. This perturbation is calculated for ellipsoidal objects of needle‐shaped, spherical, and disk‐shaped form. The perturbations by the different objects depend upon different components of electric and magnetic fields, and by combining measurements with all three, it is in theory possible to measure all the field components. Experimental checks of the calculations are described, resulting in satisfactory agreement between theory and experiment except with the needles, in which the perturbation is very sensitive to the precise shape of the object, and the needles used were not accurate enough ellipsoids to give satisfactorily quantitative results.

Determination of Field Strength in a Linear Accelerator Cavity
View Description Hide DescriptionOne theoretical and two experimental methods are described for finding the accelerating field in the M.I.T. linear acceleratorcavity, in terms of the input power. One of the experimental methods is based on measuring the power leaking out through a calibrated hole in an end wall closing the cavity, the hole being located where the field strength is to be determined. The other method is based on the perturbation of the resonant frequency of the cavity by a small conducting sphere located on the axis. All three methods of determination check satisfactorily. In terms of the resulting relations, we discuss the probable field actually existing in the accelerator under operating conditions.

Forced Thickness‐Shear and Flexural Vibrations of Piezoelectric Crystal Plates
View Description Hide DescriptionAn approximate theory is given for the vibrations of piezoelectric crystal plates in thickness‐shear and flexural modes, including the interaction between the elastic and electric fields. The problem of the rectangular, AT, quartz plate is solved and computed frequencies are compared with measurements by Sykes. Algebraic formulas are obtained relating resonant frequencies with dimensions, elastic and electric constants, and orientation of cut.

The Thermal Dependence of the Elastic Moduli of Polycrystalline Graphite
View Description Hide DescriptionYoung's modulus and the shear modulus of grade SA‐25 molded graphite and grade AUF extruded graphite were measured as functions of temperature in the range from 25°C to 2000°C. In the case of the extruded material, variations of the two moduli with position and direction relative to the axis of extrusion were also investigated. The moduli were found to increase with temperature, a behavior in contrast with that exhibited by most materials. Maxima in the low frequency shear modulus values and increases in the internal friction of both graphites observed in the range from 1550–1750°C may possibly be interpreted in terms of grain boundary relaxation. The bulk modulus and Poisson's ratio at room temperature were calculated from the data for the nominally isotropic SA‐25 graphite to be 6×10^{10} dynes/cm^{2} and 0.27, respectively.

A Nonsteady Heat Diffusion Problem with Spherical Symmetry
View Description Hide DescriptionA solution in successive approximations is presented for the heat diffusion across a spherical boundary with radial motion. The approximation procedure converges rapidly provided the temperature variations are appreciable only in a thin layer adjacent to the spherical boundary. An explicit solution for the temperature field is given in the zero order when the temperature at infinity and the temperature gradient at the spherical boundary are specified. The first‐order correction for the temperature field may also be found. It may be noted that the requirements for rapid convergence of the approximate solution are satisfied for the particular problem of the growth or collapse of a spherical vapor bubble in a liquid when the translational motion of the bubble is neglected.

The Temperature Dependence of Viscosity for Water and Mercury
View Description Hide DescriptionSmoothed values for the viscosities of water and mercury, as reported in the literature, show surprisingly large percentage deviations from the experimental data. Because water is frequently used as the calibrating fluid in viscometry, it was of interest to apply expressions, suggested by the theory of Eyring, for smoothing experimental data. It was of further interest to apply the Arrhenius expression for the variation of viscosity with temperature to the data for both water and mercury and to compare the closeness of fit with that obtained by the use of the aforementioned expressions. As judged by the Gaussian criterion of fit, an expression suggested by the Eyring theory provides smoothed values for the viscosities of both water and mercury which are believed to be more reliable than those in common use. This is especially true for the viscosity of water, for which relative viscosity data were first smoothed and then pinned to the recent value of 10.019±0.003 millipoises at 20°C as reported by Swindells and Coe.
From other empirical equations relating densities and energies of vaporization to temperature, equations are derived for expressing the activation energies for viscous flow as a function of temperature.

Instantaneous Power Spectra
View Description Hide DescriptionThe intuitive concept of a changing spectrum is discussed. The instantaneous power spectrum is defined mathematically and used to make the intuitive concepts more precise. It depends upon the past history of a signal, but not upon the future.
Integration of the instantaneous power spectrum over time yields the conventional energy spectrum. The instantaneous power spectrum of a random function may be averaged over the ensemble of functions, with a resulting stochastic average instantaneous power spectrum that is equal to the conventional time average power spectrum of a stochastic process.