every one desirous of instruction should read with attention all the articles in the “dictionnaire encyclopédique,” under the head “figure,” viz.:

“figure of the earth,” by m. d’alembert — a work both clear and profound, in which we find all that can be known on the subject.

“figure of rhetoric,” by césar dumarsais — a piece of instruction which teaches at once to think and to write; and, like many other articles, make us regret that young people in general have not a convenient opportunity of reading things so useful.

“human figure,” as relating to painting and sculpture — an excellent lesson given to every artist, by m. watelet.

“figure,” in physiology — a very ingenious article, by m. de caberoles.

“figure,” in arithmetic and in algebra — by m. mallet.

“figure,” in logic, in metaphysics, and in polite literature, by m. le chevalier de jaucourt — a man superior to the philosophers of antiquity, inasmuch as he has preferred retirement, real philosophy, and indefatigable labor, to all the advantages that his birth might have procured him, in a country where birth is set above all beside, excepting money.

figure or form of the earth.

plato, aristotle, eratosthenes, posidonius, and all the geometricians of asia, of egypt, and of greece, having acknowledged the sphericity of our globe, how did it happen that we, for so long a time, imagined that the earth was a third longer than it was broad, and thence derived the terms “longitude” and “latitude,” which continually bear testimony to our ancient ignorance?

the reverence due to the “bible,” which teaches us so many truths more necessary and more sublime, was the cause of this, our almost universal error. it had been found, in pslam ciii, that god had stretched the heavens over the earth like a skin; and as a skin is commonly longer than it is wide, the same was concluded of the earth.

st. athanasius expresses himself as warmly against good astronomers as against the partisans of arius and eusebius. “let us,” says he, “stop the mouths of those barbarians, who, speaking without proof, dare to assert that the heavens also extend under the earth.” the fathers considered the earth as a great ship, surrounded by water, with the prow to the east, and the stern to the west. we still find, in “cosmos,” a work of the fourth century, a sort of geographical chart, in which the earth has this figure.

tortato, bishop of avila, near the close of the fifteenth century, declares in his commentary on genesis, that the christian faith is shaken, if the earth is believed to be round. columbus, vespucius, and magellan, not having the fear of excommunication by this learned bishop before their eyes, the earth resumed its rotundity in spite of him.

then man went from one extreme to the other, and the earth was regarded as a perfect sphere. but the error of the perfect sphere was the mistake of philosophers, while that of a long, flat earth was the blunder of idiots.

when once it began to be clearly known that our globe revolves on its own axis every twenty-four hours, it might have been inferred from that alone that its form could not be absolutely round. not only does the centrifugal zone considerably raise the waters in the region of the equator, by the motion of the diurnal rotation, but they are moreover elevated about twenty-five feet, twice a day, by the tides; the lands about the equator must then be perfectly inundated. but they are not so; therefore the region of the equator is much more elevated, in proportion, than the rest of the earth: then the earth is a spheroid elevated at the equator, and cannot be a perfect sphere. this proof, simple as it is, had escaped the greatest geniuses: because a universal prejudice rarely permits investigation.

we know that, in 1762, in a voyage to cayenne, near the line, undertaken by order of louis xiv., under the auspices of colbert, the patron of all the arts, richer, among many other observations, found that the oscillations or vibrations of his timepiece did not continue so frequent as in the latitude of paris, and that it was absolutely necessary to shorten the pendulum one line and something more than a quarter. physics and geometry were at that time not nearly so much cultivated as they now are; what man would have believed that an observation so trivial in appearance, a line more or less, could lead to the knowledge of the greatest physical truths? it was first of all discovered that the weight must necessarily be less on the equator than in our latitudes, since weight alone causes the oscillation of a pendulum. consequently, the weight of bodies being the less the farther they are from the centre of the earth, it was inferred that the region of the equator must be much more elevated than our own — much more remote from the centre; so the earth could not be an exact sphere.

many philosophers acted, on the occasion of these discoveries, as all men act when an opinion is to be changed — they disputed on richer’s experiment; they pretended that our pendulums made their vibrations more slowly about the equator only because the metal was lengthened by the heat; but it was seen that the heat of the most burning summer lengthens it but one line in thirty feet; and here was an elongation of a line and a quarter, a line and a half, or even two lines, in an iron rod, only three feet and eight lines long.

some years after mm. varin, deshayes, feuillée, and couplet, repeated the same experiment on the pendulum, near the equator; and it was always found necessary to shorten it, although the heat was very often less on the line than fifteen or twenty degrees from it. this experiment was again confirmed by the academicians whom louis xv. sent to peru; and who were obliged, on the mountains about quito, where it froze, to shorten the second pendulum about two lines.

about the same time, the academicians who went to measure an arc of the meridian in the north, found that at pello, within the polar circle, it was necessary to lengthen the pendulum, in order to have the same oscillations as at paris: consequently weight is greater at the polar circle than in the latitude of france, as it is greater in our latitude than at the equator. weight being greater in the north, the north was therefore nearer the centre of the earth than the equator; therefore the earth was flattened at the poles.

never did reasoning and experiment so fully concur to establish a truth. the celebrated huygens, by calculating centrifugal forces, had proved that the consequent diminution of weight on the surface of a sphere was not great enough to explain the phenomena, and that therefore the earth must be a spheroid flattened at the poles. newton, by the principles of attraction, had found nearly the same relations: only it must be observed, that huygens believed this force inherent in bodies determining them towards the centre of the globe, to be everywhere the same. he had not yet seen the discoveries of newton; so that he considered the diminution of weight by the theory of centrifugal forces only. the effect of centrifugal forces diminishes the primitive gravity on the equator. the smaller the circles in which this centrifugal force is exercised become, the more it yields to the force of gravity; thus, at the pole itself the centrifugal force being null, must leave the primitive gravity in full action. but this principle of a gravity always equal, falls to nothing before the discovery made by newton, that a body transported, for instance, to the distance of ten diameters from the centre of the earth, would weigh one hundred times less than at the distance of one diameter.

it is then by the laws of gravitation, combined with those of the centrifugal force, that the real form of the earth must be shown. newton and gregory had such confidence in this theory that they did not hesitate to advance that experiments on weight were a surer means of knowing the form of the earth than any geographical measurement.

louis xiv. had signalized his reign by that meridian which was drawn through france: the illustrious dominico cassini had begun it with his son; and had, in 1701, drawn from the feet of the pyrenees to the observatory a line as straight as it could be drawn, considering the almost insurmountable obstacles which the height of mountains, the changes of refraction in the air, and the altering of instruments were constantly opposing to the execution of so vast and delicate an undertaking; he had, in 1701, measured six degrees eighteen minutes of that meridian. but, from whatever cause the error might proceed, he had found the degrees towards paris, that is towards the north, shorter than those towards the pyrenees and the south. this measurement gave the lie both to the theory of norwood and to the new theory of the earth flattened at the poles. yet this new theory was beginning to be so generally received that the academy’s secretary did not hesitate, in his history of 1701, to say that the new measurements made in france proved the earth to be a spheroid flattened at the poles. the truth was, that dominico cassini’s measurement led to a conclusion directly opposite; but, as the figure of the earth had not yet become a question in france, no one at that time was at the trouble of combating this false conclusion. the degrees of the meridian from collioure to paris were believed to be exactly measured; and the pole, which from that measurement must necessarily be elongated, was believed to be flattened.

an engineer, named m. de roubais, astonished at this conclusion, demonstrated that, by the measurements taken in france, the earth must be an oblate spheroid, of which the meridian passing through the poles must be longer than the equator, the poles being elongated. but of all the natural philosophers to whom he addressed his dissertation, not one would have it printed; because it seemed that the academy had pronounced it as too bold in an individual to raise his voice. some time after the error of 1701 was acknowledged, that which had been said was unsaid; and the earth was lengthened by a just conclusion drawn from a false principle. the meridian was continued in the same principle from paris to dunkirk; and the degrees were still found to grow shorter as they approached the north. people were still mistaken respecting the figure of the earth, as they had been concerning the nature of light. about the same time, some mathematicians who were performing the same operations in china were astonished to find a difference among their degrees, which they had expected to find alike; and to discover, after many verifications, that they were shorter towards the north than towards the south. this accordance of the mathematicians of france with those of china was another powerful reason for believing in the oblate spheroid. in france they did still more; they measured parallels to the equator. it is easily understood that on an oblate spheroid our degrees of longitude must be shorter than on a sphere. m. de cassini found the parallel which passes through st. malo to be shorter by one thousand and thirty-seven toises than it would have been on a spherical earth.

all these measurements proved that the degrees had been found as it was wished to find them. they overturned, for a time, in france, the demonstrations of newton and huygens; and it was no longer doubted that the poles were of a form precisely contrary to that which had at first been attributed to them. in short, nothing at all was known about the matter.

at length, other academicians, who had visited the polar circle in 1736, having found, by new measurements, that the degree was longer there than in france, people doubted between them and the cassinis. but these doubts were soon after removed: for these same astronomers, returning from the pole, examined afresh the degree to the north of paris, measured by picard, in 1677, and found it to be a hundred and twenty-three toises longer than it was according to picard’s measurement. if, then, picard, with all his precautions, had made his degree one hundred and twenty-three toises too short, it was not at all unlikely that the degrees towards the south had in like manner been found too long. thus the first error of picard, having furnished the foundations for the measurements of the meridian, also furnished an excuse for the almost inevitable errors which very good astronomers might have committed in the course of these operations.

unfortunately, other men of science found that, at the cape of good hope, the degrees of the meridian did not agree with ours. other measurements, taken in italy, likewise contradicted those of france, and all were falsified by those of china. people again began to doubt, and to suspect, in my opinion quite reasonably, that the earth had protuberances. as for the english, though they are fond of travelling, they spared themselves the fatigue, and held fast their theory.

the difference between one diameter and the other is not more than five or six of our leagues — a difference immense in the eyes of a disputant, but almost imperceptible to those who consider the measurement of the globe only in reference to the purposes of utility which it may serve. a geographer could scarcely make this difference perceptible on a map; nor would a pilot be able to discover whether he was steering on a spheroid or on a sphere. yet there have been men bold enough to assert that the lives of navigators depended on this question. oh quackery! will you spare no degrees — not even those of the meridian?