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about 4° broad, and from 30° to 44° long. The tails do not attain their full magnitude till the comet has left the sun. When these bodies first appear, they resemble round films of vapour with little or no tail; as they approach the sun, they increase in brilliancy, and their tail in length, till they are lost in his rays; and it is not till they emerge from the sun's more vivid light that they assume their full splendour. They then gradually decrease by the same degrees; their tails diminish and disappear nearly or altogether before the comet is beyond the sphere of telescopic vision. Many comets have no tails at all, as, for example, Encke's comet and that discovered by M. Biela, both of which are small and insignificant objects. The comets which appeared in the years 1585, 1763, and 1682, were also without tails, though the latter is recorded to have been as bright as Jupiter. The matter of the tail must be extremely buoyant to precede a body moving with such velocity; indeed the rapidity of its ascent can only be accounted for by the fervent heat of the sun. Immediately after the great comet of 1680 had passed its perihelion, its tail was 20000000 leagues in length, and was projected from the comet's head in the short space of two days. A body of such extreme tenuity as a comet is most likely incapable of an attraction powerful enough to recall matter
sent to such an enormous distance; it is therefore, in all probability, scattered in space, which may account for the rapid decrease observed in the tails of comets every time they return to their perihelia.
It is remarkable that, although the tails of comets increase in length as they approach their perihelia, there is reason to believe that the real diameter of the nebulous matter or nucleus contracts on coming near the sun, and expands rapidly on leaving him. Hevelius first observed this phenomenon, which Encke's comet has exhibited in a very extraordinary degree. On the 28th of October, 1828, this comet was about three times as far from the sun as it was on the 24th of December, yet at the first date its apparent diameter was twenty-five times greater than at the second, the decrease being progressive. M. Valz attributes the circumstance to a real condensation of volume from the pressure of the ethereal medium, which increases most rapidly in density towards the surface of the sun, and forms an extensive atmosphere around him. Sir John Herschel, on the contrary, conjectures that it may be owing to the alternate conversion of evaporable materials in the upper regions of a transparent atmosphere into the states of visible cloud and invisible gas by the effects of heat and cold. Not only the tails, but the nebulous part of comets diminishes every time they return
to their perihelia; after frequent returns they ought to lose it altogether, and present the appearance of a fixed nucleus: this ought to happen sooner to comets of short periods. La Place supposes that the comet of 1682 must be approaching rapidly to that state. Should the substances be altogether, or even to a great degree, evaporated, the comet would disappear for ever. Possibly
comets may have vanished from our view sooner than they would otherwise have done from this
In those positions of comets where only half of their enlightened hemisphere ought to be seen if they shine by reflected light, they ought to exhibit phases, but even with high magnifying powers none have been detected, though some slight indications are said to have been once observed by Hevelius and La Hire in 1682. In general the light of comets is dull,-that of the comet of 1811 was only equal to the tenth part of the light of the full moon, but some have been brilliant enough to be visible in full daylight, especially the comet of 1744, which was seen without a telescope at one o'clock in the afternoon, while the sun was shining; whence it may be inferred that, although some comets may be altogether diaphanous, others seem to possess a solid mass resembling a planet; but whether they shine by their own or by reflected
light has never been satisfactorily made out till 110W. As light is polarized by reflection at certain angles, it would afford a decisive test, were it not that a body is capable of reflecting light, though it shines by its own; so that it would not be conclusive, even if the light of a comet were polarized light. M. Arago, however, has with great ingenuity discovered a method of ascertaining this point, independent both of phases and polarization.
Since the rays of light diverge from a luminous point, they will be scattered over a greater space as the distance increases, so that the intensity of the light on a screen two feet from the object is four times less than at the distance of one foot; three feet from the object it is nine times less, and so on, decreasing in intensity as the square of the distance increases. As a self-luminous surface consists of an infinite number of luminous points, it is clear that, the greater the extent of surface, the more intense will be the light; whence it may be concluded that the illuminating power of such a surface is proportional to its extent, and decreases inversely as the square of the distance. Notwithstanding this, a self-luminous surface, plane or curved, viewed through a hole in a plate of metal, is of the same brilliancy at all possible distances as long as it subtends a sensible angle,
because, as the distance increases, a greater portion comes into view, and as the augmentation of surface is as the square of the diameter of the part seen through the hole, it increases as the square of the distance. Hence, though the number of rays from any one point of the surface which pass through the hole decrease inversely as the square of the distance, yet, as the extent of surface which comes into view increases also in that ratio, the brightness of the object is the same to the eye as long as it has a sensible diameter. For example-Uranus is about nineteen times farther from the sun than we are, so that the sun, seen from that planet, must appear like a star with a diameter of a hundred seconds, and must have the same brilliancy to the inhabitants that he would have to us if viewed through a small circular hole having a diameter of a hundred seconds. For it is obvious that light comes from every point of the sun's surface to Uranus, whereas a very small portion of his disc is visible through the hole; so that extent of surface exactly compensates distance. Since, then, the visibility of a self-luminous object does not depend upon the angle it subtends as long as it is of sensible magnitude, if a comet shines by its own light, it should retain its brilliancy as long as its diameter is of a sensible magnitude; and even