its place as seen from the earth, may be readily found by the solution of a triangle, formed by lines joining the sun and planet, the sun and earth, and the planet and the earth. The angle at the sun is equal to the difference between the heliocentric longitude of the earth and the planet. One of the sides of the triangle is equal to the distance of the earth from the sun, and the other is equal to the distance of the planet from the sun; so that from these data, the angle formed at the sun, or the difference between the geocentric place of the sun, and the geocentric place of the planet, may be easily obtained; or we may obtain the angle formed at the planet, which is the difference between its heliocentric and geocentric place.

On the Changes that have happened in the relative situation of Double Stars.

THE late Sir W. Herschel remarks, that the affections of the newly-discovered celestial bodies extend our knowledge of the construction of the solar system, which is the one best known to us; and proceeds to support, by the evidence of observation, the opinion, which he has before advanced, of the existence of binary sidereal combinations, revolving round the common centre of gravity. Dr. Herschel first considers the apparent effect of the motion of either of the three bodies concerned, the two stars, and the sun with its attendant planets; and then states the arguments respecting the motions of a few only out of the fifty double stars, of which he has ascertained the revolutions. The first example is Castor, or Alpha Geminorum: here Dr. Herschel stops to show how accurately the apparent diameter of a star, viewed with a constant magnifying power, may be assumed as a measure of small angular distances; he found that ten different mirrors, of seven feet focal length, exhibited no perceptible difference in this respect. In the case of Castor, no change of the distance of the stars has been observed, but their angular situation appears to have varied somewhat more than 45° since it was observed by Dr. Bradley in 1759; and they have been found by Dr. Herschel in intermediate positions at intermediate times. Dr. Herschel allows that it is barely possible that a separate proper motion, in each of the stars and in the sun, may have caused such a change in the relative situation, but that the probability is very decidedly in favour of the existence of a revolution. Its period must be a little more than 342 years, and its plane nearly perpendicular to the direction of the sun. The revolution of Gamma Leonis is supposed to be in a plane considerably inclined to the line in which we view it, and to be performed in about 1200 years. Both these revolutions are retrograde; that of Epsilon Bootis is direct, and is supposed to occupy 1681 years, the orbit being in an oblique position with respect to the sun. In Zeta Herculis, Dr. Herschel observed, in 1802, the appearance of an occultation of the small star by the larger one; in 1782 he had seen them separate; the plane of the revolution must therefore pass nearly through the sun; and this is all

that can at present be determined respecting it. The stars of Delta Serpentis appear to perform a retrograde revolution in about 375 years their apparent distance is invariable, as well as that of the two stars which constitute Gamma Virginis, the last double star which Dr. Herschel mentions in this paper, and to which he attributes a periodical revolution of about 708 years.

On the great Corona, or Circles which sometimes surround the Sun and Moon.

As it may be satisfactory to some of our readers to know the opinion of so celebrated a Meteorologist as Mariotte on the cause of the circular ring which sometimes appears round the sun and moon, we shall present them with the following extract from his work on Colours:

"Sometimes, when the air is pretty serene, a circle of about 45° diameter is seen round the sun or moon; the colours are not in general very lively, the blue is without, and the red within; their breadth is nearly as in the common external rainbow.

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Explanation. I take for the cause of this appearance small filaments of snow, moderately transparent, having the form of an equilateral triangular prism. I conjecture that the small flat flakes of snow which fall during a hard frost, and which have the figure of stars, are composed of little filaments like equilateral prisms, particularly those which are like fern leaves, as is easily seen by the microscope. I have often looked at the filaments which compose the hoar frost, that appears like little trees or plants in the cold mornings of spring and autumn, and I have found them cut into three equal facets; and when viewed in the sunshine, they exhibited rainbow colours. Now it is very propable that, before these little figures of trees or stars are formed, there are floating among the thin vapours in the air some of these separate prisms, which, when they unite, form the compound figures. These little stars are very thin, and very light, and the little filaments, which compose them, are still more so, and may often be supported a long time in the air by the winds: hence when the air is moderately filled with them, so as not to be much darkened, many of them, whether separate or united, will turn in every direction as the air impels them, and will be disposed to transmit to the eye for some time a coloured light, nearly like to that which would be produced by equilateral prisms of glass."

On Meteoric Stones.

It had long been conjectured by several persons in this country, that the stones said to have fallen from the air, on different parts of the earth, and lately analysed by Mr. Howard, might originally have been emitted by lunar volcanos facing the earth; and meeting with little or no resistance from the moon's atmosphere, might have risen to such a height, as to be more powerfully attracted by the earth than

by the moon, and, of consequence, to be compelled to continue their course, until they arrived at the confines of our atmosphere, and were again retarded by its resistance.

The idea has been lately renewed in France by Laplace; and the inflammation and combustion of the stones has been attributed to the intense heat which must necessarily be extricated by so great a compression of the air, as would be produced by the velocity with which these bodies must enter the atmosphere.

Mr. Biot has calculated, that an initial velocity, about five times as great as that which a cannon ball sometimes receives, would be sufficient for the projection of a body from a lunar volcano into the limits of the earth's superior attraction, which are situated at nearly one-ninth of the distance of the earth from the moon.

A body, entering the atmosphere with such a velocity, would soon experience a resistance many thousand times greater than its weight, and the velocity would therefore soon be very considerably lessened. It may easily be shown, that a stone of moderate dimensions could scarcely retain a velocity of above 200 feet in a second. With respect, however, to the actual probability of the stones in question having been projected from the volcanos of the moon, there will, perhaps, long be a diversity of opinion; and, in the absence of all accurate knowledge on the subject, it would, perhaps, be unphilosophical to attempt to establish any theory respecting their origin.

Upon the Precision to be attained with Astronomical Instruments.

MR. AMICI, in a letter addressed to Baron Zach, affirms, that, on a circle of 3 feet, one cannot, even with the aid of a vernier and simple microscope, discern two or three seconds, even though the instrument be mathematically divided with the utmost precision."To prove this," says he," I draw upon a sheet of white paper two thick vertical lines of an inch, in such a manner, that the right side of one is parallel with the left of the other. These two lines may be considered as belonging, one to the limb of the instrument, and the other to the vernier. I place this paper in a very strong light, and I raise myself perpendicularly from it to the distance of 28 feet; I look at these lines with one eye, and I see them united as though there were but one line. Here then is the utmost extent of my sight, at which I judge the lines to be joined, although in reality there is a distance equal to their own length between them. This limit expressed by the angle formed by the object in the eye of the observer answers to 51 seconds; but in a circle of 3 feet in diameter, the arc of a second occupies 0·001 of a line; and this arc forms in the eye of an observer, furnished with a simple microscope, of an inch focus, an angle of 17 seconds, consequently invisible to me."

Mr. Amici closes his letter by remarking, that no astonishment ought to be excited at the inaccuracies to which the most experienced astronomers are subject, making a difference of from 1 to 5 seconds,

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if due attention be paid to the errors which are likely to result from the optical parallax between the divisions of the limb and those of the vernier; the inequalities of the lines which form those divisions rendering their union equivocal and doubtful; the reflexion of the glasses; the unequal expansion of the metal; and the irregularity of the surface or levels.

Upon the apparent Size of Objects caused by the Refraction of Light in passing through the Atmosphere. By JEAN MILE, Professor of Physiology.

THE author, in a letter addressed to Mr. J. C. Skrodzki, Professor of Physic at Varsovie, recalls to his recollection, that, after having gone through the explanation of this well-known phenomenon, they were mutually convinced of their insufficiency. He therefore proposes an explanation founded upon the refraction of light, which enables us to perceive objects situated beyond the limits of our atmosphere. This refraction not only enables us to see objects in a situation different from their real position, but it also changes their real size. This latter effect resembles the former in this, that the nearer the objects are to the horizon, the greater is their apparent size; or, what amounts to the same thing, the greater their distance from the zenith, so in proportion is their size. The rays of light which traverse the air through a denser medium than itself, terminated by plane or parallel surfaces, follow, in issuing from the latter, a direction parallel to their incidence. But it has been falsely concluded in this case, that the object is seen under the same angle as though the rays had only passed through one medium. The author affords us eight successive theorems, which he links with each other, and the last of which explains the phenomenon of the apparent size of objects.

Theorem 1st.-An object and the observer being situated in the air, should the visual rays which pass from the one to the other traverse an intermediate medium, terminated by plane surfaces, the visual angle will become greater.

He gives a demonstration of this upon mathematical principles, which would be too long to be inserted here. The following experiment, however, will render his axiom perfectly comprehensible. Procure a tin tube, three inches in diameter, and a yard in length, the two ends of which must be closed with plain glass. The tube is then to be placed in a horizontal position, and half filled with spirits of wine, that is to say, to its central axis; and if an object then be viewed through the tube, that half of the object which is seen through the medium of the spirits of wine will appear to be much larger than the half seen through the air alone. In general, the degree of augmentation is in a direct ratio to the depth of the refracting medium, and consequently depends in this instance upon the length of the tube. Theorem 2d. The visual angle will never change, so long as the rays from the surfaces are spherical; and their radii will be respec

tively equal to the distance of the eye to each of them; in fact, the eye being situate at the centre of the curves which terminate the medium, the visual rays proceeding in the same direction will not be subject to the slightest deviation. The object then will be seen under the same angle. This may be proved by the following experiment. A conical shaped tube of tin may be half filled with spirits of wine, as mentioned above, and each end enclosed with watch glasses of different diameters, and then placing the eye in the direct centre of the two spherical surfaces in the front of the tube.

Theorem 3d.-The visual angle will become smaller when the radii from the surfaces are spherical, and are respectively smaller according to the distances of the eye from them. This may be easily proved by the above-mentioned apparatus, by placing the eye at a greater distance from the central point of the termination of the two spherical surfaces.

Theorem 4th-Is the converse of the preceding one; that is to say, the visual angle is greater when the radii from the surfaces, are spherical, which terminate the refracting medium, and are respectively greater than the distance between the eye and each of them. This is also to be proved by the before-mentioned apparatus, by placing the eye at a less distance from the tube than that between its centre and the termination of its spherical surfaces.

Observation. Should the medium in which the eye is situated be of greater density, the refraction will occasion phenomena directly the contrary. This is the case with the objects placed beyond the limits of our atmosphere.

Theorem 5th.—The surfaces of the refracting medium being spherical, and their radii being equal to the distance of the eye from each of them, the visual angle will not be changed. This would be the case were the eye situated at the centre of the earth, which is physically impossible.

Theorem 6th.-If the distance of the eye be greater than the radius of the surface of the refracting medium, the visual angle will become greater. This would be the case were an observer situated in such a manner that the centre of the earth intervened between him and the celestial bodies, which is physically impossible.

Theorem 7th.-If the distance of the eye be less than the radius of the refracting surfaces, the visual angle would be less. This is what always takes place, at least, when we look at the celestial bodies.

Theorem 8th.-Although the heavenly bodies ought to appear much smaller when seen from the surface of the earth, owing to the refraction of light, still the degree of diminution of the visual angle depends upon the greater or less extent of the refracting medium, that is, the atmosphere;-the diminution of the visual angle, therefore, is less according as these limits are more extended. Hence it results, that the heavenly bodies appear to us so much the larger, in proportion as the limits of the atmosphere are extended. These bodies, therefore, will increase in size in proportion to the increase of their distance from the zenith; for the nearer they approach the horizon, the more extensive are the limits of the atmosphere, though