alternative, that the horizon moves to the star. His horizon, then, alters its position as the observer moves, revolving continually towards those stars which are behind him, and from those which are before him. Now we have before shown that the horizon of an observer, anywhere on the earth's surface, is a plane drawn through his eye, touching the earth, —it is a tangent plane to the earth's surface; and we have now shown that this plane alters continually its direction; its position is different for different points of the earth's surface. Here then is a complete geometrical proof of the curvature of the earth; for that surface which has, at different points, tangent planes in different positions, that is, which, when produced, do not coincide with one another, must be a curved surface. And on this supposition, the phenomenon is readily explained. R P Let ABC be different positions of the eye of our observer, and we may suppose his eye to be actually within the earth's surface, since his height is comparatively very small. Then will the planes CR, BQ, AP be the horizons of the observer, or planes beneath which nothing will be seen by him in these several positions. It is apparent that, as the observer passes from a to c, his horizon, as it were, rolls with him; and, by this motion, the distance between it and any star measured on that imaginary vault of the heavens to which he refers, the position of the star is continually made to diminish; also, not being conscious of the motion of his horizon, he attributes the motion to the star which he imagines to sink continually behind him as he moves onwards. But there may be an infinity of curved forms. The question then arises, What is that particular form of curved surface which bounds the mass of the earth? What is the shape of that lump of matter of which we have ascertained it to be composed? Is it a cylinder or a cone, of an oblong or an oval form, or is it an irregularly shaped mass? We can now answer this question satisfactorily. It has been shown that, as an observer moves about on the earth's surface, his horizon, as it were, rolls with him from place to place. Now if this rolling motion of his horizon be uniform, so that, whilst he moves over the same distance anywhere on the earth's surface, and his horizon is thus made to roll over the same distance, it also is made to describe the same angle towards the stars; it is clear that the earth's surface must have everywhere the same curvature, and be a sphere; for if it have anywhere a greater curvature than elsewhere, it will there necessarily roll through a greater angle, in rolling over the same space. Thus, for instance, if we make a plane flat surface roll over an inch at the sharper or more curved extremity of an egg, it will evidently roll through a greater angle than when made to roll over an inch at the thicker extremity, or on either of the sides of the egg. Now, the angular motion of the horizon of an observer, travelling over the earth's surface, may be ascertained by its angular approach to any fixed star; and it is found, by numerous actual observations of this kind, that when the horizon of an observer is made, in any two different places on the earth's surface, by a change of the same distance in his position, to roll over the same space (say sixty-nine miles), due north or south; it revolves also through very nearly the same angle, approaching or receding from any fixed star by the same angular quantity. It follows then, with absolute certainty, that the earth is very nearly a sphere. Very nearly, because the angle through which the horizon thus rolls, in any two different places, is not exactly the same; it is slightly greater towards the equator than at the poles. The earth is, therefore, slightly more curved at the equator than at the poles. Its form, in fact, is somewhat that of an orange: the polar regions corresponding to the parts about the extremities of the shorter diameter of the orange. Let us suppose our observer, by this time, to have acquired sufficient knowledge of geometry, to perceive that the angle through which his horizon revolves between any two stations is, in point of fact, the same as the angle made between two lines drawn from those two stations to the earth's centre*; and very little knowledge of geometry is necessary for this purpose. Knowing this fact, it will at once suggest itself to him, that he may determine the complete girth or circumference of the earth by a very simple process. He has only to move on until he has made his horizon to revolve through any given portion, say to the 360th part of a complete revolution. He then knows that he has also made the line, drawn from him to the earth's centre, to revolve through the 360th part of a complete revolution. The distance between his two stations is, therefore, the 360th part of the earth's ircumference. Let him then measure this distance, and multiply it by 360, and he will get at once the complete girth of the earth; this he will thus find to be about 25,000 miles. Now, knowing the circumference of a great circle of the earth, he can find the diameter of the earth and its solidity. The polar diameter of the earth is thus found to be 7899 miles, and its equatorial diameter 7925 miles. *Thus let A and B be two positions of the observer, and let AC and Bс be perpendiculars to the horizons at those points which, if the earth were accurately a sphere, would meet in its centre. Let SA and TB be straight lines, drawn from a star to an observer, at the points A and B; these lines are parallel, since the star is infinitely distant. Let AH and BK be the horizons at A and B; then are SAH and TBK the altitudes of the star, as seen from A and B; and the descent, or sinking of the star, by reason of the motion of the observer from A to B, is the difference of these altitudes. Now since AS and BT are parallel, therefore TBK is equal to BQA, and the difference of BQA and SAH is QPA; therefore the difference of TBK and SAH is QPA. QPA is therefore the difference of the altitudes of the star at the two points of observation. Now QPA = ACB ... &c. SKETCHES FROM LIFE OF SOME EMINENT FOREIGN SCIENTIFIC LECTURERS. WE suspect that Blackwood's Edinburgh Magazine is seldom consulted by the ardent student of natural or applied science, and that if No. CCXLV of that powerfully written periodical should accidentally offer its table of contents to his observation, "PARIS MORNINGS ON THE LEFT BANK OF THE SEINE," would scarcely, as a title, induce him to suppose that anything in harmony with his pursuits would be found there. It is more than probable that he would not, agreeably to its instructions, apply to page 296 for further information. Under this impression, and anxious that this class of our readers may be able to enjoy a few minutes of these brilliant mornings, we have made some extracts. We intend that these should convey some idea of the energetic action of the moral apparatus with which the lecture-rooms of Paris are so richly furnished. In perusing them we are sure that the natural and blameless curiosity which urges us to become acquainted with the persons and manners of those whom we admire and honour, will be greatly interested. The venerable Christopher, though wandering among Institutions whose legal protector is "a citizen king," forgets, at least in the specimens we propose to give," the fierce democracy" against which he has sworn eternal war, and mingling with the doctors of the Sorbonne, puts on the professor's robe, and, with his usual vigour, lectures on those who have been all their lives lecturing to others. "Beginning at the beginning," he makes the usual flourish―chronological, antiquarian, and learned, but soon seizing the crayon, he sketches the locality and the furniture of the antique hall in which he stands, and then with his wonted breadth, and more or less of finish, he selects a head, and dashes off a "study from nature." Eminently successful, both in his subjects and his effects, he thus presents a series of highly characteristic portraits of some of the greatest men in the French capital. The force of these sketches will be universally acknowledged. We know that their fidelity must be assented to by all who have had the enviable means of judging. We can fancy ourselves once more in the vast and shabby amphitheatre of the Sorbonne, sitting upon one of its long and dirty benches, surrounded by a host of enthusiastic students, and waiting the arrival of the lecturer; though the walls may be ill painted, and the ceiling smoky, and the furniture of the roughest workmanship, yet there is about the whole so perfect an air of business, that every one who enters, at once feels that he is in no place for display and ornament, but in a thorough school for the investigation of science. In front is the long table with its load of apparatus all ready for use, whilst against the distant wall is the gigantic slab on which the professor has chalked out his illustrations, and which, before his entry, the student is now busily copying into his note-book. This slab has, indeed, been an ancient and a noble herald of information and recorder of discovery, and is well worthy of the honourable mention which has been made of him. We think that he must have leapt in his old grooves, in spite of • lute and specific, g on its back. at the "Salve" of the following gratul fins. " "Hail! old Slate of Rimorgne! what changes in the face of science have been represented on your face, since you were first brought from your dark cold bed, with marl for a mattress, and red sand-stone for a counterpane! Many a learned conjecture respecting your own bodily formation has been hazarded in your very presence; yourself the theme of discussions, on which your own revelations would have been conclusive, had nature permitted the unfolding of subterranean secrets. An unnatural conspiracy, truly, was that of brother minerals, charcoal, sulphur, and nitre, which betrayed you into the power of man, and blew up your early attachments! What has not been dared and done in those quartiers bruyans* of Paris, from which the river happily divides us, most venerable Schistus, since you were first smoothed and squared, mounted and framed ? All that Blainville quietly imparts, or Mirbel more strikingly exhibits, has been confided to you! Where be the mysteries that you have not assisted to simplify? How oft has the nisus formativust of animal, vegetable, and mineral existence been canvassed on your impartial square! How often has your intelligent panel telegraphed to the distant benches of the large audience, not only all the ́ discoveries, but all the Pseudo-Eurekas‡ of the learned! The hand of a Cuvier has lately swept over your plain! the creative touch of a Jussieu has made fair flowers spring up from your unpromising soil, amidst the winds of March! Myriads of insects, marshalled by St. Hilaire, have crept over your tableau vivant §! Fishes have I seen, how often! in all the audacity of tail and fin, sporting upon your black sea! Here the mountain has been bidden to rise by some daring geologist; there the continent has been abridged by encroaching waters;-sponged away while he yet spake! Comets have displayed their streaming banners, and clustering stars have sown their galaxy on that dark firmament! Nor is there, in fine, anything susceptible either of exhibition or of demonstration, of diagram or picture, which has not furnished its contribution, and been octroyed || on that most fertile field, which produces, often on one day, its triple and quadruple harvests." Soon after the Veteran proceeds to the professors themselves. We shall pass over those of metaphysics, history, belles-lettres, &c., and take only such as are occupied with physics. Here is the lecturer on natural history, BLAINVILLE. "What one cannot fail, I think, to be most struck with at the Sorbonne, is that unambitious, unrhetorical manner cultivated by those enviable teachers, who have devoted themselves, their talents, and sometimes even their fortunes, to the study of 'Nature;'-who interpret her laws without ostentation, and present her in such advantageous simplicity to minds not yet conversant with her charms. We have one Faraday, the French have more than one. Is it possible, I have sometimes asked myself, that a naturalist can really be peevish? Let them talk of you, Monsieur Blainville, as the most ill-tempered personage that ever exhibited the fang of a rattlesnake or the thorny lophoderme¶ of a centronate** or stickleback! but we have had ample means of ascertaining your indulgence to the persons who approach you for information, and are convinced that, au contraire, you are essentially a good-humoured and an excellent specimen of our order of mammalia; we have attended your lectures regularly, and have not only seen specimens of all your favourite fish, but can attest with what wonderful + Mares' nests! ** A kind of fishes. *Turbule § Vivid pictu points of origin. Hairy skin. sleight of hand your rapid chalk can gird on the armour of an Ophites, give its Highland cheekbone to the gurnard, spread its soft pearly coating over the mackerel, or exhibit upon the ever-changing field of the large Slate, the wonderful apparatus of the gymnotus*! We have also seen your book upon shells, or rather upon malacology, which, while it displays the deepest research, contains abounding proof that classifications may be founded on philosophy. Yes! there are higher exercises of the psychological functions, even in the study of this branch of science, than pinning a butterfly in a grove of cork, or drowning a beetle in alcohol. Surely there is nothing meaner (short of being positively vicious) than seeing some old collector, thumbing his dirty copy of Latreille, conning over, to him, hard Greek names, counting the segments in the corslet of a fly, or noting the subdivisions of the tarsus of a flea's foot. The study of nature, if this be such, so pursued, and pursued no further, does positive harm, by bringing discredit upon the science of natural history, and debasing the philosopher down to a mere accumulator of specimens. "Monsieur Blainville is about 55, evidently of a happy crasis‡, indefatigable and enthusiastic now, as they say he was twenty years ago, and never tired or tiresome, though he lectures frequently for two hours at a time. From Monsieur Blainville I have learnt to be no longer astonished at the velocity of the swimming powers of the mackerel; he has instructed me that all the Scombri§ have this property of outstripping most of their neighbours in speed, and that this facility of motion (in which they excel all other fish) depends on the bifurcation of their tails. The Tunny and Dorax (of this family) swim at the rate of eight leagues per hour! and the fleetest fliers among birds have this same peculiarity. The swallow will immediately occur, and thus a very interesting analogy is established between birds and fishes.' The erectus in terga sudes ||' of Juvenal had perplexed commentators; but Blainville interprets the poet and the passage, by showing that the rhombus actually has this property of erecting his bristles, and in a way which is truly remarkable. "In birds, reptiles and insects, there are some which have been falsely called apteroids ¶, or apods**; for they possess in concealment the members which their name declares them to want; and this analogy also extends to fish, some of which have been falsely supposed apods in consequence of their ventral fin being concealed within their body.' "All fish have what are called stones in their ears; in the scienæ, these stones are of a very large size, and are three in number. Of the percidæ, which frequent rocks, and are common at Dieppe and along that coast, I show you here the apistos, or, as he is emphatically called, sting-fish, whose large supply of spines is probably intended to protect him from being driven against the rocks by the lashing of the waves—just as the rower pushes out his oar or his boat-pole for the same purpose. As the swim-bladder is found very large in some fish which swim little, and small in others that are expert swimmers, and does not exist at all in the mackerel, which is the fleetest swimmer we know, the swim-bladder must answer other and more important ends, than the one from which it derives its name."" The next sketch is that of M. Pouillet, the professor of physics. *Electrical eel. § A kind of fishes. + Treatise on soft-shelled fishes. **Without feet or fins. Temperament. Wingless. |