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which increases most rapidly in density towards the surface of the sun, and forms an extensive atmosphere around him. It did not occur to M. Valz, however, that the ethereal fluid would penetrate the nebulous matter instead of compressing it. Sir John Herschel, on the contrary, conjectures that it may be owing to the alternate conversion of evaporable materials in the upper regions of the transparent atmosphere of comets into the states of visible cloud and invisible gas by the effects of heat and cold; or that some of the external nebulous envelopes may come into view when the comet arrives at a darker part of the sky, which were overpowered by the superior light of the sun while in his vicinity. The first of these hypotheses he considers to be perfectly confirmed by his observations on Halley's comet, made at the Cape of Good Hope, after its return from the sun. He thinks that, in all probability, the whole comet, except the densest part of its head, vanished, and was reduced to a transparent and invisible state during its passage at its perihelion; for when it first came into view, after leaving the sun, it had no tail, and its aspect was completely changed. A parabolic envelope soon began to appear, and increased so much and so rapidly that its augmentation was visible to the eye. This increase continued till it became so large and so faint, that at last it vanished entirely, leaving only the nucleus and a tail, which it had again acquired, but which also vanished ; so that at last the nucleus alone remained. 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. M. de 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 cause.
The comet discovered at Florence by Signore Donati, on the 2nd of June, 1858, was one of the most beautiful that has been seen from our planet for many years, whether for the brightness of the nucleus, or the length and graceful form of the coma; when first discovered it was near the star , in the constellation of the Lion, being then at a distance of 288,000,000 miles from the earth ; during the month of August its nucleus assumed an almost planetary aspect from the concentration of its light; on the 27th of September the head appeared almost as bright as Mercury, but smaller ; when near its perihelion passage, on September 30th, its diameter, as ascertained by Signore Donati, was 3''; during the early part of October it continued to increase in brilliancy, the tail becoming more elongated, and describing a beautiful arc in the heavens, occupying a space of nearly 40°, or a length of 40,000,000 miles in the solar system, On the evening of the 5th of October it was seen from most parts of Britain, within 20' of Arcturus, the brightest star in the northern heavens, across which the densest part nearly of the tail passed, and through which notwithstanding the star shone with undiminished brilliancy. On the 30th of October, when in perihelio, the comet was only 55,000,000 miles from the sun ; on the 10th it approached nearest to the earth, from which it was then distant 51,000,000 miles ; and on the 15th of the same month near to Venus, being at that time less than one-tenth the distance of the earth from the Sun ; if the comet had reached its perihelion a few days earlier, Venus might have passed through its nucleus, the consequences of which to the planet it would be very difficult to imagine. The motion of Donati’s comet is what astronomer's call retrograde, or from east to west. It ceased to be visible in our northern latitudes in the last week in October, having passed into the southern heavens, where it will traverse the constellations of Sagittarius, Telescopium, and Indus, approaching the large star of Toucan ; after which it will disappear until it has nearly completed its revolution round the sun. The observed orbit of this remarkable comet coincides more nearly with an ellipse than a para
the longer diameter of the ellipse being 184 times that of the earth's orbit, or the immense distance of 35,100,000,000 miles--a space which, however great, is less than the thousandth of the distance of the nearest fixed star. According to the calculations of M. Loewy, and adopting an elliptic orbit, Donati's comet will not return to the same places in the heavens for 2495 years, being 500 less than the period of revolution of the great comet of 1811,
Signore Donati observed that between the 25th and 30th September two concentric, luminous, semicircular envelopes, with a
dark space between them, were formed in the head. From the extremities of these the cone of the tail extended, and a nonluminous or dark space stretched for 200 from the nucleus into the tail. On the 1st October the two envelopes were combined
This comet, like Halley's, has shown some singular irregularities, supposed to arise from the action of the sun when near its perihelion. At different periods of its apparition a violent agitation was observed in its nucleus, with luminous jets, spiral offshoots, &c., as in the great comets of 1680, 1744, 1811. A ray of light was thrown out from one side of the nucleus towards the sun, while a gas-like jet proceeded from the other side, which appeared to form the origin of a second tail within the great tail, and which was traced for half a degree by Mr. Hind on the 19th September. He observed decided spiral convolutions in the tail, which show that this comet has a rotatory motion about an axis passing through the tail.
If comets shine by borrowed light, they ought, in certain positions, to exhibit phases like the moon ; but no such appearance has been detected, except in one instance, when they are said to have been observed by Hevelius and La Hire, in the year 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 moonyet 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. Hence 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 now. Even if the light of a comet were polarized, it would not afford a decisive test, since a body is capable of reflecting light, though it shines by its own. M. Arago, however, bas, 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 whole, 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 decreases 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 after it has lost an apparent diameter, it ought to be visible, like the fixed stars, and should only vanish in consequence of extreme remoteness. That, however, is far from being the case—comets gradually become dim as their distance increases, and vanish merely from loss of light, while they still retain a sensible diameter, which is proved by observations made the evening before they disappear. It may therefore be concluded that comets shine by reflecting the sun's light. The most brilliant comets have hitherto ceased to be visible when about five times as far from the sun as we are. Most of the comets that have been visible from the earth have their perihelia within the orbit of Mars, because they are invisible when as distant as the orbit of Saturn : on that account there is not one on record whose perihelion is situate beyond the orbit of Jupiter. Indeed, the comet of 1756, after its last appearance, remained five whole years within the ellipse described by Saturn without being once seen. More than a hundred and forty comets have appeared within the earth's orbit during the last century that have not again been seen. If a thousand years be allowed as the average period of each, it may be computed, by the theory of probabilities, that the whole number which range within the earth's orbit must be 1400 ; but, Uranus being about nineteen times more distant, there may be no less than 11,200,000 comets that come within the orbit of Uranus. M. Arago makes a different estimate; he considers that, as thirty comets are known to have their perihelion distance within the orbit of Mercury, if it be assumed that comets are uniformly distributed in space, the number having their perihelion within the orbit of Uranus must be to thirty as the cube of the radius of the orbit of Uranus to the cube of the radius of the orbit of Mercury, which makes the number of comets amount to 3,529,470. But that number may be doubled, if it be considered that, in consequence of daylight, fogs, and great southern declination, one comet out of two must be hid from us. According to M. Arago, more than seven millions of comets come within the orbit of Uranus.
The different degrees of velocity with which the planets and comets were originally propelled in space is the sole cause of the diversity in the form of their orbits, which depends only upon the mutual relation between the projectile force and the sun's attraction.
When the two forces are exactly equal to one another, circular motion is produced ; when the ratio of the projectile to the central force is exactly that of 1 to the square root of 2, the motion is parabolic; any ratio between these two will cause a body to move in an ellipse, and any ratio greater than that of 1 to the square root of 2 will produce hyperbolic motion (N. 229).
The celestial bodies might move in any one of these four curves by the law of gravitation : but, as one particular velocity is necessary to produce either circular or parabolic motion, such motions can hardly be supposed to exist in the solar system, where the bodies are liable to such mutual disturbances as would