Volume 25, Issue 12, 01 December 1954
Index of content:
25(1954); http://dx.doi.org/10.1063/1.1702366View Description Hide Description
The nonlinear partial differential equation for heat conduction in an infinite cylinder with heat generated by a chemical reaction has been solved by means of an electronic differential analyzer. Solutions of the equations in dimensionless variable form have been obtained for a zero‐order heat‐release term and a first‐order heat‐release term. Altogether 162 solutions were obtained covering a range of activation energies from 10 to 20 kcal/mole. Empirical relations have been derived for the maximum temperature at the center of the cylinder as a function of the experimental variables involved. Also relations relating to the approximate completion of reaction in terms of the experimental variables were derived from the tabulated data. Several calculations were made to demonstrate the general nature of the numerical solutions.
25(1954); http://dx.doi.org/10.1063/1.1702367View Description Hide Description
Considerable noise voltages appear across sliding contacts mainly because of the fact that the current across the contact consists of a random series of short pulses, corresponding to the minute, fugacious conducting spots on the contact surface. The properties of this noise within a wide range of contact conditions (i.e., varying sliding speed and operating current) are analyzed theoretically and experimentally. Most of the observed noisecharacteristics can be explained by various thermic phenomena in the contact interface. Several basic ranges as to operating current and sliding speed may be distinguished, each dominated by a different mechanism.
25(1954); http://dx.doi.org/10.1063/1.1702368View Description Hide Description
A number of investigators have reported that the apparent electric strengths of straight‐chain hydrocarbon liquids increase in a regular manner with increasing molecular chain length. In a recent publication we have presented evidence that this phenomenon is an illustration of a kind of Paschen's law for liquids. An observed linear dependence of the electric strengths of such hydrocarbons upon density suggested that chain length variation merely provided a means of changing the electron mean free path in the liquid.
In the present paper we describe the development of an improved technique for measuring electric strengths of liquids, and the application of this technique to a series of pure straight‐chain and branched‐chain liquid alkanes. As had been observed previously, the strengths of the straight‐chain members of the series exhibit a linear relationship with density. The introduction of branches into the hydrocarbon chain, however, results in a definite decrease in strength. Extension of the measurements to hydrocarbons of more complicated structure has apparently introduced a kind of fine structure.
Measurement of the time dependence of electrical breakdown in liquid hydrocarbons shows that the formative time lag is relatively insensitive to changes in viscosity or molecular weight. For an electrode separation of 0.002 inch, it is approximately one microsecond.
25(1954); http://dx.doi.org/10.1063/1.1702369View Description Hide Description
The history of experimental and theoretical investigations of water vapor condensation phenomena in supersonic nozzles is reviewed. It is then shown empirically for a given experiment that the shocklike disturbance visible in flow pictures delineates the collapse of the supercooled state of the water vapor present in the air. All flow properties are calculated through this extended condensation zone from pressure distribution measurements, and it is seen that no shock waves are involved in the process. Finally a conversion of these data to an equivalent constant‐area flow reveals that the latter would be an example of a weak detonation observed in nature as predicted by Burgers and by Reed.
25(1954); http://dx.doi.org/10.1063/1.1702370View Description Hide Description
A proposed method of determining average underground formation characteristics by means of short‐time tracer injection has been investigated both theoretically and experimentally. Streamline travel times for the passage of either an ideal gas or an incompressible fluid through a homogeneous permeable formation, from an injection well to a production well, have been calculated using an electronic digital computer. With only minor modifications, the methods of solution employed could be used in the investigation of more complex well systems. For a fixed ratio of injection well pressure to production well pressure the streamline travel times, expressed in terms of a dimensionless time parameter θ, are approximately independent of the well spacing to well radius ratio. A procedure has been devised for predicting the produced tracer concentration as a function of time using the calculated streamline travel times. Preliminary field tests indicate that the short‐time tracer injection method is of practical value, but that additional study is necessary before the method can be used most advantageously.
25(1954); http://dx.doi.org/10.1063/1.1702372View Description Hide Description
An equivalent circuit is proposed for a linear, passive, nonreciprocal, four‐terminal network. It introduces an ideal amplifier and phase shifter. It is shown that the proposed equivalent circuit has certain advantages over equivalent network representations that use gyrators. In particular, standard measuring techniques used on reciprocal networks lead directly to the determination of six elements of the equivalent circuit. One additional measurement gives the remaining two parameters.
25(1954); http://dx.doi.org/10.1063/1.1702373View Description Hide Description
A picture of the early stage of graphitization of a carbon black has been obtained from an x‐ray study of a Fine Thermal (FT) carbon black heated for two hours at 2300°C. Nearest neighbor pairs of layers take on the graphite relation independently, producing both ABA and ABC sequences. There are two nearest neighbor layer spacings 3.35 A and 3.44 A corresponding to pairs with the graphite relation and pairs with random orientation. The (00l) peaks must be corrected for the distortion broadening resulting from the two spacings, to obtain the parallel layer group thickness Lc . The probability for the ordering of nearest neighbor layers P 1 is defined as the ``degree of graphitization.'' A logarithmic plot is used for a rapid determination of P 1 and the layer diameter La from the modulated two dimensional (hk) reflections.
25(1954); http://dx.doi.org/10.1063/1.1702374View Description Hide Description
A definition of passive linear network is made:
(a) The network is linear.
(b) If currents of any wave form are fed to the terminals of the network, the total energy delivered to the network is not negative.
(c) No voltages appear between any pair of terminals before a current is fed to the network.
When this definition is applied to two terminal networks, i.e., impedances, a necessary and sufficient condition that a two‐terminal network be linear passive is that its impedance function be a positive real function.
An analysis of multiterminal networks yields as a necessary and sufficient condition from the foregoing hypotheses that a certain Hermitian quadratic form be positive definite. In the case of three‐terminal networks, it reduces towhere Rij +jXij =Zij are the terms of the matrix of impedances of the network. The relation of this formula to similar but not identical formulas of Gewertz and Llewellyn, and other consequences of the condition, are discussed.
25(1954); http://dx.doi.org/10.1063/1.1702375View Description Hide Description
From theoretical considerations of the fluctuations in an electron beam, an expression for the noise figure of a transverse‐field amplifier is derived. There are found to be three statistically uncorrelated sources of noise in the beam of such a tube—(1) that arising from the fluctuations in the transverse emission velocity of electrons in a direction normal to the surface of the beam, (2) that arising from fluctuations in the transverse emission velocity of electrons in a direction parallel to the surface of the beam, and (3) that arising from fluctuations in the mean position of the beam and depending on its thickness. The analysis shows that the use of a collimator is required to give low noise figures. This is illustrated by the following example: for a tube designed to operate at 1000 mc with a collimator whose width is 0.004 in., the theoretical noise figure is 2 db. Without the collimator, the noise figure would be 11 db.
Measurement of Temperatures in Flames of Complex Structure by Resonance Line Radiation. I. General Theory and Application to Sodium Line Reversal Methods25(1954); http://dx.doi.org/10.1063/1.1702376View Description Hide Description
Sodium line reversal temperature measurement by low resolving power spectroscopic instruments on complex flame structures gives temperatures intermediate between the highest and lowest temperature in the line of sight. This intermediate temperature is determined by the temperatures, optical depths and arrangement of the individual zones. By taking into account these factors, it is possible to derive temperatures for the inner zones of a complex flame. The theory, numerical data needed to apply the theory, and experimental examples are given.
Measurement of Temperatures in Flames of Complex Structure by Resonance Line Radiation. II. Sodium Line Reversal by High‐Resolution Spectroscopy25(1954); http://dx.doi.org/10.1063/1.1702377View Description Hide Description
Sodium line reversal temperature measurement by low resolving power spectroscopic instruments on complex flame structures gives temperatures intermediate between the highest and lowest temperature in the line of sight. An apparatus is described which was designed especially for determining the temperature structure in a complex flame by a modified sodium line reversal technique. Experimental data testing the validity of the method and a description of how it may be applied to complex flames is given.
Measurement of Temperatures in Flames of Complex Structure by Resonance Line Radiation. III. From Absolute Intensity Measurements at High Resolution25(1954); http://dx.doi.org/10.1063/1.1702378View Description Hide Description
A method for measuringflametemperatures is described which requires the determination of the intensity and emissivity of the flame at wavelengths within the intensity contour of a resonance spectral line such as a D line of sodium. An experiment is cited to illustrate the method in which a Fabry‐Perot interferometer was used as the spectroscopicdispersion instrument. The emissivities were determined by comparing the brightnesses of the mirrored and unmirrored flame. The theory, procedure, and an example of using the method to find the temperature of a submerged zone of a flame are given.
25(1954); http://dx.doi.org/10.1063/1.1702379View Description Hide Description
Grain boundary penetrations of radioactive silver into copper bicrystals having a common cubic direction have been measured using an autoradiographic technique. Diffusion occurred along directions forming an angle φ=0°, 45°, and 90° with the common cubic direction. For very low angles of disorientation Θ, no preferential intergranular penetration was observed; for low and intermediate relative orientations, grain boundarydiffusion was found to be most rapid along the common direction (φ=0°); for high angles of misfit, little anisotropy of boundary diffusion was detected. The observed asymmetry about Θ=45° of the curves of grain boundary penetration versus Θ is in agreement with the known dependence of the density of boundary dislocations on the angle between grains and on grain boundary direction. The anisotropy measurements may be qualitatively explained in terms of the distribution and relative amounts of elongated areas of ``fit'' and ``misfit'' in the grain boundary, and they confirm the earlier proposed model of grain boundaries in the region of angles where the simple dislocation model does not apply.
25(1954); http://dx.doi.org/10.1063/1.1702380View Description Hide Description
The method of Marcum for finding the probability density function associated with a pulsed radar with integration and a square law detector is extended to include the case of a randomly modulated sinusoidal signal. Two mathematical procedures are developed, the well‐known Edgeworth asymptotic series and a convergent series suggested by Varma. Sets of curves are drawn for probability of detection vs average signal‐to‐noise power ratio.
Some previous work has shown very high values for probability of detection resulting if it is assumed necessary to detect only one out of many pulses. Such probability levels are reduced if a slowly varying random amplitude of signal is postulated.
25(1954); http://dx.doi.org/10.1063/1.1702381View Description Hide Description
25(1954); http://dx.doi.org/10.1063/1.1702382View Description Hide Description
25(1954); http://dx.doi.org/10.1063/1.1702383View Description Hide Description
25(1954); http://dx.doi.org/10.1063/1.1702384View Description Hide Description
25(1954); http://dx.doi.org/10.1063/1.1702385View Description Hide Description