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On the Bending of Electromagnetic Micro-Waves below the Horizon

An interesting phase in the development of the modern radio technique are the experiments conducted during the last few years with very short wave-lengths. Marchese Marconi [1] reported about an extensive series of successful radio connections over distances up to 260 km., in which waves of from 50 cm. to 60 cm. were used, concentrated with the help of a parabolic reflector. Clavier and Gallant [2] went even to still shorter waves of only 17.4 cm. which they sent over a distance of 61 km. also concentrating them with a reflector of 3.8 m. in diameter. The most remarkable feature of Marchese Marconi's results is that the distances covered by him exceed several times the range of rectilinear visibility from the sending station. The memory is still fresh of the great surprise which was caused among physicists by the unusually long range of long wave radio-reception. The explanation of these puzzling facts about long waves was traced, in the meantime [3], to the influence of the Kennelly-Heaviside layer of the upper atmosphere, and the question, naturally, arises to what extent atmospheric influences are responsible for the phenomena observed by Marchese Marconi with micro-waves. The first step in answering this question must be an investigation of how much bending is to be expected from the point of view of the wave theory completely neglecting the atmosphere. Such an investigation is the subject of this paper. The simple method which we propose is based on Huyghens' principle and treats the surface of the earth as a perfectly absorbing screen. As far as we know, it was not used heretofore and there are good reasons for this: In the case of long waves, the properties of the soil play an important part both in their production and their propagation. The height of the receiving station is only a fraction of the wave-length, so that only the so-called "surface wave" is of practical interest. On the other hand, the micro-waves are produced away from the soil and independently from it and, after they strike the earth, the surface wave is so thin as to be entirely unimportant. The transmission is, in this case, a matter of space propagation on which the physical properties of the earth surface have no material influence. It is therefore, perfectly permissible to replace it by a perfectly absorbing screen. The results of our calculations and their comparison with Marchese Marconi's observations are summarized in the last section

Electronic charge density in helium in the first order shielding approximation

Electronic charge density for ground state of helium as function of nuclear charg

The role of stable isotopes in geochemistries of all types

Although I was surprised by the invitation to write a prefatory chapter for the Annual Review of Earth and Planetary Sciences, I decided to accept this opportunity to write about my experiences as a participant in the isotope geochemistry revolution that occurred 40–50 years ago. My own experiences during the early stages of my life were uniquely intertwined with those of many of the leaders of this revolution, and thus I was allowed to witness and participate in many remarkable changes in the science as a whole. In addition, I thought that my contribution might be of some interest to the members of a younger generation, to help them judge whether a scientific career could be interesting, rewarding, and worth working hard for to accomplish something. This chapter also gives me the opportunity to express my appreciation to some of the teachers, early colleagues, and students whose influences were important in my life

Variational method 3 - Steady state time dependent perturbation theory

Steady state time dependent perturbation theory and variational principle

The variational method 2 - Perturbation theory

Variational method to approximate solutions of perturbation equations, perturbation analyses, and use of perturbation theory to infer variational principl

Variational methods and degenerate perturbation theory

Variational methods and degenerate perturbation theor

Note on the nature of cosmic rays

The recent experiments of Bothe and Kolhoerster(1) have led to an important and interesting conclusion. The ionization phenomena, by means of which cosmic rays are measured, are produced by highly penetrating corpuscular rays. It remains, however, an open question whether this corpuscular radiation is identical with the cosmic rays themselves, or is secondary in its nature, produced by primary rays of an electromagnetic character. Bothe and Kolhoerster admit both possibilities, but they seem to lean toward the first, owing to the fact that their corpuscular rays show a penetration of the same order of magnitude as that of the cosmic rays themselves