The tail of a comet does not invariably point directly away from the Sun, as above mentioned, and sometimes the deviation is considerable; for instance, the tail of the comet of 1577 deviated 21° from the point opposite to the Sun.
In general, the tail inclines its extremity towards the regions of space which it has just left, always presenting its convex border to the regions towards which it is moving. It is also a remarkable fact that this convex border, moving first in space, always appears brighter and sharper than the opposite one, which is often diffused. From these peculiarities it would seem that in moving about the Sun the comets encounter some resistance to their motion, from the medium through which they pass, and that this resistance is sufficient to curve their tails away from the course in which they move, and to crowd their particles together on the forward side. It is especially when they approach their perihelion, and move more rapidly on a curve of a shorter radius, that the comets' tails show the greatest curvature, unless their position in regard to the observer prevents their being advantageously seen. The tail of Donati's comet presented a fair illustration of this peculiarity, its curvature having augmented with the velocity of the comet's motion about the Sun. But possibly this phenomenon has another cause, and may be found rather in the solar repulsion which acts on comets and is not instantaneously propagated throughout their mass.
Although, in general, comets have but one tail, it is not very rare to see them with multiple tails. The comets of 1807 and 1843 had each a double tail; Donati's comet, in 1858, showed several narrow, long rectilinear rays, issuing from its abruptly curved tail. The comet of 1825 had five branches, while that of 1744 exhibited no less than six distinct tails diverging from the coma at various angles. In general character the multiple and single tails are similar. When a comet has two tails, it is not rare for the second to extend in the general direction of the Sun, as was the case with the great comet of 1881, III., represented on Plate XI. From July 14th to the 21st it exhibited quite an extended conical tail, starting obliquely downwards from the right side of the coma, and directed towards the Sun. From the 24th of July to the 2d of August this secondary tail was exactly opposite in its direction from that of the primary tail, and gave to the head a very elongated appearance. Comet 1881, IV., also exhibited a secondary appendage, not directed towards the Sun, but making an angle of about 45° with the main tail.
These cometary appendages sometimes attain prodigious dimensions. The comets of 1680 and 1769 had tails so extended that, after their heads had set under the horizon, the extremities of these immense appendages were still seen as far up as the zenith. In a single day the tail of the comet of 1843 extended 100°, and it was thrust from the comet "as a dart of light" to the enormous distance of 48,500,000 miles, and yet of this immense appendage nothing was left on the following day. The tail of Donati's comet, in 1858, attained a real length of 42,000,000 miles, while that of the great comet of 1843 had the enormous length of 200,000,000 miles. If this last comet had occupied the position of the Sun, which it approached very nearly for a moment, the extremity of its tail would have extended 60,000,000 miles beyond the orbit of Mars.
In some cases the tails of comets have been seen undulating and vibrating in a manner similar to the undulations and coruscations of light characteristic of some auroras. Many observers report having seen such phenomena. The comet of 1769 was traversed by luminous waves and pulsations, comparable to those seen in the aurora borealis. I myself observed these curious undulations in Coggia's comet in 1874, while the head of this object was below the horizon. For an hour the undulations rapidly succeeded each other, and ran along the whole length of the tail.
Some of the brightest comets have shone with such splendor that they could be observed easily in full sunshine. Many comets, such as those of 1577 and 1744, have equaled Sirius and Venus in brilliancy. The great comet of 1843, which suddenly appeared in our sky, was so brilliant that it was seen by many observers at noon time, within a few degrees from the Sun. I remember that I myself saw this remarkable object in the day time, with a number of persons, who were gazing at the wonderful apparition. So brilliant was this comet, that besides its nucleus and head, a portion of its tail was also visible in the day time, provided the observer screened his eyes from the full sunlight by standing in the shadow of some building.
Of all the bodies revolving around the Sun, none have been known to approach so near its surface as did the comet of 1843. When it arrived at perihelion, the distance from the centre of its nucleus to the surface of the Sun's photosphere was only 96,000 miles, while the distance from surface to surface was less than 60,000 miles. This comet, then, went through the solar atmosphere, and in traversing it with its tremendous velocity of 366 miles per second, may very possibly have swept through some solar protuberances, many of which attain much higher elevations than that at which the comet passed. The comet of 1680 also approached quite near the surface of the Sun, and near enough to encounter some of the high solar protuberances, its distance at perihelion being about two-thirds of the Moon's distance from the Earth. The rapidity of motion of the comet of 1843 was such, when it approached the Sun, that it swept through all that part of its orbit which is situated north of the plane of the ecliptic in a little more than two hours, moving in this short time from one node to the other, or 1800.
But if some comets have a very short perihelion distance, that of others is considerable. Such a comet was that of 1729, whose perihelion distance was 383,000,000 miles, the perihelion point being situated between the orbits of Mars and Jupiter.
While some comets come near enough to the Sun at perihelion to be volatilized by its intense heat, others recede so far from it at aphelion that they may be said to be frozen. The shortest cometary aphelion distance known is that of Encke's comet, whose greatest distance from the sun is 388,000,000 miles. But that of the comet of 1844 is 406,000,000,000 miles from the Sun. The comets of 1863 and 1864 are so remote in space when they reach their aphelion points that light, with its velocity of 185,500 miles a second, would require 171 days in the first case, and 230 in the last, to pass from them to the Earth.
The period of revolution of different comets also varies immensely. While that of Encke's comet is only 3½ years, that of comet 1864, II., is 280,000 years.