Assuming a density perturbance in the form of an Archimedes spiral and an exponential decrease of matter density along the z-direction, Poisson's equation governing the perturbed gravitational field is solved with Hankel's integral transform and the method of steepest descent. For shortwave perturbances in the plane z=0, a simple analytical expression is given. In our approximation, the form of the perturbed field is determinate and is also an Archimedes spiral.
In this paper our numerical solution of the transfer equations of the Stokes parameters in the presence of magnetic fields is used to calculate the intensity ratios of the components of Zeeman triplets and their relations with the intensity and direction of magnetic fields. From this we have shown that the application of Seares' formulae to the determination of the direction of the magnetic fields in sunspots may give rise to very large errors. A suggestion for the improvement of this method is made.
The sizes of 64 radio components of quasars have been determined using their angular diameters and redshifts. No significant correlation is found between their sizes and their mutual separation whether different initial luminosity ranges are considered separately or together. This result implies that the sizes of the components do not change much during the lifetime of quasars with a resolved radio structure.
A statistical analysis has been made on the polarization properties of those quasars in which the Faraday depolarization is mainly responsible for the inverse relationship between the degree of polarization and the wavelengrh. Our results are: (1) There is no significant correlation between and D; there is, however, an obvious correlation between and . (2) The statistical relation between mmax and D shows that the random component of the magnetic field increases as the quasar evolves. (3) There is no evident evolutionary trend in the magnetic field given by minimizing the total energy. (4) The representation by a Gaussian of the Faraday depth distribution makes it obvious that the thermal electron density in the components decreases as the quasar evolves:
As it is difficult to determine accurately the station height from simultaneous observations of satellites, we propose to use the λ-component of the chord direction in the station-station coordinate system to find the longitude and latitude of the unknown station, the computation being weighted in favour of this component. Results show that this method is better than the usual methods of intersecting chord directions and of intersecting synchronous planes. A method of data control and external accuracy analysis is also set out.
The question of the additional perturbations due to the motion of the coordinate system in the theory of artificial satellites is discussed in some detail. Basic ideas are clarified and an error in Lambeck's 1973 paper is pointed out. It is demonstrated again that the most suitable coordinate system to use in the theory of motion of artificial satellites is the orbital system, and not the orbital system.
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