On the Electric Field due to Tides III

In this paper the author will discuss briefly some results of theoretical work carried out by Dr. Longuet-Higgins, Dr. Malkus and others (Section 2). The theory of field due to streams of elliptical cross-sction will also be described (Section 3), and a method of generalization of this theory will be discussed (Section 4). In Section 5 the results of numerical computation concerning the streams of elliptical cross-section will be shown, and in Section 6 the approximate relation between the mean velocity and potential difference will be discussed for two types of streams

On the Electric Field due to Tides II

In the previous paper, the electric field induced by tidal current was discussed in some detail for the case where the earth's magnetic field is vertical. In this paper we shall consider the effect of the horizontal magnetic field on the electric field and current distribution in the sea water and the sea bed. A general description will be made in Section 2 concerning the phenomenon in the tidal current of rectangular cross-section, and a method of obtaining the electric potential in general case of velocity distribution will be given Section 3. In Section 4, a method of solving so-called two-layer problems will be discussed in general, and in Sections 5 and 6, some results of numerical computation will be shown. The method by which some of these results have been obtained will be explained in Appendix I, while Appendix II will be devoted to a list of the formulas for electric potential, electric field and electric current due to horizontal component of the earth's magnetic field in the streams of rectangular cross-section with various velocity distributions

An Experiment on Phrase Structure Analysis by an Electronic Computer

This paper is a report on the syntactical analysis of the English language by an electronic computer. In this experiment a tree system is used in recognizing the phrase structure of English. The experimental results by the electronic digital computer KDC-1 are also included in this report

On a Generalized Problem of Disc Electrodes II

A formal solution of a set of quadruple integral equations is given. The integral equations are reduced to a pair of simultaneous integral equations of Fredholm type which may be solved by a method similar to that used for a single equation. As an example, the problem of a circular plate condenser with guard rings is considered. It is shown that all the well-known disc electrode problems may be treated as special cases

Some Contributions to the Theory of Electrostatic Field

The problem of disc electrodes is discussed. Riemann's solution and the solution by the method of images are shown to be unacceptable, and a method based on an integral equation is devised to acquire a more satisfactory solution. In the second half of this paper, the problem of two tangent spheres is studied, using tangent-sphere coordinates. Potential distirbutions due to charged tangent spheres and also due to tangent spheres in an external electric field are analytically obtained

On the Resistance between the Two Disc Electrodes Applied to an Infinite Plate Conductor

The problem of disc electrodes is discussed on the basis of a Fredholm integral equation of the second kind. To compute the resistance between the two electrodes, numerical analysis is carried out utilizing the Laguerre-Gauss quadrature formula. The result is compared with that obtained from Riemann's solution which contains a physical contradiction. A formula of infinite integral involving a Bessel function is also given

A Method of Evaluation of the Function Kᵢₛ(x)

The modified Bessel function of the second kind with imaginary order, which is important in the potential theory, is considered from the stand point of numerical computation. A computing method based on the integral representation of this function is proposed. The accuracy and the computing time are also discussed. A short table and a graphical representation of this function are given

On the Electric Field due to Tides

It has been pointed out that one of the main causes of faults on submarine cables would be the electrolytic corrosion due to the current which is induced in the cable by tides moving across the earth's magnetic field. In this paper, some formulas for electric field due to a stream of water which flows in a tide-way of rectangular cross-section are derived, and results of numerical computations are shown. The effects of conductivity of the bottom are also treated as boundary value problems. It is found that the sides of tide-way are the most dangerous places as the intense electrolytic corrosion of cable occurs there

On a Generalized Problem of Disc Electrodes I

A problem of disc electrodes is discussed on the basis of dual integral equations both for an electrostatic problem and for a steady current field problem in the unified manner. It is shown that two well-known problems, 1) the plate condenser problem and 2) the disc electrode problem for steady current may be treated as special cases