Volume 18, Issue 12, 01 December 1947
Index of content:
18(1947); http://dx.doi.org/10.1063/1.1697587View Description Hide Description
The bird navigation theory as presented implies an organ or organs in the bird's physiology which are sensitive to the effect of its motion through the vertical component of the earth's magnetic field and to the effort exerted to overcome the coriolis force, due to the earth's rotation. Both these influences involve a set of lines which together form a navigational gridwork. By correlating its instantaneous land speed with the two above effects, a bird can fly to its home which is a unique point in this gridwork, or to related companion points existing in the gridwork at positions other than its home. Experimentation with homing pigeons between the home and spurious home points (conjugate or companion points) has yielded data which supports the theory.
18(1947); http://dx.doi.org/10.1063/1.1697588View Description Hide Description
This paper presents an extension of the method of inversion to certain electromagnetic problems and rectifies at the same time an error of long standing in the solution of an elementary problem which seems to have acted as a bar to just this extension.
If the image of a charge in a sphere is derived by the method of inversion, as is done in this paper, it becomes immediately obvious that the image of radially oriented dipole is another radial dipole plus a free charge proportional to the moment of the dipole. The potential caused by the free charge is not of negligible magnitude, and this indicates that the solution given by Sir J. Larmor and independently by S. P. Thompson and Miles Walker for the case of a magnetic dipole outside a sphere of infinite permittivity cannot be correct, for the image used therein consists of a simple dipole. However, it can be shown in addition that the latter image is not void of physical significance: the vector potential of such an image transforms in a simple manner and from this in turn follow simple laws of transformation for flux linked with loops and for mutual inductance between such loops.
This extension of the method of inversion is used in the second part of the paper to deal with a problem complementary to that of Larmor‐Thompson, namely, with that of a spherical wall impermeable to magnetic flux. This problem is of practical importance as an idealization of an inductor used at radiofrequencies and placed inside a metal screen, and it has for this reason been dealt with by direct attack on several previous occasions. It is shown here that the action of such a screen on the field produced by the loop can be replaced by the introduction of a simple image loop. From this follows then a simple way of calculating the change in self and mutual inductance produced by such a screen, even in cases more general than considered heretofore. The losses caused by the screen can also be easily calculated by the use of H. A. Wheeler's concept of equivalent magnetic skin thickness.
18(1947); http://dx.doi.org/10.1063/1.1697589View Description Hide Description
Attempts to analyze stress‐strain‐time relationships observed in experiments with textile fibers have been reported in a series of papers. This work has led to some general conclusions: First, the simplest three element model (spring in parallel with another spring and a dashpot in series) is adequate for the approximate explanation of a wide range of the data obtained. Second, the viscous element (dashpot) almost always appears to be non‐Newtonian while the springs less frequently are non‐Hookean. Third, the most striking deviations from simple behavior indicate, not a more complex model consisting of many simple elements, but that the assumed laws governing the viscous, or less frequently, elastic elements are themselves too simple.
Frequently a more complex law or laws will restore the three‐element model to approximate agreement with the experimental facts. Finally, any system so far investigated can be made to show the presence of a number or a distribution of relaxation times by prolonging the experiment over a period of time, or more positively, by going to a point of no instantaneous relaxation, and waiting for the inevitable long period of relaxation to appear. Procedures to deal with the general situation described here are presented.
The paper begins with a condensed but essentially self‐contained summary of the theoretical portions of the series of papers that preceded it. The original presentation has been clarified and recast in a form more in harmony with the present work. For experimental evidence, and supplementary information, the reader is referred to the original series.
The paper continues with a discussion of the various aspects of non‐linear viscouselasticity, including the topics: Six rules for analyzing stress‐strain curves (presented at the meeting of the Division of High‐Polymer Physics of the American Physical Society, January 31, 1947); the thixotropic viscous element, where for convenience, complex situations, in which the populations of various states enter into a time‐variable viscosity, have been gathered under the name ``thixotropy''; constant force springs, where a particularly non‐Hookean behavior is described.
18(1947); http://dx.doi.org/10.1063/1.1697590View Description Hide Description
The present exposition deals with the fundamental multiplet spectrum of a multi‐sectorial cavity or vane‐type magnetron and specific applications involving the evaluation of the π‐mode wave‐length thereof. The consequence of mutual coupling between the sectorial cavities through the interaction space of an infinitely long anode is evaluated for the linear case and subsequently applied to the cylindrical case. Although both the qualitative and quantitative results are reasonable in the limit for relatively very long anodes, in practice the latter are relatively short and since the mode separation, order thereof, and hence the component wave‐lengths are more or less influenced by the actual relative anode and end cavity lengths at each end of the anode, the results naturally differ from ``cold'' test data. Predictions of π‐mode wave‐length have been obtained to about 10 percent, depending upon the degree to which the parameters of the actual vane magnetron approximate the assumptions on which the present treatment is based. With the aid of ``cold'' test data the preliminary theoretically derived resonator geometry may be appropriately ``trimmed'' to produce the exact π‐mode wave‐length desired.
Included in this article is a discussion of the need and function of straps of the resonator system and dimensional scaling, which preserve certain desirable properties of the prototype at the new wave‐length, or operating point, in terms of magnetron performance‐chart parameters. Finally, in Part III, a brief consideration is allotted to the derivation of the rectangular cavity or slot‐type resonator system from the more general relation for the sectorial cavity in this article.
18(1947); http://dx.doi.org/10.1063/1.1697591View Description Hide Description
An analytical investigation is made to determine the influence on a vibrating elastic system of a high speed rotating element. A fundamental condition for the presence of any gyroscopic effect is that the vibration be such as to produce a tilt of the spin vector of the rotor. Equations are derived showing (a) that if precession be prevented, no gyroscopic effects are present, and (b), that if precession be permitted, the gyroscopic action contributes a force opposed to the tilt, and proportional to the angle of tilt, in effect increasing the stiffness of the elastic system. Calculations based on an arbitrarily chosen rotor intended to approximate a typical small motor armature indicate that this additive spring force is small, and that the increase in natural frequency caused by the added stiffness is exceedingly small—on the order of 0.1 percent—in the case where the precessional motion is not restrained.
18(1947); http://dx.doi.org/10.1063/1.1697592View Description Hide Description
A 2K50 microwave oscillator has been electronically coupled to the NH3 3,3 rotational spectrum line at 23,870 megacycles in such a manner as to maintain the frequency of the oscillator at the spectrum‐line frequency. The theory of the ``spectrum‐line discriminator'' designed to produce this frequency stabilization is developed.
18(1947); http://dx.doi.org/10.1063/1.1697593View Description Hide Description
The generation of electrical energy from thermal energy by thermoelectric means cannot be accomplished with thermocouples made of the available alloys generally used for temperature measurements, their efficiency being less than one percent.
A review of the theoretical efficiency calculations shows that higher efficiencies can be attained with thermocouple materials to which the Wiedemann‐Franz‐Lorenz relation is applicable, when their thermoelectric power is greater than 200 microvolts/°C. Some zinc‐antimony alloys with added metals approach the above conditions and have produced an experimental efficiency in excess of five percent, in accordance with the theoretical calculations.
The criteria of higher efficiency are applied to semi‐conductors, deriving the optimum conditions. Lead sulfide with excess lead was found to be the only suitable material at present, which in combination with the zinc‐antimony alloy produces an efficiency of seven percent.
Higher thermoelectric efficiencies can be produced only by developing new materials which can attain the theoretically required high values of thermoelectric power, low heat conductivity, and low specific resistance.
18(1947); http://dx.doi.org/10.1063/1.1697594View Description Hide Description
The following results have been obtained in an exploratory investigation of the cesium chromate pellets used in the manufacture of photo‐tubes: (1) hydrogen evolution or titration can be used to measure the yield of cesium with reasonable precision. Each method has limitations. (2) The theoretical yield could be obtained from cesium chromatesilicon pellets. (3) Within limits, the actual yield increases with the rate of heating; the maximum yield is not highly sensitive to composition in the range investigated. (4) No marked advantage was observed when titanium or zirconium was substituted for silicon as reducing agent. (5) An excess of hydrogen above the theoretical was consistently observed with nickel pellet holders, which points to a reaction of water vapor with reactive nickel formed during the heating and flashing of the pellet. The substitution of the less volatile molybdenum for nickel eliminated this difficulty. An excess of hydrogen was formed also when the reducing agent in the pellets was titanium.
It was suggested for purposes of further study that the complex process occurring when such pellets are induction heated be subdivided into two reactions of elementary silicon: (1) a preliminary exothermic reduction of hexavalent chromium, which initiates (2) a rapid reduction of monovalent cesium. The two reactions may proceed concurrently. This picture explains several observations made in the laboratory or in the factory.
- LETTERS TO THE EDITOR
Remarks on Some Recently Developed Devices for Summing Fourier Series for Crystal Structure Analysis18(1947); http://dx.doi.org/10.1063/1.1697595View Description Hide Description