scholarly journals The transmission of electric waves over the surface of the Earth

1915 ◽  
Vol 91 (627) ◽  
pp. 219-219
Keyword(s):  
Sea Water ◽  
Wave Length ◽  
Diffraction Theory ◽  
Small Extent ◽  
The Earth ◽  
Similar Series ◽  
Moderate Resistance ◽  
Perfect Conduction ◽  
Electric Waves ◽  
Good Agreement

An analytical solution of the general equation of electrodynamics is obtained for the case of waves generated by a vibrating doublet in presence of a conducting sphere, and is adapted to obtain the known solution for perfect conduction, and the correction for moderate resistance, such as that of sea-water. The known solution is expressed by the sum of a series involving zonal harmonics, and the correction by a similar series. Different results have been obtained by different writers who have investigated the numerical value of the former sum. In the paper a new method of summing the series is explained, and worked out in detail for the wave-length 5 km. In the case of perfect conduction the result confirms that found by H. M. Macdonald. The effect of resistance is found to be a slight increase of the strength of the signals at considerable distances, counteracting to some small extent the enfeebling effect of the curvature of the surface. A comparison is instituted between the results of the theory and those of recorded experiments. From these it had previously been inferred that the diffraction theory fails to account for the facts; but, after a discussion of the experimental evidence, it appears that the observations may admit of a different interpretation, according to which the results of the diffraction theory would be in good agreement with those of daylight observations at great distances.

scholarly journals IV. The transmission of electric waves over the surface of the Earth

1915 ◽  
Vol 215 (523-537) ◽  
pp. 105-131 ◽  
Keyword(s):  
Sea Water ◽  
Wave Length ◽  
Diffraction Theory ◽  
The Other ◽  
Critical Survey ◽  
The Earth ◽  
Theoretical Investigations ◽  
The Waves ◽  
Perfect Conduction ◽  
Electric Waves

1. Ever since the time, about 1902, when Marconi first succeeded in sending wireless signals across the Atlantic the question of explaining the mechanism of such transmission has attracted attention among mathematicians. The question may be put in the following form:—The electric waves generated by the sending apparatus differ from waves of light only by having a longer wave-length, which is, nevertheless small compared with the radius of the earth; and the curved surface of the earth may therefore be expected to form a sort of shadow, effectively screening the receiving apparatus at a distance. How, then, does it happen that in practice the waves penetrate into the region of the shadow ? Unfortunately, the question has been investigated by different methods without adequate co-ordination, and the results that have been obtained are somewhat discordant. In these circumstances it appears to be desirable to undertake a critical survey of the question. The various theoretical investigations may be classified as developments of three suggestions: (l) The imperfectly conducting quality, or resistance, of the material, generally sea-water, over which the transmission takes place, may cause the effect observable at a distance to be greater than it would be if the material were perfectly conducting. (2) Owing to the numerical relations connecting the actual wave-lengths used in practice, the size of the earth, and the distances involved, the amount of diffraction, even in the case of perfect conduction, may be greater than would, at first sight, be expected. (3) Transmission through the atmosphere may be notably different from transmission through a homogeneous dielectric. We may refer to these suggestions briefly as the “resistance theory,” the “diffraction theory,” and the “atmospheric theory.” It may be said at once that the atmospheric theory has arisen from the alleged failure of the other two, and that it has not yet been formulated in such a way as to admit of being tested in the same precise analytical fashion as they can. It is still rather speculative and indefinite. In what follows I propose to attend chiefly to the first two suggestions, and to investigate the result that can be obtained by combining them.

scholarly journals The transmission of electric waves around the Earth's surface

1916 ◽  
Vol 92 (643) ◽  
pp. 493-500 ◽  
Keyword(s):  
General Formula ◽  
Magnetic Force ◽  
Wave Length ◽  
Angular Distance ◽  
Electric Force ◽  
Present Communication ◽  
The Earth ◽  
Perfect Conduction ◽  
Electric Waves

The value of the magnetic force at a point on the earth's surface, due to a simple oscillator placed on the surface with its axis normal to the surface, has been recently calculated by Love for a wave-length of 5 kilom. at certain distances from the oscillator. His results for the case of perfect conduction are the same as the corresponding series when the surface of the earth is supposed to be imperfectly conducting, The object of the present communication is to obtain the general formula for the case of imperfect conduction. Let r, θ, ϕ be the polar co-ordinates of a point, where r is its distance from the centre of the earth, θ its angular distance from the oscillator, E r , E θ , E ϕ the components of the electric force, and α, β, γ , the corresponding components of the magnetic force. Then, Since there is symmetry round the axis of the oscillator, α =0, β =0, γ =0; and throughout space outside the surface

PROPAGATION OF RADIO FREQUENCY ENERGY THROUGH THE EARTH

Geophysics ◽  
1954 ◽  
Vol 19 (3) ◽  
pp. 459-477 ◽  
Author(s):  
F. M. McGehee
Keyword(s):  
New Mexico ◽  
Radio Frequency ◽  
Propagation Characteristics ◽  
Attenuation Constant ◽  
Radio Frequency Energy ◽  
The Earth ◽  
Similar Series ◽  
Set Up ◽  
Good Agreement ◽  
Made In

Measurements have been made of some propagation characteristics in the earth of 1,614 and 1,700 kc radio frequency energy. The experiments were conducted at Carlsbad Caverns, New Mexico, and Mammoth Cave, Kentucky. Transmitters were set up on the surface 710 ft above an unwired tunnel in Carlsbad Caverns and the signal strength was measured at many points in the tunnels. A similar series of measurements was made in Mammoth Cave in a tunnel 270 ft below the surface. The data show that the attenuation constant is about 0.012 and 0.02 to 0.064 neper/meter at the two locations respectively. These values are in good agreement with theory.

scholarly journals On the connection between the ray theory of electric waves and dynamics

1931 ◽  
Vol 132 (819) ◽  
pp. 83-98 ◽  
Keyword(s):  
Phase Velocity ◽  
Critical Frequency ◽  
Wave Length ◽  
Ray Theory ◽  
Electronic Density ◽  
Short Waves ◽  
The Earth ◽  
Variable Distribution ◽  
The Waves ◽  
Electric Waves

1. In the study of the transmission of electric waves round the earth (especially in the case of what are now known as short waves of frequencies between 3·3 X 10 7 and 3·3 X 10 6 , 10, to 100 M in wave-length) we have to consider the behaviour of such waves in the ionised region of the upper atmo­sphere. For the purposes of the analysis of the wave motions, this region may be considered as one in which there is a variable distribution of electronic density represented by N ϵ , say, which is taken as a function of the co-ordinates x, y, z . The electronic density is of major importance, the ions, in general, being so heavy that their reaction on the waves is small compared with that of the electrons. The phase velocity V in the medium is then, as is well known, c /√1 — v 0 2 / v 2 where v 0 is the critical frequency of the medium at any point x, y, z given by v 0 2 = N e 2 c 2 /π m , and in respect of this (the quantity N) is a function of the co-ordinates x, y, z . The group velocity U is c √1 — v 0 2 / v 2 , so that UV = c 2 .

scholarly journals Diffraction

1930 ◽  
Vol 229 (670-680) ◽  
pp. 87-124 ◽  
Keyword(s):  
Exact Solution ◽  
Simple Form ◽  
London Math ◽  
Wave Length ◽  
Diffraction Theory ◽  
Acta Math ◽  
Infinite Plane ◽  
History Of ◽  
Special Case ◽  
Electric Waves

When HUYGEN’s principle is applied to the problem of the straight edge, FRESNEL’s diffraction phenomena in the neighbourhood of the geometrical shadow can be accounted for, and the theory agrees closely with observation. But so many approximations are involved in the application of FRESNEL’s theory, that an outstanding event in the history of diffraction theory was the discovery of the exact solution for waves impinging upon a semi-infinite plane. This problem constitutes the only one in diffraction theory which has been solved completely in a comparatively simple form. It is a special case of the wedge problem, the successful treatment of which is due to the fact that there are no dimensions concerned which bear a relation to the wave-length of the incident disturbance. The solution of the problem is due to the labours of a number of mathematicians, among whom POINCARE (‘ Acta Math.,’ vol. 16, p. 297 (1892-3 )), SOMMERFELD (“ Math. Theorie der Diffraction,” ‘ Math. Ann.,’ vol. 47, pp. 317-374 (1895 ) ), MACDONALD (“ Electric Waves,” and ‘ Proc. London Math. Soc.,’ ser. 2 , vol. 14, part 6), and BROMWICH {ibid.) , may be mentioned.

Part 2. The deeper structure of the Atlantic - Geological hypotheses and the earth's crust under the oceans

1954 ◽  
Vol 222 (1150) ◽  
pp. 341-348 ◽  
Keyword(s):  
Heat Flow ◽  
Recent Work ◽  
Sea Water ◽  
Volcanic Rocks ◽  
The Other ◽  
Ocean Floor ◽  
Peridotite Xenoliths ◽  
The Earth ◽  
Southern Rhodesia ◽  
Mohorovičić Discontinuity

Recent work has determined the depth of the Mohorovičić discontinuity at sea and has made it likely that peridotite xenoliths in basaltic volcanic rocks are samples of material from below the discontinuity. It is now possible to produce a hypothetical section showing the transition from a continent to an ocean. This section is consistent with both the seismic and gravity results. The possible reactions of the crust to changes in the total volume of sea water are dis­cussed. It seems possible that the oceans were shallower and the crust thinner in the Archean than they are now. If this were so, some features of the oldest rocks of Canada and Southern Rhodesia could be explained. Three processes are described that might lead to the formation of oceanic ridges; one of these involves tension, one compression and the other quiet tectonic conditions. It is likely that not all ridges are formed in the same way. It is possible that serpentization of olivine by water rising from the interior of the earth plays an important part in producing changes of level in the ocean floor and anomalies in heat flow. Finally, a method of reducing gravity observations at sea is discussed.

ON THE ACOUSTIC RADIATION FIELD OF THE PIEZO-ELECTRIC OSCILLATOR AND THE EFFECT OF VISCOSITY ON TRANSMISSION: PART II

1934 ◽  
Vol 11 (4) ◽  
pp. 484-488 ◽  
Author(s):  
L. V. King
Keyword(s):  
Radiation Field ◽  
Sea Water ◽  
Acoustic Radiation ◽  
Wave Length ◽  
Numerical Data ◽  
Transmission Part ◽  
Coefficient Of Viscosity ◽  
Theoretical Results ◽  
Piezo Electric

Numerical data on the distance of transmission of sound in sea water from a 10-in. piezo-electric oscillator are discussed in the light of theoretical results obtained in a previous paper. It is shown how by the principle of similitude the chart for transmission at optimum wave-length calculated for a 50-watt, 60 cm. oscillator can be used for a transmitter of any given diameter and output. A comparison with some experiments of Boyle's points to the fact that at supersonic frequencies, in the neighborhood of 100,000 cycles, a considerably higher coefficient of viscosity than that obtained by flow methods must be used.

The continuous absorption of light in alkali-metal vapours

1953 ◽  
Vol 219 (1136) ◽  
pp. 89-101 ◽  
Keyword(s):  
Cross Section ◽  
Alkali Metals ◽  
Theoretical Calculations ◽  
Wave Length ◽  
Energy Difference ◽  
Continuous Absorption ◽  
Absorption Of Light ◽  
Sodium Vapour ◽  
Good Agreement ◽  
Dipole Length

The first section of this paper is an account of some experiments on the absorption of light in sodium vapour from the series limit at 2412 Å to about 1600 Å (an energy difference of 2·6 eV). The absorption cross-section at the limit is 11·6 ± 1·2 x 10 -20 cm 2 . The cross-section decreases giving a minimum of 1·3 ± 0·6 x 10 -20 cm 2 at 1900 Å and then increases to 1600 Å. A theoretical calculation by Seaton based on the dipole-length formula gives good agreement with the experiments at the series limit and also correctly predicts the wave-length for the minimum, but it predicts a significantly lower absorption at the minimum. The experiments described in the first section of the paper conclude a series on the absorption of light in the alkali metals. The second section consists of a general discussion of the results of these experiments and of their relation to theoretical calculations. There is good agreement between theory and experiment except in regard to the magnitude of the absorption at the minimum.

scholarly journals The bending of electric waves round a conducting obstacle: amended result

1904 ◽  
Vol 72 (477-486) ◽  
pp. 59-68 ◽  
Keyword(s):  
Royal Society ◽  
Wave Length ◽  
High Order ◽  
Electric Waves

I have recently (May 3) received an intimation from the Secretaries of the Royal Society that Lord Rayleigh has questioned the validity of my analysis of the problem of bending of electric waves round a conducting obstacle, the ground of the criticism being that the shortness of the wave-length involves that the important harmonics in the expansion are of high order comparable with the ratio of the circumference of the sphere to the wave-length, and that for them the approximations in the paper are not valid. Subsequently I have learned that M. Poincare has made a similar objection.

scholarly journals The effect of junctions on the propagation of electric waves along conductors

1913 ◽  
Vol 88 (601) ◽  
pp. 103-110
Keyword(s):  
Cylindrical Shell ◽  
Wave Length ◽  
General Character ◽  
Original Form ◽  
Annular Space ◽  
Approximate Methods ◽  
Positive Direction ◽  
Positive Side ◽  
The Waves ◽  
Electric Waves

Some interesting problems in electric wave propagation are suggested by an experiment of Hertz. In its original form waves of the simplest kind travel in the positive direction (fig. 1), outside an infinitely thin conducting cylindrical shell, AA, which comes to an end, say, at the plane z = 0. Co-axial with the cylinder a rod or wire BB (of less diameter) extends to infinity in both directions. The conductors being supposed perfect, it is required to determine the waves propagated onwards beyond the cylinder on the positive side of z , as well as those reflected back outside the cylinder and in the annular space between the cylinder and the rod. So stated, the problem, even if mathematically definite, is probably intractable; but if we modify it by introducing an external co-axial con­ducting sheath CC (fig. 2), extending to infinity in both directions, and if we further suppose that the diameter of this sheath is small in comparison with the wave-length (λ) of the vibrations, we shall bring it within the scope of approximate methods. It is under this limitation that I propose here to consider the present and a few analogous problems. Some considerations of a more general character are prefixed.

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