METHODS OF MAKING LECHER-WIRE MEASUREMENTS

1930 ◽  
Vol 3 (6) ◽  
pp. 516-520 ◽  
Author(s):  
Geo. S. Field
Keyword(s):  
Wave Length ◽  
Neon Lamp ◽  
Electric Waves

Several methods of measuring the wave-length of electric waves on wires have been investigated. It was found that incorrect results were obtained when neon glow-tubes were moved along the wires to indicate the voltage nodes. By placing the neon lamp at the far end of the wires, however, and using shorting bridges to indicate the nodes, it was found possible to obtain quite consistent results. A thermogalvanometer, used in a similar manner, proved to be a somewhat better indicator and gave results which were more precise.

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.

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

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 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 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 diffraction of electric waves round a perfectly reflecting obstacle

1911 ◽  
Vol 210 (459-470) ◽  
pp. 113-144 ◽  
Keyword(s):  
Differential Equation ◽  
Magnetic Force ◽  
Wave Length ◽  
Conducting Sphere ◽  
Common Axis ◽  
Previous Communication ◽  
Pass Through ◽  
Mathematical Relations ◽  
Electric Waves

In a previous communication it was verified that the effect at a point on a perfectly conducting sphere due to a Hertzian oscillator near to its surface was negligible in comparison with the effect that would have been produced at that point but for the presence of the sphere, when the point is at some distance from the oscillator and the radius of the sphere is large compared with the wave length of the oscillations. In what follows it is proposed to find the effect at all points produced by a Hertzian oscillator placed outside a conducting sphere whose radius is large compared with the wave length of the oscillations. For simplicity the axis of the oscillator will be assumed to pass through the centre of the sphere, but this assumption will not affect the generality of most of the results. An Appendix is added in which the more important mathematical relations required are established. 1. Let O be the centre of the conducting sphere of radius a, and let the oscillator be at a point O 1 , the direction of the axis of the oscillator being OO 1 , and the distance OO 1 being r 1 .In this case the lines of magnetic force are circles which have the line OO 1 for common axis. If γ denotes the magnetic force at any point P, ρ the distance of P from OO 1 , and z the distance of P from the plane through O perpendicular to OO 1 , γρ satisfies the differential equation ∂ 2 /∂ p 2 (γ p )-1- p ∂/∂ p (γ p ) + ∂ 2 /∂ z 2 (γ p )+ k 2 γ p = 0, where 2 π/ k is the wave length of the oscillations. Transforming to polar co-ordinates ( r, θ ), where r is the distance OP and θ the angle POO1, z = r cos θ and p = r sin θ ; hence, writing cos θ = μ, the differential equation becomes ∂ 2 /∂ r 2 (γ p )+1-μ 2 / r 2 (γ p )+ k 2 γ p = 0 ...........(1).

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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