Researches of M. E. Roche upon the form and equilibrium of the atmospheres of celestial bodies under the combined influence of gravitation, solar heat, and a repulsive force–Figure of equilibrium of a solid mass submitted to gravitation and the heat of the sun–Comets should have two opposite tails–Completion of the theory of cometary tides by the admission of a repulsive force, real or apparent–Accordance of the theory so completed with observation.

M. Edouard Roche has devoted a series of highly interesting memoirs to the discussion of the figure assumed by the atmosphere of celestial bodies under the action of the forces of the solar system. He has more particularly given his attention to the study of cometary atmospheres, and to all the phenomena which take place in and around cometary masses.

M. Roche begins by reducing the question to its simplest form. He assimilates a comet to ‘ an entirely fluid mass, sensibly homogeneous, and having no movement of rotation. ’ The forces which act upon it are the mutual attraction of its own particles and gravitation towards the sun. For such a mass to be in equilibrium under the action of these forces it must have the figure of a prolate spheroid with its centre at the centre of gravity, and its axis of revolution coincident with the radius vector from the sun.