perhaps the best that can be employed to obtain promptly the total amplitude of a great arc of parallel, not only because it is independent of the errors which might result from the ordinary method of absolute time determined at intermediate stations at a short distance from one another, but because it is not liable to the irregularities in the diurnal movement of chronometers. Nevertheless, as it is of importance to compare together different arcs of the same parallel, it will be highly useful to ascertain separately the difference between the meridians of Brest and Paris, and that between the meridians of Paris and Strasburg. The parallel of the 45th degree, of which we have just spoken, is joined in one direction to one of the sides of the meridian of France, and in the other to the base of Beccaria, near Turin, being verified by the French geographical engineers, as well as by M. Plana, and other Italian philosophers; so that the method laid down by La Place in the third Supplement to his "Analytical Theory of Probabilities," might be easily applied for correcting in the most advan tageous manner this arc and its several parts, by the difference existing between the entire base measured directly, and its length, as deduced from the chain of triangles.. The calculations relative to the comparison of an arc of the parallel with an arc of the meridian, are capable of being effected in a manner analogous to that made use of for determining the oblateness of the earth, by the measure of two arcs of meridians under different latitudes. In fact, there exists a relation between the length of an arc of the meridian, considered as elliptical, and the latitude of its extremities; and this relation is essentially a function of the radius of the equator, and of the oblateness of the earth. In like manner, an arc of the parallel in any given latitude, is a function of its amplitude, of the radius of the equator, and of the same oblateness; thus, proceeding by the ordinary mode of elimination, we can obtain these two last unknown quantities; that is to say, the dimensions of the oblate spheroid at the point where the two combined arcs cut one another, and consequently can ascertain whether the figure of this solid is the same generally attributed to the whole earth, according to the comparison made of the arcs of meridians measured in France and at the equator. If the parts of the parallel thus examined are not proportional to their amplitudes, it will be advisable to determine the spheroid which corresponds best upon the whole with the observations of longitude, and this by using the method of the smallest squares, invented by M. Legendre, and demonstrated by M. Laplace to be the most advantageous. In this case, conditional equations must be formed between the errors to which observations are liable and the oblateness of the earth; and if among the smallest probable errors which affect the observation of longitude, there should be any too considerable to be really attributable to the observations, it may be concluded that the spheroid sought is not that of revolution. The surest method will then be to have recourse to the admirable theory given in the third book of the Celestial Mechanics of La Place. The grand trigonometrical surveys undertaken to furnish materials for the new topographical map of France, and the numerous observations of the pendulum carefully collected by the Board of Longitude in that kingdom, concur to throw a new light upon the difficult question of the figure of the earth. And it is to be earnestly hoped that, in other countries besides France, similar exertions in favour of science and public utility will be promoted and patronised. On the Agency of the Earth in producing Meteors. THIS gentleman, in a memoir read to the Natural Society of Halle, proves, in various ways, the existence of a lower terrestrial atmosphere; he thinks himself justified, by the reasons he alleges, in concluding with certainty, that this atmosphere, which may penetrate to a depth of twenty geographical miles into the interior of the earth, is already compressed at a smaller depth, so that without being liquid, it forms a fluid equivalent to water. Hence there results for the lower terrestrial atmosphere a mass, in comparison of which, the higher atmosphere, which is known to be equal in weight to a column of water, about thirty feet high, appears very small. It is to this mass of inferior air, contained in the pores of fossils, in cavities, in abysses, and even constituting part of the elements of fossils, that the professor attributes the greater part of meteors; while that insignificant mass of air, disseminated in the form of vapour, and hitherto called the atmosphere, at most contributes but slightly to their creation. As he attributes the barometrical phenomena to the inferior atmosphere, he likewise denies the influence of the moon upon the weather. On the Colours of the Atmosphere. If the earth's atmosphere consisted of a medium unlimited, and perfectly homogeneous, the sun and planets would shine in a firmament of the most intense darkness, similar to what has been observed by travellers on the elevated summits of the Alps and the Andes. As the atmosphere, however, is of a limited extent, and composed of strata of variable density, the light of the sun which falls upon it is reflected in every direction, and reaches the surface of the earth with that chaste tinge of blue, which forms such a fine relief to the yellowish light of the heavenly bodies. The blue colour of the sky was attributed by Fromondus, Otto Guericke, Wolfius, and Muschenbroek, to a mixture of light and shadow. Sir Isaac Newton and Bouguer, on the contrary, were of opinion, that the particles of air reflect the blue rays more copiously, and transmit the red. This explanation, which was then little better than a mere conjecture, has been rendered highly probable by the experiments of Dr. Brewster on the polarisation of light. He observed that one of the images of certain parts of the sky, formed by a doubly refracting crystal, was much bluer than the other, and that the images changed their tints alternately. Upon the supposition, therefore, that the light of the sky consists of two portions of light, one blue and the other nearly colourless, we may explain all the phenomena which appear, when the light of the sky is examined in different azimuths, and in different planes passing through the sun. The phenomena of blue shadows, which have been so often observed, arise from the illumination of the shadows of bodies by the blue light of the sky, the parts without the shadow being illuminated by some other light, such as that of the sun or of a candle. These coloured shadows are generally seen with most distinctness at sun-rise and sun-set, when the sun's light has a yellow tinge. The colours of shadows illuminated by the sky, vary in different countries, and with different seasons of the year, from pale blue to a violet black; and when there are yellow vapours in the horizon of yellow light reflected from the lower part of the sky, either at sunrise or at sun-set, the shadows have a strong tinge of green, arising from the mixture of these accidental rays with the blue tint of the shadow. The phenomena of coloured shadows are often finely seen in the interior of a room. They arise from the blue light of the sky, and the light reflected either from the furniture, or the painted walls of the room. M. Hassenfratz has written a very elaborate memoir on the subject of coloured shadows, and has deduced the following conclusions from his various experiments and observations. 1 That the shadows formed by the direct light of the sun and that of the atmosphere, vary from a meadow green to a violet black, in a gradation through the blue, indigo, and violet; and that the variation depends on the intensity of the light of the sun, compared with that of the atmosphere. 2. That the shadows formed in apartinents by the light of the atmosphere and reflected lights, may present all the prismatic colours, more or less changed by black. 3. That the shadows produced on a piece of pasteboard, illuminated by artificial light, are reddish and blueish, more or less deep; and, that very probably, the blueish and reddish tints of the shadows, depend on the proportion of hydrogen and carbon in the combustible bodies. |