the star in the direction FE. Suppose now that the stratum of air DE is suddenly displaced, and replaced by another of different density, then the ray CD will not be refracted in DF, but in DI, and will not reach the eye; it is the ray CHF that arrives there, and the star that appeared to be in the direction FD is found in the line FH. If this new mass of air has no great volume, or if its temperature differs but little from that of the mass which it replaces, then the displacement and the change in the intensity of the light are not very notable. Planets scintillate less than stars, because, as the latter appear to us as points, the least displacement, were it merely 5 seconds, would be sensible to our eye. The planets having an apparent diameter of 30 or 40 seconds, it is more difficult to appreciate their apparent change in volume; however, through telescopes we frequently see the edges scintillate, especially if they are near the horizon. Under certain circumstances, the same phenomenon is observed on the circumference of the limb of the sun. We can easily imagine, that the light passing from stars situated near the horizon, which has a much longer course to traverse, may on its way meet with a mixture of strata of air of more variable density than those do that are placed above the head of the observer.

M.

Scintillation not only consists in the displacement of the star, but also in changes in its brilliancy and colour. Arago deduced these two orders of phenomena from the interference of luminous rays. Luminous rays that form together a small angle, and cut each other, may be mutually reduced and increased; under certain circumstances they destroy each other, and this fact, which is inexplicable if we consider light as a material emanation, is a very simple consequence of the system of undulations, and even the best proof that may be given of its reality. Throw a stone into quiet water, there will be formed a system of concentric circular waves, the common centre of which will be the point where the stone fell. Now, throw two stones at the. same time, at a certain distance from each other, each of the systems of circular waves will extend as if it were isolated, and, at the point where the two waves meet, their form is not changed, merely their height is increased. When the hollow interval between two waves, or the furrow that separates two successive waves, meets the interval of two waves of the other system, the furrow becomes deeper; but if on a certain point the wave of one system tends to raise the water, while the wave of the other system tends to

lower it, these two opposite movements destroy each other, and the water is quiet, or much less agitated than if there were only one system of concentric circles.

The system of undulations teaches us that the intensity of light increases when the luminous particles oscillate greatly around their mean position, as a bell or a chord resounds more powerfully at the moment when they are moved, because their oscillations are then greatest. The amplitude of these oscillations, that is to say, the deviations of two successive waves, are not the same for the different rays of the spectrum; as in the different tones of the musical gamut, one of them makes in a second a number of oscillations less by one-half than that which is an octave higher hence it follows that the amplitude of the oscillations of the first is double that of the second. Exact measurements have proved that the deviation of two waves is less as we advance from the red toward the blue end of the spectrum.

These principles being established, we may easily deduce from them the changes in the intensity and colour of a star. Among the rays which leave it simultaneously, and which are differently refracted, a great number unite either in our eye, or in their course through the atmosphere. If they so meet each other that their waves are united, they mutually reinforce each other; but, if a wave is added to an interval, then they weaken or destroy each other: hence the alternate increase and decrease of light. As, in the atmospheric state that we have described, the refraction changes at every moment, the rays also meet and reinforce or reduce each other every instant. As the light that comes from the stars is susceptible of decomposition into its elementary colours, like that coming from the sun, we must attribute its increase and its diminution to the meeting of its elementary rays. It may, therefore, happen that the red is annihilated by the meeting of two rays of this colour, whilst the blue becomes more intense: the star will then appear blue; a second afterwards, the contrary may occur, and the star will assume a red tint.

MIRAGE.-Like as the rays that come from the stars are refracted so that they appear to us more elevated, so also those that come from terrestrial objects undergo an analogous deviation. This consideration is of the highest importance for the measurement of mountains by landsurveying. It is only when the object is in the zenith, or in the same horizontal plane as our eye (supposing the stratum containing both to be of the same density), that

there is no refraction: this last condition is seldom realised, on account of the action of the ground on the aërial strata with which it is in contact.

Look at distant objects during calm and fair weather, or at the shadow projected by trees on a surface heated by the sun, you will see their form continually oscillating; this effect is much more marked, if we look through a telescope at objects situated in the horizon. Very frequently pieces of the horizon seem to be detached, and to float in the air, and then fall again. If the object is small, it will appear double or multiple: thus M. Biot, on looking through a telescope at a very distant light, saw it double, the coloured and extended image was placed vertically above the real light. An instant after, instead of two lights he saw several, which appeared and disappeared at regular intervals; the lowest, which were nearest to the real light, were the largest and most brilliant. Sometimes objects situated in the middle of a plain appear double, and several images are formed above and beneath them: this phenomenon is known under the name of mirage, on the north coast of Germany it is called Kimmung.

Let O (pl. v. fig. 4) represent the eye of the observer: the line HH' represents the horizon. If the ray OH traversed a stratum of air of equal density, the object H would be seen in the place it really occupies; but, if the weather is calm, and the earth highly heated, the temperature diminishes rapidly from the surface of the ground, and the change of density in the lower strata, which is the consequence, changes the refractions. The ray H'C, in passing at C from a hotter into a colder, and consequently a denser stratum of air, approaches the vertical: and, as this effect takes place in each stratum, it follows that it describes the curve H'CA, and does not reach the eye: but another lower ray describes the curve HDO, and reaches the eye, and, the object seen at H appearing inverted, we might imagine that it is reflected on a transparent liquid. The illusion is the stronger, as the rays from the points intermediate between H and H' do not reach the eye, and it appears as if there were a void space in the neighbourhood of the inverted image-a space, which we are the more tempted to regard as water, because the currents of air that mix make the objects tremble, and resemble a surface agitated by wind. If the air is colder at the surface of the sea, or of fields of ice, than it is a few decimetres above, the inverted image is above the object; and above the first image is a second that is not inverted. Wollaston points out a very simple

experiment, by which this phenomenon is realised: a cubical vessel with plane surfaces is selected; into this is poured first water and then sulphuric acid by means of a funnel, the extremity of which touches the bottom. When the experiment is carefully made, the sulphuric acid occupies the bottom of the vessel, but its strata go on diminishing in density as they approach the surface of the water. If now we place behind the vessel a paper covered with a few letters, and the eye is on the same horizontal line, we may see the object directly and by refraction.

The mirage for the most part occurs in extensive plains, when the weather is calm, and the ground heated by the sun; the plains of Asia and Africa have become celebrated in this respect thus, during the expedition of Egypt, the French army frequently experienced cruel deceptions. The ground of Higher Egypt forms a plain perfectly horizontal; the villages are situated on small eminences. In the morning and evening, they appear in their proper places, and at their real distance; but, when the ground is highly heated, the country resembles a lake, and the villages appear built on islands, and reflected in the water. As we approach, the lake disappears, and the traveller, devoured by thirst, is deceived in his hope. This phenomenon is so common in these countries, that the Koran designates every thing deceitful by the word serub, which means mirage. It says, for example: "The actions of the incredulous are like the serab of the plain; he who is thirsty takes it for water, and finds it to be nothing." Although it is more common in the East, yet the mirage exists in our plains much more frequently than is imagined, expecially when we bring the head near the surface of the ground: I have observed it in the neighbourhood of Halle, in the country of Magdebourg, and on the coasts of the Baltic, where I often have thought myself in the midst of a large bed of water.

If the ground is colder than the air in contact with it, then the temperature of the aerial strata rapidly increases with the height, and we not only see above the object its inverted image, but the visual circle of the spectator is singularly augmented. Scoresby made a great number of observations of this kind in the seas about Greenland. June 19, 1822, the sun was very hot, and the coast suddenly appeared to come 25 or 35 kilometres nearer; the different eminences were so raised that they were seen as easily from the deck of the ship as they were before from the fore-top. The ice in the horizon assumed singular forms, the larger blocks seemed columns; icebergs and fields of ice, a chain

of prismatic rocks; and, in many places, the ice appeared to be in the air at some minutes above the horizon. Ships, that were in the neighbourhood, assumed the most whimsical forms; in some, the mainsail seemed reduced to nothing, whilst the foresail appeared four times larger than it really is; the topsail appeared shortened. There were also other whimsical appearances. Above the topsails was seen a sail resembling top-gallant-sails loose from the bolt-rope; in others, the topsail seemed divided into two, inasmuch as the true sail was separated from its image by an interval. Above distant ships, their own image was seen inverted and magnified; in some cases, it was very high above the ship, and then it was always smaller than the original. The image of a ship, that was itself below the horizon, was seen for several minutes; a ship was even surmounted by two ships, one in the right position, the other inverted. Some days later, Scoresby saw the same appearances: "The most curious phenomenon," said he," was to see the inverted and perfectly distinct image of a ship, that was below our horizon. We had observed similar appearances; but the peculiarity of this was the distinctness of the image, and the great distance of the ship it represented. Its outline was so well marked, that, on looking at this image through one of Dollond's telescopes, I distinguished the details of the rigging, and of the hull of the vessel, I recognised it as being my father's ship; and, when we compared our logbooks, we saw that we were then 55 kilometres apart, namely, 31 kilometres beyond the real horizon, and many myriametres beyond the limit of distinct vision."

There is a mirage, in the proper acceptation of the term, when we see below the object its inverted image; and then the air is hotter in the neighbourhood of the ground than at a certain height. This phenomenon evidences an anormal state of the atmosphere, and the calm, indispensable for its production, is often troubled by ascending currents and violent gales of wind: so that several observers say that the mirage is the precursor of a tempest.

CORONE AND HALOS IN GENERAL.-When the light coming from the stars falls on condensed vapours in the vesicular state, or on icy particles, it experiences different modifications; thence follow phenomena known under the name of corone and halos; generally these two words are used to designate phenomena that are very different in their aspect and their origin. When the sky is covered with light clouds, we often see a coloured circle, in which red predominates, surrounding the moon or the sun;