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 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 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

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 .

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.

An experimental investigation of the nature and origin of microseisms at St. Louis, Missouri

1940 ◽  
Vol 30 (2) ◽  
pp. 139-178
Author(s):  
J. Emilio Ramirez
Keyword(s):  
Wave Length ◽  
Vertical Axis ◽  
The Other ◽  
Wave Form ◽  
Stationary Waves ◽  
Retrograde Motion ◽  
Time Signals ◽  
Group Form ◽  
Triangular Network ◽  
The Waves

Summary Over a period of six months, from July to December, 1938, an investigation on microseismic waves has been carried out in the Department of Geophysics of St. Louis University. Four electromagnetic seismographs, specially designed for recording microseisms, were installed in the city of St. Louis in the form of a triangular network. Two of these were E-W components, one at the St. Louis University Gymnasium and the other 6.4 km. due west at Washington University. The other two were arranged as N-S components, one at the St. Louis University Gymnasium and one 6.3 km. due south at Maryville College. The speed of the photographic paper was 60 mm/min., and time signals were recorded automatically and simultaneously on each paper from the same clock every minute and at shorter intervals from a special pendulum and “tickler” combination by means of telephone wires. The results have demonstrated beyond doubt that microseismic waves are traveling and not stationary waves. The same waves have been identified at each one of the stations of the network, and also at Florissant, 21.8 km. away from St. Louis University. The speed of microseismic waves at St. Louis was determined from several storms of microseisms and it was found to be 2.67±0.03 km/sec. The direction of microseisms was also established for most of the storms and it was found that about 80 per cent of incoming microseisms at St. Louis were from the northeast quadrant during the interval from July to December, 1938. No microseisms were recorded from the south, west, or southwest. The period of the waves varied between 3.5 and 7.5 sec. The average period was about 5.4 sec. The microseismic wave length was therefore of the order of 14¼ km. A study of the nature of microseismic waves from the three Galitzin-Wilip components of the Florissant station reveals in the waves many of the characteristics of the Rayleigh waves; that is, the particles in the passage of microseismic waves move in elliptical orbits of somewhat larger vertical axis and with retrograde motion. A comparison carried over a period of more than a year between microseisms and microbarometric oscillations recorded by specially designed microbarographs showed no direct relationship between the two phenomena in wave form, group form, period, or duration of storms. The source of microseisms is to be found not over the land, but rather out over the surface of the ocean. The amplitudes of microseisms depend only on the intensity and widespread character of barometric lows traveling over the ocean. Several correlations between the two phenomena seem to make this conclusion rather evident. Special emphasis is laid on the fact that all the determined directions of incoming microseisms at St. Louis point to a deep barometric low over the ocean. The period of microseisms seems to be a function of the distance between the station and the source of microseisms. The exact mechanism by which barometric lows over the ocean water result in the production of microseisms needs further investigation. Large microseisms have been produced without any indication of surf near the coasts, or with winds blowing from the land toward the ocean.

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.

scholarly journals XX. Discovery of the metamorphosis in the second type of the cirripedes, viz. the lepades, completing the natural history of these singular animals, and confirming their affinity with the crustacea

1835 ◽  
Vol 125 ◽  
pp. 355-358 ◽  
Keyword(s):  
North America ◽  
Natural History ◽  
Sea Water ◽  
The Other ◽  
External Appearance ◽  
The Real ◽  
Real Nature ◽  
History Of ◽  
The Mediterranean ◽  
The Waves

The Fourth Memoir, published in my Zoological Researches and Illustrations, No. III. page 69, &c., having first made known the real nature of the Cirripedes , the key of which remained concealed in their metamorphosis, it might have been expected that some naturalist favourably situated to investigate the oceanic tribe of these animals, would have been the first to make the same discovery in regard to these, and thereby complete their natural history. It was scarcely to be expected that the honour of this discovery also should be reserved for the author, fixed to one spot, where none of them naturally exist, and are but casually thrown upon our shores by the waves of the Atlantic, attached to pieces of wreck, or brought into port fixed to the bottoms of ships returning from distant voyages. Fortunately, however, two ships of this description came into this harbour (Cork), one from the Mediterranean, the other from North America, which, not being sheathed with copper, had their bot­toms literally covered with Barnacles of the three genera of Lepas , Cineras , and Otion ; and having persons employed expressly for the purpose, numbers of these were brought alive in sea water, amongst which were many with the ova in various stages of their progress, and some ready to hatch, which they eventually did in prodigious numbers, so as to enable him to add the proof of their being, like the Balani, natatory Crusta­cea in their first stage , but of a totally different facies and structure; a circumstance which determines the propriety of the separation of the Cirripedes into two tribes, and evinces the sagacity of Mr. MacLeay in being the first to indicate that these two tribes, the Balani and Lepades , were not so closely related as generally supposed. The larvæ of the Balani , described in Memoir IV. under the external appearance of the bivalve Monoculi ( Astracoda ), have a pair of pedunculated eyes, more numerous and more completely developed members, approximating to those of Cyclops , and of the perfect Triton ; while, in the present type, or Lepades , the larva resembles some­what that of the Cyclops , which Müller, mistaking for a perfect animal, named Amymone , and which can be shown to he common to a great many of the Entomostraca ; or the resemblance is still more striking to that of the Argulus Armiger of Latreille, which, in fact, is but an Amymone furnished with a tricuspidate shield at the back.

On an instrument for the measurement of the length of long electric waves, and also small inductances and capacities.

1905 ◽  
Vol 74 (497-506) ◽  
pp. 488-498 ◽  
Author(s):  
John Ambrose Fleming
Keyword(s):  
Wave Length ◽  
Resonant Circuit ◽  
Practical Matter ◽  
The Waves ◽  
Electric Waves

The measurement of the length of the waves used in connection with Hertzian wave telegraphy is an important practical matter. Since the wave-length of the radiated wave is determined by the frequency of the electric oscillations in the radiator, the determination of this frequency is all that is required. The principle of resonance is generally called into assistance to effect this measurement. It may be done by the employment of either an open or a closed resonant circuit.

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.

The Propagation of Radio Waves in an Ionised Atmosphere

1931 ◽  
Vol 27 (4) ◽  
pp. 578-587 ◽  
Author(s):  
D. Burnett
Keyword(s):  
Wave Length ◽  
Upper Atmosphere ◽  
Radio Waves ◽  
Free Electrons ◽  
Positive Ions ◽  
Electrons And Ions ◽  
Method Of Solution ◽  
Velocity Of Propagation ◽  
The Waves ◽  
Electric Waves

Larmor has shown that if the upper atmosphere contains electrons (charge ε, mass m, density ν) and if collisions between these electrons and molecules—and also the forces between the electrons themselves—are negligible, then electric waves are propagated as if the dielectric constant of the medium were reduced by , from which it appears that, so long as the approximations are valid, the velocity of propagation of the waves can be increased indefinitely by increasing either the electron density or the wave-length λ. Several later authors have attempted to take account of the collisions between electrons and molecules, assuming free paths or velocities according to Maxwell's laws for a uniform gas, and it appears that the above law holds only for short waves; but it is doubtful how far the properties of a uniform gas can be assumed when periodic forces are acting. In the first part of this paper an alternative method of solution is given by means of Boltzmann's integral equation for a non-uniform gas, the analysis being similar to that used by Lorentz in discussing the motion of free electrons in a metal. Only the case when ν is small is considered, i.e. the interactions of electrons with one another and with positive ions are neglected. How far it is possible to increase the velocity of propagation by increasing ν is a more difficult question, but it seems possible that the forces between the electrons and ions may impose a limit just as collisions with neutral molecules limit the effect of increasing the wave-length.

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