traced, was now for the first time practically shown; to the rude mariner, as to the astronomer, the limitation of our globe in all directions, and its isolation in space, were from this date evident; and to the abstract but little diffused methods of geometry was now added a new means for forming an idea of the dimensions of the earth. Elcano, in effect, though encountered by many unexpected obstacles, had performed, in little more than three years and three months, a complete voyage of circumnavigation.

From the memorable epoch referred to, geographical discoveries have succeeded one another with greater rapidity than ever, the earth has been explored in all directions, the width of the seas calculated, and the surface of the continents measured; but all these labors, however vast their importance, have been those of detail, and have added no new idea to the results of the bold navigation performed in the fifteenth and beginning of the sixteenth centuries, as respects the general form and approximate dimensions of the planet we inhabit. To these last dates must be referred, if not the first clear conception, the definitive verification of the nearly spherical figure of the earth.

Looking back, however, it must be conceded that neither the voyages of Columbus nor Magallanes were absolutely necessary for the demonstration of the spherical figure of the earth, since this fact might have been deduced with sufficient clearness from geographical principles already verified; from the delusion indulged by every nation that its own territory was central, as regarded the rest of the earth; from the general and changeable aspect of the heavens upon every change of country; from the apparent sphericity of the sun, and especially that of the moon, still more conspicuous through the succession of its phases, and from the circular outline of the earth's shadow during the eclipses of the lunar planet. But all these indications of the limitation and roundness of the earth, however conclusive for reflecting and studious minds, would have carried no conviction to the generality of mankind, without the incontestable support of those other proofs which might be called material or tangible. With what obstacles did Columbus meet before finding himself intrusted with three frail vessels-how much incredulity in all countries, even to the extent of being charged with madness-and for what? Columbus said: "The Portuguese seek the gold and spices of India by steering towards the east; and I, who cherish the persuasion that the earth is round, propose to trace a more expeditious route by reaching the same point in an opposite direction." Had there been many who at that time held the doctrine of the earth's sphericity, no one would have treated so logical and obvious a thought as extravagant; nor would Columbus have been indebted to the noble instinct of a woman for the successful issue of his enterprise if modern society had inherited from the ancient that vast store of science attributed to the latter, instead of having to rear from the very foundation the edifice of its own knowledge.

What has been just said in regard to the form of our globe may, with even more propriety, be asserted of its movement of rotation. We shall admit, without discussion, that among the Indians, the Chinese, the Chaldeans, there might possibly be a few who recognized and maintained the reality of this movement; that the same might be true of ancient Egypt, and that certain Greek philosophers, especially of the school of Pythagoras, also taught at a later period the same truth. To explain the alternation of day and night two hypotheses were feasible, and there was nothing to forbid men of special talent adopting the more rational one; but was the merit of Copernicus, therefore, less in having reproduced the right idea about the middle of the sixteenth century? How many years must still elapse, how many angry and deplorable discussions ensue before the ideas of Copernicus became firmly established even among men of science and systematic cultivation. On the other hand, did the Greek philosophers, who admitted the rotation of the earth, build their doctrine on the difficulty of reconciling in any other manner the phenomena of the heavens, or

was it maintained rather in the spirit of the school, by which same spirit they might have been induced to support the direct contrary? It is certain that Hipparchus, Ptolemy, Euclid, and Archimedes, eminent minds and founders of true astronomy, of geometry, and of mechanics, more versed certainly in observation and calculation than in the subtleties of metaphysics, denied the movement of the earth, and for many ages strengthened the opposite belief with their imposing authority. Hence this belief was the prevailing one when Copernicus appeared in the world to overthrow it, at the epoch of great geographical discoveries, as if the Creator had designed that after the form and distinct features of our planet were unveiled, its relations of analogy with the rest of the universe should also be disclosed.

Copernicus was not only a consummate methematician, a skilful observer, capable of deducing great results with rude and inefficient instruments, but he was likewise, as we are assured by his biographer, Czynski, a man of profound piety, full of faith in the wisdom of the Creator, and penetrated with the simplicity of his works. With these elements of character the astronomer of Thorn studied the movements of the celestial bodies, perceived their inextrica ble complication upon the principles then received, the infinity of occult agencies and of forces distinct in direction and intensity, which must concur in the operation to carry all the heavenly bodies around the earth without varying their relative distances, or altering in the minutest particular the harmony of the creation, and instead of confining himself to saying, with the sage King of Castile, "it is strange that this should be so," resolutely pronounces, “this cannot be so."

*To show that we exaggerate nothing in thus expressing ourselves, we shall here retrace, with all possible brevity, the different opinions of the Greek philosophers on the form of the earth and its situation in space, making use for that purpose of the work by G. Lewis, entitled, An Historical Survey of the Astronomy of the Ancients.

Thales of Miletus, who flourished between 639 and 546 years before our era, likened the earth to a bark floating in a limitless ocean.

According to Anaximander, likewise of Miletus, and disciple of Thales, the earth was cylindrical, and occupied the centre of the created universe.

Anaximenes, a disciple of the former, assigned to the sun the form of a thin disk, and to the earth that of a trapezium sustained in the air, and the same opinion was entertained by Anaxagoras of Clazomene, likewise a philosopher of the Ionic school.

Xenophanes of Colophon, founder of the Eleatic school, supposed the earth to be illimitable and supported in the abyss on immovable foundations. Parmenides and Empedocles, dissenting from this opinion of Xenophanes, pronounced, perhaps before any one, the doctrine of the sphericity of the earth and of its isolation in space.

The cosmical opinions of the Pythagoreans, as stated by Philolaus, a disciple of the great master, were these: in the centre of the universe there exists a mass of fire, the soul of the world, around which revolve in a circle ten bodies in the following order: first and most distant, the heavens with the fixed stars; next the five planets; then the sun, the moon, the earth, and finally the Antichthon, a mysterious conception, which, indulgently interpreted, would seem to signify the terrestrial hemisphere opposite to that inhabited by ourselves. The basis of this system, one of the most judicious bequeathed us by antiquity, was purely mental, or the offspring of an invention governed by mystical abstractions and vague axioms respecting the virtues of numbers. To support it, instead of having recourse to the observation of natural phenomena, it was assumed, for instance, as a principle, that fire, being of a more exalted or worthy nature than earth, must by right occupy the place of greatest dignity, and that in any series of different bodies that place must correspond either with the centre or the extremes. From this reasoning the reader may form an estimate of the system of Philolaus, a system, however, which not all the Pythagoreans received without restriction and modification, for while some, as Hicetas, Heraclides and Epiphantus, attributed to the earth a movement of rotation from west to east, others, and among them perhaps Pythagoras himself, whose original ideas have not been transmitted to us, thought the earth immovable in the midst of the universe.

Leucippus and Democritus, both of the Atomic sect, maintained, towards the middle of the fifth century, like the Ionic philosophers, that the earth was a plane disk immovable in space and supported by the air.

It was in the early half of the fourth century before Christ that astronomy, based on the observation of the celestial phenomena, began to flourish among the Greeks. At that time

The great truth announced by Copernicus, the basis of existing astronomy, encountered at the time more opponents than partisans; nor was it possible that, in defect of good instruments and delicate observations, he could corroborate by incontestible facts the surprising revelations of his intellect; he could but consign to after ages the confirmation of his theory. In vain did Tycho Brahe, contrary to what might have been expected from his profound knowledge of celestial phenomena, impugn in the name of science, and that so late as the close of the sixteenth century, the astronomical system of Copernicus; in vain, at the commencement of the seventeenth, was it sought, in the name of more sacred but ill understood interests, to convert into a stumbling block the public belief in the movement of the earth: the truth wrought its own way, and from Galileo onward, for every adversary there were hundreds who sustained it. At present there is no longer any discussion about it; he who controverts it is regarded as irrational, and meets in universal indifference the reproof of his stolid incredulity.

II.

If the knowledge, whether certain or presumptive, of the ancient philosophers and mathematicians respecting the roundness and rotation of the earth, cannot be considered as the origin or basis of the ideas at present received on both those points, but merely as a remote antecedent completely forgotten at the revival of the discussion in modern times, the same thing nearly may be predicated of the researches undertaken to find the value of the radius of the earth's circumference. The analogy, it is true, is not entirely exact, for in these latter researches two things are to be distinguished: the method or principle on which they are founded, and the results finally obtained. The first as devised, two or three centuries before our era, by Eratosthenes and Posidonius, both of the school of Alexandria, is the same with that employed in our own time, as is shown in our Annual for 1862; the results of the method, whether from the imperfec

lived Eudoxus of Gnidus, a disciple of Plato, usually resident at Cizycum at the entrance of the Euxine, and one of the most distinguished among the learned of his time in the field, both of theory and practice. To explain the appearances of the heavens, on the hypothesis of the repose of the earth, Eudoxus conceived the first idea of crystalline spheres with axes in different directions, and also with different movements. New facts having been discovered, Calippus, a disciple of Eudoxus, in place of 26, admitted 33 spheres, a number which Aristotle found it necessary to raise to 55. These spheres, supposed at pleasure and symbolical of as many insoluble difficulties in the cosmical system followed by these savants, became established principles in the minds of the philosophers who had imagined them, as well as in those of their disciples, and consequently obtained unquestioned currency in the world. Aristotle, taking up anew and analyzing the ideas of his predecessors, and rejecting almost all of them, a proof of their fundamental impracticability, admitted, however: 1st. That the earth is spherical, because such is the apparent form of all the firmamental bodies; such also the form which a body, as a drop of water for instance, assumes when left to the free gravitation of its particles; and such the form of the earth's shadow in eclipses of the moon. 24. That the dimensions of the earth cannot be extended in an indefinite plane, seeing that with every change of place there is a change also in the aspect and number of the visible stars; and 3dly, That it cannot be movable in space, since its hypothetical mobility meets with no reflection in the constant position of other bodies of the universe. The system of Aristotle, based on the observations and conjectures of Eudoxus and his disciples, was that adopted by Euclid, Archimedes, Hipparchus and Ptolemy.

A generation after Euclid, who entitled one of his theorems "The earth the centre of the universe," and while the opinions of Aristotle and his followers were in the highest favor, there was a formidable protest against them advanced by Aristarchus of Samos, who flourished in the earlier half of the third century before our era, and who was one of the most distin"guished luminaries of his age. Aristarchus exploded all the spheres of Eudoxus and Aristotle, set the earth again at liberty, assigned to the sun and stars their true position, and laid, in a word, the basis of the Copernican system; but in opposition to Aristarchus appeared Archimedes, on behalf of science, and Cleanthes, chief of the stoic sect, in defence of the faith and religious prepossessions of the age, and the happy conception of the sage of Samos remained sunk in oblivion, or passed into the category of dreams, until, in the process of time, it revived with new vitality and brighter evidence in the mind of the recluse of Thorn.

tion of instruments, the want of precision on the part of observers, or from having reached us in obscure expressions or in units vaguely understood, have been of no service to modern geometers. Five of these final results are cited by Bailly in his History of Ancient Astronomy, and these, doubtless, are not all that might have been cited; it is sufficient to compare them with one another, to perceive how little guarantee of exactness either of them affords a priori, or without subsequent corroboration. According to Aristotle, the opinions received in his time assigned 400,000 stadia as the circumference of the earth; Ptolemy adopted 180,000; Eratosthenes and Posidonius respectively 250,000 and 240,000; Cleomedes 300,000. The learned historian above mentioned explains these enormous discrepancies, which could not have resulted from the ignorance or dullness of the observers, in a sufficiently natural manner, by assigning a different value in each case to the stadium; assuming, as the state of knowledge at his time respecting ancient measures seemed to indicate, four kinds of stadia, approximately of 100, 136, 170 and 230, metres each, he arrives at the conclusion that these results, so discordant in appearance, are in the main identical, and not remote from those obtained by modern investigation. But Bailly himself, one of the most enthusiastic defenders of ancient science, agrees with us in thinking that the geodesic labors of the astronomers but little anterior to his own epoch, as well as those of his cotemporaries, were conducted in complete independence of the investigations of remote ages and without reference to a coincidence of numbers. Leaving to himself, therefore, the responsibility of his ideas, which we shall neither attempt to defend nor contravene, and judging this to be no occasion for reporting the earnest arguments adduced by highly respectable authors both for and against his views, let us concede, not to antiquity in general, but to a part of its philosophers, a knowledge, however loosely approximate, of the dimensions of the earth; and with this concession, let us pass to an exposition of the geodesic labors of times nearer our own and of more authentic character, though not all marked by an undoubted stamp of

exactness.

Towards the year 830 of our era, the Arabian astronomers measured, by order of the wise Caliph Almamon, an arc of the meridian in the plain of Sindgiar, near the coasts of the Red Sea; but the result of this operation made but little approach to the truth, or was either confusedly expressed at first or has been corrupted in the transmission.

In the year 1490, as Martin de Navarette relates in his compendious History of the Spanish Marine, our learned countryman Antonio de Nebrija, determined by various measurements and observations the quantity of a terrestrial degree, and obtained a number more near the truth than those before deduced. Subsequently, Glareans, in Switzerland, and Oroncio Fineo, in France, undertook and accomplished a labor analogous to that of Nebrija; and the same thing, with even better success, was effected by the French physician Fernel, who founded his estimate on the number of revolutions made by the wheel of a carriage in its transit from Paris to Amiens, cities situated under nearly the same meridian.t

In 1617, the Dutch astronomer Schnell revived the method of Eratosthenes, and applied it, with better means and more accuracy than had yet been observed,

*The reader who may desire to know the slight or deficient foundations on which rest the conjectures of the authors who maintain the profound astronomical science of the ancients may consult the treatise of Sr. Vasquez Queipo, entitled, Essay on the Metric and Monetary Systems of Ancient Nations, tome 1, pp. 65, 66, and note 10, corresponding thereto.

Upon the points here treated of, and other analogous ones not less deserving to be known, the reader will find critical notices of great value in the discourse relative to the progress of geodesy, read by Sr. Saavedra Meneses, at the beginning of the present year, on his reception into the Academy of Sciences.

to the measurement of the arc of 1° 11' 30" comprised between Alkmaar and Bergen-op-Zoom; but the result of his undertaking, calculated and discussed by Muschembrock, did not see the light until a later period, when others had been obtained of the same kind with higher pretensions to certainty.

In like manner with Schnell, Norwood determined, in 1635, the difference of latitude between York and London, equal to 2° 28', by the difference of the altitude of the sun between their respective horizons at the period of the solstices; and afterwards measuring the distance between those cities, he arrived at a valuation, too great however, of the length of a degree of the meridian; making it 57,442 toises, or about 111,955 metres.

For its novelty, if nothing else, there should be mentioned in connexion. with the preceding attempts the method proposed by Maurolico, at that epoch of measurements, to determine the terrestrial radius. Assuming the unquestionable fact that the extension or breadth of land which, seen from the sea-shore, or in the interior of a nearly level country, depends at once on the height at which the spectator is stationed, and on the curvature or radius of the earth, Maurolico thought that by measuring the height of a mountain near the sea and the route traced without change of direction by a bark until it disappears below the horizon, the value of the radius sought might be deduced, without reference to any astronomical observation. This process, put in practice at a later period, with some variations, and only by way of trial, has led to a result greater than might have been expected, being complicated with some causes of error and uncertainty; we do not know that the solution of the problem was ever attempted in the lifetime of its author.

Another idea, ingenious like all proceeding from the same source, occurred to Kepler, and Riccioli undertook to realize it, although in practice, from the imperfection of instruments among other considerations, it could not but lead to a result very distant from the true one. The idea consists in measuring upon any given surface of ground the greatest lineal distance possible, and then calculating the angles of the two respective verticals with the common line of vision comprised between the extremes of the base. It requires but a slight notion of geometry to comprehend how delicate was the operation which Riccioli took charge of, and how little reliance could be placed on results deduced from such a process.

These different estimates-for they merit no other name towards ascertaining the magnitude of the earth, were but the prelude to other more exact processes, and show the necessity that was felt, but 200 years ago, of obtaining a preeise knowledge of the dimensions of our planet, as well as the oblivion into which the labors of antiquity had fallen or the small importance attached to them. In proof of this, let us remember that at the end of the fifteenth century and beginning of the next, Columbus shaped his course towards the unknown shores of India and Magallanes traced his adventurous progress across the Pacific, upon the delusive supposition that the earth was of much less size than it really is; and that, in the midst of the seventeenth century, Newton himself, in whom the highest genius was not at variance with extensive erudition and a sound judgment, found himself under the necessity of suspending his researches respecting the reciprocally attractive action of the earth and the moon, in consequence of the want of an approximate valuation for the radius of our globe. So pressing did the necessity referred to appear, that when the Academy of Sciences of Paris was instituted, in 1666, one of its first acts was to commit to Picard, a distinguished member of that learned assembly, the measurement of a new arc of the meridian; a work which this astronomer completed before the end of 1670, by the method adopted by Eratosthenes and Posidonius, as well as by Schnell and Norwood, but which was executed with so much accuracy in the details as to form an epoch in the annals of astronomy and geodesy.