The paraboloidal shape of the bright envelope separated by a dark interval from the head of the great comet of 1811, and constituting, as it were, the _root_ of its tail, seemed to the astronomer of Bremen to reveal the presence of a double repulsion; the expelled vapours accumulating where the two forces, solar and cometary, balanced each other, and being then swept backwards in a huge train. He accordingly distinguished three classes of these bodies:--First, comets which develop _no_ matter subject to solar repulsion. These have no tails, and are probably mere nebulosities, without solid nuclei. Secondly, comets which are acted upon by solar repulsion _only_, and consequently throw out no emanations _towards_ the sun. Of this kind was a bright comet visible in 1807.[272] Thirdly, comets like that of 1811, giving evidence of action of both kinds. These are distinguished by a dark _hoop_ encompassing the head and dividing it from the luminous envelope, as well as by an obscure caudal axis, resulting from the hollow, cone-like structure of the tail. Again, the ingenious view subsequently propounded by M. Bredikhin as to the connection between the _form_ of these appendages and the _kind_ of matter composing them, was very clearly anticipated by Olbers. The amount of tail-curvature, he pointed out, depends in each case upon the proportion borne by the velocity of the ascending particles to that of the comet in its orbit; the swifter the outrush, the straighter the resulting tail. But the velocity of the ascending particles varies with the energy of their repulsion by the sun, and this again, it may be presumed, with their quality. Thus multiple tails are developed when the same comet throws off, as it approaches perihelion, specifically distinct substances. The long, straight ray which proceeded from the comet of 1807, for example, was doubtless made up of particles subject to a much more vigorous solar repulsion than those formed into the shorter curved emanation issuing from it nearly in the same direction. In the comet of 1811 he calculated that the particles expelled from the head travelled to the remote extremity of the tail in eleven minutes, indicating by this enormous rapidity of movement (comparable to that of the transmission of light) the action of a force much more powerful than the opposing one of gravity. The not uncommon phenomena of multiple envelopes, on the other hand, he explained as due to the varying amounts of repulsion exercised by the nucleus itself on the different kinds of matter developed from it.