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We analyze a prominence model containing a flux rope which is completely detached from the photosphere. The maximum magnetic energy which can be stored in the configuration does not exceed the open-energy limit proposed by Aly and Sturrock. However, a loss of ideal-MHD equilibrium can occur and create a current sheet which is likely to undergo rapid reconnection.

Magnetic Reconnection is often invoked as the primary mechanism for driving a flare or a prominence eruption. Here I argue that a catastrophic loss of mechanical equilibrium, rather than reconnection, is probably the primary mechanism for driving these phenomena. However, reconnection is still essential in order for any significant amount of energy to be released. To illustrate this idea we present some recent results from an MHD simulation based on a catastrophe mechanism first proposed by Van Tend and Kuperus. In order for this mechanism to be effective a substantial amount of reconnection must occur within a few Alfvén-scale times. Such rapid reconnection is plausible since the loss of mechanical equilibrium can generate flows which drive the reconnection at a rapid rate.

Following Dungey's original magnetohydrodynamic formulation, a solution is obtained for the nonlinear evolution of a current discharge in the vicinity of a magnetic neutral line. For an ideal gas with constant conductivity and uniform mass density we obtain a particular exact solution in the limit of an initial, nearly sheet-like configuration. This particular solution implies special boundary conditions for the pressure and electric field at the surface of the conductor. If These conditions are not met, then the solution eventually breaks down before the current density becomes infinite. The time required for complete breakdown is determined by the wave propagation times from the surface of the fluid to the neutral line and by the diffusion time for the magnetic field through the fluid. For large conductivity and a small sound speed, the maximum current density achieved at the time of the solution's complete breakdown depends upon the ratio of the characteristic diffusion time to the Alfvén wave propagation time. In the limit of infinite conductivity or infinite extension of the fluid, the current density along the neutral line becomes infinite at π/23/2 times the Alfvénic scale time. At this same time the inflow Alfvenic Mach number approaches 21/2i while the outflow Alfvenic Mach number approaches infinity.

An important aspect of pre-flare current sheets in the solar atmosphere is the sudden enhancement of the effective electrical resistivity in the sheet due to the onset of a plasma micro-instability. Numerical and analytical solutions to the isothermal MHD equations are here presented that describe the evolution of a current sheet subsequent to such an enhancement in the resistivity. The solutions show that, if the initial width of the current sheet is less than the acoustic-diffusion length obtained by dividing the resistivity by the sound speed, then isomagnetic shocks are formed. These shocks propagate outward from the the centre of the current sheet and are transformed into fast-mode magneto-acoustic waves when they reach the edges of the current sheet. The fast-mode waves thus formed continue to propagate outward beyond the confines of the current sheet. In contrast to a previous study by Cheng, the present solutions demonstrate that flow speeds several times greater than the local fast-mode wave speed can be produced if the plasma beta parameter and the initial sheet width are sufficiently small. The results may be relevant to the triggering of a solar flare, as in the emerging flux model of flares.

This paper describes the historical background to the Göttingen Professor Tobias Mayer's bid under the terms of the Act 12 Queen Anne, cap. XX (1714) to obtain a reward for having constructed lunar tables of unprecedented accuracy (to about ± ½′) which promised to make both useful and practicable the lunar-distance method of finding longitude at sea. Parliament's decision in 1765 to award £3000 to Mayer's heirs marked the end of an eleven-year period of lively correspondence conducted on the latter's behalf between Professor Johann David Michaelis, Secretary of Hanoverian Affairs in Göttingen, and William Philip Best, one of George III's Privy Secretaries in London. The Nautical Almanac came into existence as a direct consequence of the success of these diplomatic negotiations.

Using ideal, one-dimensional MHD equations, numerical and analytic solutions are presented which describe the nonlinear behaviour of an imploding current sheet in a low-fl plasma. Initially the current density is uniformly distributed in asheet of finite thickness, and the Lorentz force tending to pinch the plasma together is unopposed by any fluid pressure force. As the implosion develops the current density in the sheet is concentrated into a thin layer at the centre of the sheet, and both the current density and the current in this layer become infinite in a finite time if β = 0. At the moment this occurs, fast-mode shocks are produced which propagate outward from the centre of the current sheet, and as the shocks move away an infinitely thin current sheet is left behind. Although the solutions are related to electric discharges, they are also closely related to a problem posed by Dungey concerning the evolution of a uniformly distributed current in the vicinity of an X-type magnetic neutral line. The implications of these solutions for Dungey's problemare discussed.

The work of the Greenwich Observatory throughout the three centuries of its existence has been characterized by the painstaking efforts of its eminent directors to attain an ever-increasing degree of precision in pinpointing the positions of the heavenly bodies, with a view to the improvement of the science of navigation. The pursuit of this purpose, in accordance with the express desire of its founder King Charles II, has been assisted by the steady improvement in the accuracy of the instruments with which it has been equipped, and these have naturally also been applied to investigating problems of a purely theoretical nature. Nevertheless, the tradition pioneered by the first Astronomical Observator (or Astronomer Royal) John Flamsteed (1646–1719) whom the King in 1675 charged with rectifying the coordinates and motions of the heavenly bodies, has remained predominantly practical and utilitarian.

Soon after the middle of the eighteenth century, improvements in the design and construction of astronomical and nautical instruments, coupled with the increased accuracy of tables of the Moon's motion, at last made the accurate determination of longitude at sea by lunar distance a practical possibility. The Astronomer Royal, Nevil Maskelyne, was quick to appreciate the importance of publishing the calculated solar and lunar ephemerides, together with other relevant tables and explanations, in the form of a Nautical Almanac, which was first printed under his supervision in 1766 and immediately distributed to mariners in different parts of the world. The present article is concerned with the circumstances relating to the origin and development of this publication during the first fifty years of its existence.

“Tobias Mayer is universally considered as one of the greatest astronomers not only of the eighteenth century, but of all times and of all countries.” This is how the French astronomer, Jean Delambre, in his posthumously published Histoire de l'astronomie au XVIIIième siècle (Paris, 1827), introduces his readers to the Göttingen professor, whom Leonhard Euler had already recognized in 1760 as “undoubtedly the greatest astronomer in Europe”. Delambre's placing of Mayer in a historical perspective assumes special significance on account of the fact that he had previously written three volumes on ancient and medieval astronomy.

Numerical solutions were obtained by Forbes, Priest & Hood (1982) for the resistive decay of a current sheet in an MHD fluid. To check the accuracy of the numerical solutions, a linear, analytical solution was also deived for the regime where diffusion is dominant. In a subsequent reinvestigation of this problem an error in the linear, analytical solution has been discovered. For the parameter values used in the numerical solution this error is too small (≲ 2%) to produce any significant change in the previous test comparison between the numerical and analytical solutions. However, for parameter values much different from those used in the numerical solution, the error in the linear solution can be significant.

In continuation of researches communicated to the Royal Society of Edinburgh, 1880 (February 16), in which I gave the probable position of an ultra-Neptunian planet, I have now to inform the Society that I have detected the existence of perturbations in the motion of Uranus, agreeing remarkably in character and period with those which would be produced by the new planet. These results are obtained from observations of Uranus extending over more than a century. The position of the planet, from this point of view, is found, from the first rough examination, to be the same as that given by me in my former memoir. This gives a means of determining the mass of the new planet.