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Excerpt from The Solitary Wave and Periodic Waves in Shallow WaterNumbers in square brackets refer to the bibliography at the end of the article.The theory given by Boussinesq involves a number of phys ical assumptions in addition to those of the basic hydro dynamical theory, it also leads to a differential equa tion for the wave profile. Both of these methods assume that the depth of the water is small compared to some horizontal dimension, a...

Excerpt from The Solitary Wave and Periodic Waves in Shallow WaterNumbers in square brackets refer to the bibliography at the end of the article.The theory given by Boussinesq involves a number of phys ical assumptions in addition to those of the basic hydro dynamical theory, it also leads to a differential equa tion for the wave profile. Both of these methods assume that the depth of the water is small compared to some horizontal dimension, a...

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Excerpt from Derivation of the Bohr-Sommerfeld Quantum, Conditions From an Asymptotic Solution, of the Schroedinger EquationWe wish to examine the asymptotic behavior of the of (1) as Planck's constant h approaches zero. To this end we assume that as h approaches zero.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important histo...

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This w...

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This w...

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Excerpt from Determination of Reflected and Transmitted Fields by Geometrical OpticsAs a matter of fact R. K. Luneberg has shown quite generally that the first terms in asymptotic expansions of the space dependence of the electric and magnetic field vectors is that given by geometrical optics.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduct...

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This w...

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This w...

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This w...

Excerpt from Excitation and Propagation of Surface WavesRays in Space can be defined in terms of the propagation velocity by Fermat's principle or by the differential equations which follow from it. Complex rays can be defined by applying Fermat's principle to complex curves, or by considering complex solutions of the ray equations. In either case it is necessary that c(x) be defined for complex values of x which is the case if is an analytic ...

Excerpt from Decay Exponents and Diffraction Coefficients for Surface Waves on Surfaces of Non-Constant CurvatureWhen a wave is incident upon an opaque object large compared to the incident wavelength a shadow is formed. Some radiation penetrates into the shadow. The first quantitative analysis of this penetration effect for the case of a smooth object was that of G. N. Watson[1]. He showed that the field in the shadow of a sphere consists of ...

Excerpt from Thin Unsteady Heavy JetsTwo questions which immediately arise are: What is the relationship between the two theories? And How can the results of the hydraulic theory be improved? In this paper we answer these questions by presenting a method of solution of the hydrodynamic problem as a series in powers of the jet thickness divided by some other typical length of the jet.About the PublisherForgotten Books publishes hundreds of thou...

Excerpt from Diffraction by an Aperture IThe present treatment of diffraction of a wave by an aperture in a thin screen is based upon a new theory of wave propagation. This theory is called 'the geometrical theory of because it is an extension of geometrical optics which describes diffraction phenomena. It is like geometri cal optics inasmuch as it postulates that fields propagate along certain lines or curves called rays. However, it goes bey...

Excerpt from Back Scattering From a Finite ConeThe back scattering from a finite cone is calculated in this report by means of the geometrical theory of diffraction. Three different physical problems are considered. One is that of an acoustic wave incident upon a rigid cone. The second is that of an acoustic wave incident upon a perfectly soft (pressure-release) cone. The third, and perhaps most important, is that of an electromagnetic wave in...

Excerpt from Basic Mathematical Investigations in Electromagnetic Wave Theory: Final Report, January 1, 1964 December 31, 1968The object of the research was to extend existing knowledge of classical electromagnetic theory with emphasis on electromagnetic wave guiding radiation and communication, and diffraction problems.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks...