In 1879 Brédikhine fully developed his cometary theory. Assuming the reality of the repulsive force, he concluded that to produce tails of the first type, the repulsion requires to be twelve times greater than the solar attraction; the production of tails of the second type necessitates a repulsive force about equal to gravity; while the force producing third-type tails has only one-fourth the power of gravitation. It was concluded that the tails are formed by particles of matter repelled from the comet by the repulsive force of the Sun, and in tails of the first type the velocity with which these particles leave the body of the comet is four or five miles a second. Brédikhine reached the conclusion that the Sun’s repulsive force is invariable, and that the different types of tails are formed by the same force acting on different elements. The numbers 12, 1, and ¼, are inversely proportional to the atomic weights of hydrogen, hydrocarbon gas, and iron vapour. Here, then, was the key to the mystery. Brédikhine pointed out that in all probability the first-type tails are formed of hydrogen, the second of hydrocarbon, and the third of iron, with a mixture of sodium and other elements. Within a few years of the publication of Brédikhine’s theory, five bright comets made their appearance, and there was abundant chance of testing the theory spectroscopically. In 1882 Well’s comet was particularly studied at Greenwich by Maunder, who discerned a sodium-line in its spectrum. The magnificent comet which appeared in 1882 was spectroscopically studied at Dunecht in Aberdeenshire by _Ralph Copeland_ (1837-1905), Astronomer-Royal of Scotland, who identified in its spectrum the prominent iron-lines as well as the sodium-line. These observations were certainly confirmatory of Brédikhine’s theory. It should also be stated, however, that several comets have shown, in addition to the hydrocarbon spectrum, that of reflected sunlight, which proves that the light we receive from comets is of a compound nature. The comet which appeared in 1880 was announced by _Benjamin Apthorp Gould_ (1824-1896) to be a return of the great comet of 1843. Calculations by Gould, Copeland, and Hind revealed a close similarity between the elements of the two orbits. Eventually it had to be admitted that the comets were separate bodies travelling in the same orbit. Then, two years later, the great September comet of 1882 was found to revolve in the same orbit as those of 1668, 1843, and 1880. Four years later, another comet, discovered in 1887, was found to move in the same path.