Volume 15, Issue 5, 01 May 1944
Index of content:
15(1944); http://dx.doi.org/10.1063/1.1707447View Description Hide Description
This paper is a continuation of a paper by the author entitled ``The Resolution of Boundary Value Problems by Means of the Finite Fourier Transformation: General Vibration of a String.'' A general boundary value problem of the transverse vibrations of a hinged beam was resolved into the solution of a pair of boundary value problems with much simpler boundary conditions. The finite sine transformation and its property of convolution were used to accomplish this. The transformedboundary value problem was solved by the introduction of a fundamental set of solutions of the homogeneous transformed problem.
15(1944); http://dx.doi.org/10.1063/1.1707448View Description Hide Description
15(1944); http://dx.doi.org/10.1063/1.1707449View Description Hide Description
Interference patterns resulting from a system of orderly arranged sources, whether they be radio, light, or sound waves, can be conveniently analyzed by the use of the exponential operator ej . This paper illustrates the application of the exponential operator in the development of the equation for the general antenna array.
15(1944); http://dx.doi.org/10.1063/1.1707450View Description Hide Description
The methods of determining object thickness in electron microscopy are briefly reviewed. Uncertainties in interpretation of surface replicas from a consideration of intensities alone are discussed and three different replicas of etch figures in pure aluminum are presented. The stereoscopic method is analyzed and an equation is derived relating the parallax of image points in stereo micrographs to the elevations in an object. This equation is the parallax equation of aerial photography but written in the form,where σ is the stereo angle and M the total magnification. The equation is experimentally verified utilizing the cubic etch figures of aluminum. Elevations in the range 0.1–2μ can be determined to within 10 percent and frequently with greater accuracy. A new cartridge for obtaining stereo micrographs at an angle of 10° is described and thicknesses as small as 150±50A are measured using this cartridge. Examples of the use of stereo micrographs are given illustrating different orientations of pearlite in steel and the scratches on a polished steel surface. Elevation changes of 200A and less can be measured in the silica replica of the polished surface. The theoretical resolution of the stereo method is given by,where ω is the resolution normal to the optic axis and σ is the stereo angle.
15(1944); http://dx.doi.org/10.1063/1.1707453View Description Hide Description
Extreme values for the negative pressures and the degrees of superheat which water will withstand without forming bubbles are contrasted with the ease of forming bubbles by vibration or by the turbulent flow of liquids. The subject of bubble nuclei is briefly reviewed, and it is pointed out that such nuclei usually function by virtue of sorbed or trapped air which can be removed, rendering the nuclei ineffective. Technique for avoiding extraneous bubble nuclei is presented with some experiments on the formation of bubbles by mechanical action. It is pointed out that free vortices in liquids produce sufficient tension to rupture the liquid, and it is suggested that mechanical disturbance produces bubbles only in such vortices and not by general pressure lowering in sound waves.
15(1944); http://dx.doi.org/10.1063/1.1707454View Description Hide Description
Thermal and electrical conductivities of graphite and carbon were measured at various temperatures in the range between −191°C and 100°C. Thermal conductivity of graphite was found to increase at an increasing rate as the temperature was lowered and two values were always found for Acheson graphite, a longitudinal and transverse conductivity, the latter being about ½ the former. This effect has not been reported for artificial graphite although Wooster reported an anisotropy in natural graphite with respect to thermal conductivity, the values along the axis being about four times that at right angles. X‐ray patterns give no evidence of crystalline alignment in Acheson graphite and the explanation of this anisotropy has not been found. The electrical conductivity of graphite increases with rise of temperature as contrasted with the decrease of the thermal conductivity with temperature rise. Thus the Wiedmann‐Franz law does not hold, nor is the Lorentz number a constant. Carbon shows no anisotropy. The thermal and electrical conductivities both increase with temperature rise, the thermal conductivity linear, in the temperature range −191° to 100°C.