Theory of the formation and development of cometary atmospheres under the influence of gravitation and a repulsive force–Calculations of M. Edouard Roche– Masses of the comets of Donati and Encke as determined by this method.

We are now about to see the same question, when investigated by another method, lead to results quite different to those of M. Babinet. Between the opinions–entirely conjectural, be it observed–of the savants of the eighteenth century who held that comets were bodies dense and massive as the planets, and those of some contemporary astronomers who regard them as visible nonentities, there is room for a determination which is removed from both extremes, and is moreover better justified.

For this method of determination we are indebted to M. Edouard Roche, professor in the Faculty of Sciences at Montpellier. In a series of very remarkable researches into the theory of cometary phenomena, which we shall analyse further on, M. Roche shows that there is a determinate relation between the distance of the comet from the sun, its mass, and the diameter of the portion of its nebulosity subject to the attraction of the nucleus, otherwise called the diameter of its true atmosphere. This relation holds at distances so remote from the sun that the repulsive force, either apparent or real which engenders the tail may be neglected.