A SPECTATOR, placed on any part of the earth's surface, sees around him a certain limited portion of its surface, and this portion is called the visible horizon of that place. If the spectator advances twenty or thirty miles from his first position, in any direction, either east, west, north, or south, he will have an entirely new visible horizon, which will not contain any one of the objects which were seen in his first position. By advancing still farther, he will have another visible horizon, filled again with fresh objects, and bounded by a different portion of the earth. If the earth were perfectly globular, the boundaries of all these visible horizons would, in every position, be circles; but as the figure of the earth is that of an oblate spheroid, the boundaries of all the visible horizons, except when the spectator is at either of the poles, will be ellipses. Now the perpetual change of objects in the visible horizon cannot pos sibly arise from the inequalities of the earth's surface, considered as a plane of indefinite extent; for even from the highest mountains in one of the horizons, we cannot see the ob jects contained in the other. It fol lows, then, that the surface of the earth is not plane, but convex; and since this change in the visible hori zon takes place equally, as to obser vation, in every part of the earth which has been visited, we are entitled to conclude that the earth is round. When the visible horizon is composed wholly of sea, we have occular proof of the earth's convexity. As a ship comes in sight, the top of the mast first appears, while the hull and the sails, at least the lower parts of them, are invisible. We next perceive more of the rigging, and, as she approaches, the whole of the vessel rises, as it were, above the horizon, or above the convexity of the sea; and the surface of the earth is nothing more than the continuation of the surface of the sea, in all directions, and raised a little farther from the earth's centre. The globular form of the earth is still more satisfactorily proved by the variation in the mid-day altitudes of

VOL. XV.

the sun, and the meridian altitudes of all the other heavenly bodies, when seen from different parts of its surface, or in different latitudes; and this variation, when accurately observed at two places, whose distance is known, or which we can measure, enables us to determine, with great accuracy, the diameter of the earth. It is difficult, however, when measuring the meridional distance between two places, to keep always exactly in that meridian; we may deviate a little to the one side or to the other, in consequence of which, our measured distance between the two places will be greater than the true distance. We can place upright poles, or other objects, in the meridian which lies between the two places, in the following manner: Let a transit instrument, at one of the places, be placed in the meridian, by the help of circumpolar stars, or otherwise; direct the telescope towards a distant object, some part of which is in the meridian. Upon this object make a mark, exactly in the direction of the vertical wire in the middle of the telescope; this point will be in the meridian: the same kind of operation may be made at the second station which was made at the first; and, in this manner, the meridian line may be continued as far as we please. When the distance between the two places is measured, and the difference between the zenith distances of a star situated on the same meridian, corresponding with the measured distance, is ascertained; this is what astronomers call the measure of a degree of the meridian. The measurement of two degrees, in the direction of the meridian, in two different latitudes, is sufficient to determine the two axes of the generating ellipse, and, consequently, the figure of the earth, supposing it to be elliptical. Several degrees have been measured, in different latitudes, and the result of these measurements is, that the mean diameter of the earth is about 7912 miles ;-that a degree of the meridian is longer at the poles than at the equator; and, therefore, that the earth is an oblate spheroid,

D

a solid generated by the revolution of an ellipse about its shorter axis, and that the proportion of the less axis is to the greater as 300 to 301. The difference, however, in the results which have been obtained by making use of various degrees measured in different parts of the earth, by collating them in pairs, was sufficient to induce Laplace to suspect that the earth is really not a solid of revolution, but that the terrestrial meridian is a curve of double curvature. That illustrious philosopher was led to this erroneous conclusion, partly by making use of the incorrect de gree of the meridian measured by Maupertius and his associates in Lap land, and some similar wrong results given by La Caille, deduced from measurements and experiments made at the Cape of Good Hope, and partly by an error in his own calculations, which affected his results. From subsequent experiments, however, inore accurately conducted, it is now extremely probable that the carth is a solid of revolution, and that both hemispheres are exactly similar. The degree in Lapland has been re-measured, and an error detected in the old measurement of about 200 fathoms. Professor Playfair ascribed the small discrepancies, which arise from making use of measured degrees in different places, to the unequal density of the materials of which the earth may be composed at those places near its surface, by means of which the direction of gravity may

be disturbed.

the gratuitous suppositions which Newton had adopted, that if a planet, supposed to be fluid and homogeneous, be composed of particles which attract in the ratio of their masses, and inversely as the square of their distances, at the same time that it revolves round an axis in a given time, it will remain in equilibrium if it have the form of an elliptic spheroid, whatever may be the ratio of the axis. Maclaurin has only employed in his demonstrations the synthetic geometry of the ancients; but we regard his method as a master-piece, superior to any thing which Archimedes or Apollonius has left us." Maclaurin divided the prize given by the Academy of Sciences at Paris with Euler and Daniel Bernouilli. Now, although it was thus demonstrated that the parts of a homogeneous fluid, (on which the figure of the earth, just described, was any how induced,) would be in equilibrio, yet it was not shown inversely, that whenever an equilibrium takes place in such a fluid mass, the figure of the mass must be the oblate spheroid in question. D'Alembert, indeed, showed that there are more spheroids than one, in which the state of equilibrium may be maintained, and this result, though it was not observed by Maclaurin, might easily, however, have been inferred from his solution. Legendre afterwards proved that the solids of equilibrium must always be elliptic spheroids; and that, in general, there are two spheroids that will satisfy the specified conditions. In the case of a homogeneous mass of the mean density of the earth, revolving in the space of 23 hours, 56 minutes, 4 seconds, one of the spheroids is that above mentioned, the other is one in which the equatorial diameter is to the polar as 681 to 1. Laplace has added the following limitations. A fluid and homogeneous mass cannot be in equilibrium with an elliptic figure, if the time of its rotation be less than 2 hours, 25 minutes, 17 seconds. If the time of revolution be greater than this, there will always be two elliptic figures, or spheroids, and not more, in which an equilibrium may be maintained.

If the earth be not homogeneous, but composed of strata that increase in density as they approach the cen

parts, occupied by water, where they will acquire a horizontal stratification, and, by certain mineral opera tions, be afterwards consolidated into stone; such a body, in the course of ages, must acquire a surface every where at right-angles to the direction of gravity, and consequently more or less approximating to a spheroid of equilibrium. The natural history of the earth gives considerable countenance to these suppositions, and seems to furnish us with a very rational explanation of the ellipticity or spheroidal form belonging to the earth, and to the planets which are known to revolve about an axis. The distribution of the solid materials in the interior of the earth will very much affect the nature of this solid; and the manner in which the figure is acquired must probably prevent the approximation from ever being entirely complete. The distribution, however, of the materials, at any considerable distance below the surface, must remain to us for ever unknown; we have no means of examination, except by the measurement of degrees, the experiments on pendulums, or from observations made on the deviation of the plumbline from the perpendicular similar to what has just been described as

having taken place at Schehallien. These latter observations ought to be repeated on different mountains, the interior construction of which can be ascertained; but the most eligible method which has ever yet been suggested, is that of making observations on the large Pyramid of Ghizeh, in Egypt, the materials of which, as well as its exact figure, being known, would render observations made on it particularly desirable; especially as they would afford certain data, and reduce the calculations, which are now extremely complicated, to almost nothing. This method was recommended by Dr C. Hutton, in his last paper published in the Philosophical Transactions of London; when that veteran declared, that if ill health and old age did not prevent him, he would make a journey to Egypt, entirely for that purpose "On the whole, the facts known from observation agree in general with the theory; but there are, in the expression of that theory, so many quantities which are yet indeterminate, that a perfect coincidence of the two cannot be strictly affirmed; in fact, the business is not yet completed; something further still remains for future philosophers to accomplish."

H. G. B.

MY DEAR FRIEND,

April 1818.

THOUGH I had no desire to stay long at H—, yet I did not expect to have left it quite so soon: left it, however, I have, and after another little journey, I have arrived here in safety, and supplied with materials sufficient to furnish another letter of travelling adventures.

But to give you something like a regular narrative, I must begin where my last letter left off. With a fixed determination to perform my duty in a conscientious manner, and with my father's strong warnings against "eye service" deeply impressed upon my mind, I joined my companions in labour; and, along with them, be gan the toils and duties of that station of life in which Providence has placed me. At every interval of labour, every breathing-time, I stole a few cautious scrutinizing glances at my companions, anxious to observe them, but fearful of being myself observed. They were all like strangers to me, and most of them strangers to one another also; the greater part about middle age, and none so young as myself. They appeared to be well acquainted with that world which was so new to me; and nothing surprised me more, than the easy and unembarrassed manner with which they talked to each other, though, till that very day, they had perhaps never met. Some of them accosted me in different ways, as their several inclinations led them; one speaking upon any indifferent subject; another upon the proper cultivation of this or the other species of plant; a third, gaily, but I thought cruelly and officiously, bantering me, asking how long I had left my mother, and if I was not well "speaned" yet? I shrunk from their familiarity, and plied my work with a sick heart. One young man, apparently about two or three years older than myself, perceived my distress, spoke to me kindly, and endeavoured, by talking upon agreeable and diverting subjects, to turn my mind from its melancholy musings, and he partly succeeded. In a short time I be

came considerably attached to him ; and the more so, because I found in him a considerable similarity of taste. At our leisure hours we read and talked about our favourite authors; and though he had much less need of me than I had of him, he was evidently pleased with my company. In this manner time passed slowly on; the day employed in my common occupation, working along with the rest, and thinking on other scenes, and dearer friends; the evening spent in reading, talking with my only companion, or hearing him play a few tunes upon his fiddle, which he often did when he perceived me more than commonly inclined to sadness; and well he knew how to wake a strain concordant with my feelings, and lead my mind away from itself, by the associations stirred by plaintive measures, till the grief which I continued to feel became in itself a pleasure. Meanwhile the weather, which had been unsteady, became worse and worse; the wind blew from the northeast with the most bitter keenness, bearing along, at short intervals, thick drifting showers of snow and sleet. Often, during the showers, we cowered under the feeble shelter of the thin leafless beech-hedges, looking wistfully out for the re-appearance of blue-sky, and shivering till we were unable to speak; and always at the "fair blinks" working as fast as possible, to acquire some warmth. Many a thought of the comfortable fire-side of home did these chill blasts awake in my mind, while I was trembling at the very heart; but these I kept to myself, as I imagin ed it would be altogether disgraceful for me to appear overcome with cold, like a child. After some days of such weather, the wind shifted into the south-west, the skies cleared, the sun shone out bright and warm, and the little birds began to sing their joyful notes. I felt the renovating influence, and my heart at one time danced with delight, at another melted away in tender recollections of that home whence the wind was now blowing, whose whisperings seemed to me like the voice of a friend.