摘要:

This is Part I of a systematic discussion of axially symmetric magnetic fields, both central and remote from the origin, search coils reporting the field or gradient at a single point, and mutual inductances. Here the central uniformity of symmetrical fields and gradients is analyzed by zonal harmonic expansion. Laplace's equation and symmetry restrict these fields to a few types, regardless of the detailed geometry of the generating system. Universal error‐contour maps are derived for the central field or gradient in systems having errors of second, fourth, or sixth order, and for hybrid types combining second and fourth. One hybrid has an oblate error field suitable for cloud‐chamber and orbital applications.Source systems include circular filaments, cylindrical or plane circular current sheets, and thick solenoids of rectangular or notched section. Each type of source may be designed to produce any of the field patterns. To this end, source constants derived for the particular source type are combined into a set of over‐all coefficients that express the field constants for a complete system. Rapid methods are given for computing the source constants and from them all the field derivatives, using recurrence relations or tables of Legendre functions. In particular, computing time for thick‐solenoid fields or gradients is greatly reduced, using a new series with a recurrence formula. The text includes tabular aids and reference formulas, and discusses the rate of convergence of series for central and remote fields, and for mutual inductances.Special systems briefly described include several infinite series of systems like that which starts with Ampere's loop, the Helm‐holtz pair, and Maxwell's three‐loop system. These have integral numbers of circular filaments from two to infinity. More practical are the thin solenoids. Those that produce a fourth‐order (Helm‐holtz) field by omission of central turns are fully tabulated for all lengths. A short solenoid with double‐wound ends and sixth‐order error may realize greater uniformity in actual practice than any previously described system. Still greater (theoretical) uniformity is achieved in two eighth‐order combinations of a short solenoid with a loop pair; these are described and depicted, with error limits.

ISSN:0021-8979    

DOI:10.1063/1.1700115

出版商:AIP    

年代:1951

数据来源: AIP

摘要:

Shannon's theorem about the capacity of a channel is discussed, and it is shown that the most efficient coding is the one yielding the most probable distribution of the code symbols. A specific rule is obtained for this most probable distribution. Most efficient coding is essential for communication channels or memory devices in large scale computers.

ISSN:0021-8979    

DOI:10.1063/1.1700116

出版商:AIP    

年代:1951

数据来源: AIP

摘要:

An integral equation for the current in an apex‐driven symmetrical V‐antenna is derived and solved by successive approximations. General formulas for the distribution of current and the impedance are obtained. The zeroth‐order impedance is evaluated for a leg‐lengthh=&lgr;0/4 as a function of the enclosed angle and used to estimate experimental results.

ISSN:0021-8979    

DOI:10.1063/1.1700117

出版商:AIP    

年代:1951

数据来源: AIP

摘要:

In the first part of this note the stress‐function approaches of Boussinesq and Timpe to the rotationally symmetric problem in the classical theory of elasticity are referred to general orthogonal axisymmetric curvilinear co‐ordinates. Although the underlying computations are of a routine character, it is felt that the presentation of the final results may serve a useful purpose. In the second part of the note, a connection between the two stress‐function approaches is established.

ISSN:0021-8979    

DOI:10.1063/1.1700118

出版商:AIP    

年代:1951

数据来源: AIP

摘要:

A new type of wave‐guide circuit element has been described that has a number of desirable electrical and mechanical properties. These include ease and accuracy of adjustment, and simple analytical expressions for some of the more important properties.The capacitive junction allows the practical construction of capacitively coupled resonant cavities. Such cavities have a relatively constant band width over their tuning range, as compared with the more commonly used inductively coupled cavities.

ISSN:0021-8979    

DOI:10.1063/1.1700119

出版商:AIP    

年代:1951

数据来源: AIP

摘要:

A study of the motion of electrons moving in the presence of crossed electric and magnetic fields is presented. Special electromagnetic regions are selected for discussion which assist in the controlling of electron discharge on positive ion sources when used with large mass‐spectrograph units. The article compares the components of motion parallel and perpendicular to the magnetic field in the following regions: uniform crossed electric and magnetic fields; electric field produced by nonparallel plane condenser plates, uniformHparallel to one plate; electric field produced by coaxial circular cylindrical condensers, uniform magnetic field normal to axis of cylinders; uniform electric field, circularly bowed magnetic field. The components of motion are expressed in terms of mathematical functions, and where it is deemed useful, additional results are presented in graphical form so that the conclusions can be applied with a minimum of calculations.

ISSN:0021-8979    

DOI:10.1063/1.1700120

出版商:AIP    

年代:1951

数据来源: AIP

摘要:

The capacity of the plates of an oscilloscope charged to 35 or 40 volts is discharged repeatedly by approaching electrodes of carbon, active silver, and inactive silver. Facts about the discharges, which are arcs of very short duration, are inferred from resulting open circuit potentials and calculated electrode separations.The separation at the first arc varies in different experiments but corresponds on the average to a nominal electric field of 0.6×106volts/cm for carbon or active silver and to 2×106volts/cm for inactive silver. Each arc is initiated by a very small number of field emission electrons. The hypothesis that a single electron may perhaps be sufficient is consistent with observations at later stages of each closure when the electrodes are closer and the field much higher.The earlier observation, that the potential across a short arc is constant and independent of current, is not true if the arc time is sufficiently short. For active silver a time comparable with 2×10−8sec is required to establish the steady arc voltage characteristic of later stages of arcs which last longer than this. The initial time during which the potential is decreasing toward its final steady value is 100 times the transit time of a silver ion across the gap.

ISSN:0021-8979    

DOI:10.1063/1.1700121

出版商:AIP    

年代:1951

数据来源: AIP

摘要:

Whereas extinction effects would be expected to decrease the x‐ray transmission through a crystal when it is set at a reflecting angle, it is shown experimentally that in many cases the transmission increases at the Bragg angle.This is believed to be due to the fact that the decrease in the effective absorption coefficient overshadows the losses due to reflection.A reconsideration of Darwin's presentation of extinction allowing for variable &mgr; shows that the transmission may increase or decrease depending on the values of &mgr; andp.Thus the earlier observations of Bragg and co‐workers are reconciled with the observations reported here.The importance, to crystal structure workers, of determining how &mgr; varies with direction in periodic media is obvious.

ISSN:0021-8979    

DOI:10.1063/1.1700122

出版商:AIP    

年代:1951

数据来源: AIP

摘要:

Three phenomenological models are considered from which can be constructed a macroscopic statistical description of varieties of electronic noise, of which shot, thermal, and Barkhausen noise, electron multiplier and precipitation noise, clutter, ignition, and impulsive random noise in general are representative examples. The models examined are (I)non‐overlapping, periodic noise waves, common in pulse‐time modulation and other communication schemes, where the amplitude, phase, duration, and epoch in a period interval are subject to statistical variations; (II),non‐overlapping, nonperiodic disturbances, encountered in servo‐mechanism operation and keyed‐carrier communication techniques, for instance, which are like (I), but lack the basic periodic structure; and (III),poisson noise, consisting of the superposition of independent, randomly occurring elementary impulses. Much of the electronic noise mentioned above belongs to this more comprehensive type, where overlapping of the basic pulses is the characteristic feature. Becauseall(second‐order) moments are required in general for the analysis of noise in nonlinear systems, the attempt is made here to determine explicitly on the basis of the appropriate model the second‐order probability densityW2in the important stationary cases. For noise of types (I) and (II) this appears impractical except in the simplest cases: only the lower order moments prove tractable. However, for poisson noise (III) an explicit treatment is possible for impulsive random noise, nearly normal random noise, and for the limiting, normal random cases (of which shot and thermal noise are examples). In Part I the main features of the models (I–III) are discussed, and the general probability densityWl(X1,t1; …;Xs, ts) in the nonstationary instances is formally constructed. In Part II, the distribution density for nearly normal random noise is given, the first and second (second‐order) moments of the various distributions are determined, and from these in turn are found the spectral distribution of the energy in the random waves.

ISSN:0021-8979    

DOI:10.1063/1.1700123

出版商:AIP    

年代:1951

数据来源: AIP

摘要:

Part II is devoted to the detailed evaluation of the first and second (second‐order) moments, namely, average values and the cross‐ and autocorrelation functions for stationary random noise waves for models I–III, whose statistical description is given in Part I. From these in turn are determined the cross‐ and auto‐spectral intensities governing the distribution of energy in the random disturbances. Finally, the asymptotically normal distributions characteristic of the high density poisson noise (III) are evaluated, together with higher order correction terms and their associated characteristic functions.

ISSN:0021-8979    

DOI:10.1063/1.1700124

出版商:AIP    

年代:1951

数据来源: AIP