A(8)dOexp [2ni{(Xsin 8+Zcos B)/h-nt)].t We shall use capital letters such as X, Y , 2 to represent distances measured in terms of the unit of length, and small letters, such as x, y , z , to represent distances measured in terms of the wavelength of the radiation as a unit.3 A case of more general polarization can be considered as a sum of these two special cases. Complex numbers will be rendered throughout in heavy type.t This diffracting screen would be such that it transmitted an amplitude which was a cosinusoidal function of distance x , and to do this it would have to be provided with phase-reversing sections to produce the negative parts of the amplitude distribution.
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An analysis is made of the diffraction effects produced when a plane wave is incident upon an irregular diffracting screen, and the results are applied to the problem of the reflexion of radio waves from an ionosphere which is irregular in the horizontal plane. The nature of the irregular screen is assumed to be given in terms of the variation of electric wave-field in a plane just beyond the screen, and it is assumed that variations occur over the plane in one direction only. It is further assumed that the screen is 'random’ in the sense that it is one of an assembly all of which differ from each other, but have statistical properties in common, and deductions are made about the diffraction patterns averaged over the assembly. It is shown that many aspects of the problem can be investigated by use of the theory of ‘random’ electrical noise as developed by Rice and Uhlenbeck. The angular spectrum (Fraunhofer diffraction pattern) and the Fresnel diffraction pattern are described in terms of their spatial auto-correlation functions, and there is some discussion of a related method of dealing with Fresnel diffraction problems from completely determined screens. In part II of the paper the irregular ‘fading’ exhibited by a radio wave returned from the ionosphere is discussed in terms of two models in which the fading is assumed to be produced by movements of the diffracting centres in the ionosphere. The temporal auto-correlation function of the amplitude of the irregularly fading signal is related to the velocity of the ionospheric diffracting centres.
A quick and approximate method was used to analyse (h′ ‐ f) records of radio waves reflected from the ionosphere so as to give the total number (n) of electrons below the level of maximum electron density in a column of unit cross‐section in the F2 region. The, analysis was carried out on records obtained at Watheroo (Australia), Huancayo (Peru), and College (Alaska) for two magnetically quiet days per month in a year of sunspot maximum and a year of sunspot minimum. It was found that the quantity n was closely related to the zenith angle (χ) of the sun's rays, whereas it is well known that the maximum electron density Nm in the F2 layer is not simply related to this angle. The well‐known anomalies which are apparent when Nm is studied as a function of time of day, time of the year, and geographical position, all seemed to disappear when the quantity n was studied instead. A new kind of anomaly which was observed at Huancayo in years of sunspot minimum is described and discussed. A relation between the thickness and the height of the F2 layer is established and the possibility of using it in ionospheric forecasting and theory is discussed. Since the deductions of this paper are made on data from only three stations, it is suggested that a similar analysis should be made for other stations. This is all the more necessary because two other sets of workers have reported results in disagreement with those obtained in this paper.
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