CHAP. III.

Of the Figure of the Earth, and its Magnitude.

THE figure of the earth, as composed of land and water, is nearly spherical; the proof of this assertion will be the principal object of this chapter. The ancients held various opinions respecting the figure of the earth; some imagined it to be cylindrical, or in the form of a drum: but the general opinion was, that it was a vast extended plane, and that the horizon was the utmost limits of the earth, and the ocean the bounds of the horizon. These opinions were held in the infancy of astronomy; and, in the early ages of christianity, some of the fathers went so far as to pronounce it heretical for any person to declare that there was such a thing as the antipodes. But by the industry of succeeding ages, when astronomy and navigation were brought to a tolerable degree of perfection, and when it was observed that the moon was frequently eclipsed by the shadow of the earth, and that such shadow always appeared circular on the disc or face of the moon, in whatever position the shadow was projected, it necessarily followed, that the earth, which cast the shadow, must be spherical; since nothing but a sphere, when turned in every position with respect to a luminous body, can cast a circular shadow; likewise all calculations of eclipses, and of the places of the planets, are made upon supposition that the earth is a sphere, and they all answer to the true times when accurately calculated. When an eclipse of the moon happens, it is observed sooner by those who live eastward than by those who live westward; and, by frequent experience, astronomers have determined that, for every fifteen degrees difference of longitude, an eclipse begins so many hours sooner in the easternmost place, or later in the westernmost. If the earth were a plane, eclipses would happen at the same time in all places, nor could one part of the world be deprived of the light of the sun, while another part enjoyed the benefit of it. The voyages of the circumnavigators sufficiently prove that the earth

The first who attempted to

is round from west to east. circumnavigate the globe, was Magellan, a Portuguese, who sailed from Seville in Spain, on the 10th of August, 1519; he did not live to return, but his ship arriv ed at St. Lucar, near Seville, on the 7th of September, 1522, without altering its direction, except to the north or south, as compelled by the winds, or intervening land. Since this period, the circumnavigation of the globe has been performed at different times by Sir Francis Drake, Lord Anson, Captain Cook, &c. The voyages of the circumnavigators have been frequently adduced by writers on geography and the globes, to prove that the earth is a sphere; but when we reflect that all the circumnavigators sailed westward round the globe, (and not northward and southward round it) they might have performed the same voyages had the earth been in the form of a drum or cylinder; but the earth cannot be in the form of a cylinder, for if it were, then the difference of longitude between any two places would be equal to the meridional distance between the same places, as on a Mercator's chart, which is contrary to observation.-Again, if a ship sail in any part of the world, and upon any course whatever; on her departure from the coast, all high towers or mountains gradually disappear, and persons on shore may see the masts of the ship after the hull is hid by the convexity of the water (See Figure III. Plate I.)-If a vessel sail northward, in north latitude, the people on board may observe the polar star gradually to increase in altitude the farther they go: they may likewise observe new stars continually emerging above the horizon which were before imperceptible; and at the same time, those stars which appear southward, will continue to diminish in altitude, till they become invisible. The contrary phanomena will happen if the vessel sail southward; hence, the earth is spherical from north to south, and it has already been shown, that it is spherical from east to

west.

The arguments already adduced clearly prove the rotundity of the earth, though common experience shows us that it is not strictly a geometrical sphere; for its surface is diversified with mountains and valleys: but these irregularities no more hinder the earth from being

reckoned spherical, considering its magnitude, than the roughness of an orange hinders it from being esteemed round.*

When philosophical and mathematical knowledge arrived at a still greater degree of perfection, there seemed to be a very sufficient reason for the philosophers of the last age, to consider the earth not truly spherical, but rather in the form of a spheroid.† This notion first arose from observations on pendulum clocks, which being fitted to beat seconds in the latitudes of Paris and London, were found to move slower as they approached the equator, and at, or near, the equator, they were obliged to be shortened about of an inch, to agree with the times of the stars passing the meridian. This dif

* Our largest globes are in general 18 inches in diameter. The diameter of the earth is about 7964 miles. Chimboraco, one of the Andes mountains, the highest in the world. is about 20608 feet, or nearly 4 miles high. The radius of the earth is 3982 miles, and that of an 18 inch globe 9 inches. Now, by the rule of three, 3982m: 3982m+4 :9 in.: 9009, from which, deduct the radius of the artificial globe, the remainder .009=1000111 of an inch, nearly, is the elevation of the Andes on an 18 inch globe, which is less than a grain of sand.

+ Aspheroid is a figure formed by a revolution of an ellipsis about its axis, and an ellipsis is a curve-lined figure in geometry, formed by cutting a cone or cylinder obliquely but its nature will be more clearly comprehended, by the learner, from the following description :

Let TR (in Plate IV Figure V.) be the transverse diameter, or Jonger axis of the ellipsis, and CO the conjugate diameter, or shorter axis. With the distance TD or DR in your compasses, and C as a centre, describe the arch Ff: the points F. f, will be the two foci of the ellipsis. Take a thread of the length of the transverse axis TR, and fasten its ends with pins in F and f, then stretch the thread Fif and it will reach to I in the curve, then by moving a pencil round with the thread, and keeping it always stretched, it will trace out the ellipsis TCRO. If this ellipsis be made to revolve on its longer axis TR it will generate an oblong spheroid, or Cassini's figure of the earth; but if it be supposed to revolve on its shorter axis CO, it will form an oblate spheroid, or Sir Isaac Newton's figure of the earth.-The orbits or paths of all the planets are ellipses, and the sun is situated in one of the foci of the earth's orbit, as will be observed farther on.-The points F, f, are called foci, or burning points; because, if a ray of light is suing from the point F meet the curve in the point I, it will be reflected back into the focus f. For lines drawn from the two foci of an ellipsis to any point in the curve, make equal angles with a tangent to the curve at that point; and by the laws of optics, the angle of incidence is equal to the angle of reflection. Robertson's Conic Sections, Book III. Scholium to Prop. ix.

Philosophical Transactions, No. 386.

ference appearing to Huygens* and Sir Isaac Newton, to be a much greater quantity than could arise from the alteration by heat only, they separately discovered that the earth was flatted at the poles.-By the revolution of the earth on its axis (admitting it to be a sphere) the centrifugal force at the equator would be greater than the centrifugal force in the latitude of London or Paris, because a larger circle is described by the equator, in the same time; but as the centrifugal force, (or tendency which a body has to recede from the centre) increases, the action of gravity necessarily diminishes; and where the action of gravity is less, the vibrations of pendulums of equal lengths become slower; hence, supposing the earth to be a sphere, we have two causes why a pendulum should move slower at the equator than at London or Paris, viz. the action of heat which dilates all metals, and the diminution of gravity. But these two causes combined, would not, according to Sir Isaac Newton, produce so great a difference as th of an inch in the length of a pendulum, he therefore supposed the earth to assume the same figure that a homogeneous fluid would acquire by revolving on an axis, viz. the figure of an oblate spheroid, and found that the " diameter of the earth at the equator, is to its diameter from pole to pole, as 230 to 229." Notwithstanding the deductions of Sir Isaac Newton, on the strictest mathematical prin

* A celebrated mathematician, born at the Hague in Holland, in 1629. + Motte's translation of Newton's Principia, Book III. Page 243. Calling the equatorial diameter of the earth 7964 English miles, the polar diameter will be 7929.-For as 230 229: 7964: 7929 miles, the polar axis. Hence, the polar axis is shorter than the equatorial diameter by 35 miles, and the earth is higher at the equator than at the poles by 17 miles, a difference imperceptible on the largest globes that are made. Suppose a globe to be 18 inches in diameter at the equator, then 230: 229 : : 18 : 1719 the polar diameter: the difference of the diameters is T of an inch, half difference is of an inch, the flatness of an 18 inch globe at each pole, which is less than the 23d part of an inch, or not much thicker than the paper and paste, a quantity not to be discovered by the appearance; and on smaller globes the difference would be considerably less. Hence, the learner should be informed, that though the earth be not strictly a globe, it cannot be represented by any other figure which will give so exact an idea of its shape; and a lecturer who informs his hearers that it is in the shape of a turnip, or an orange, gives a very false idea of its true figure.

ciples, many of the philosophers in France, the principal of whom was Cassini, asserted that the earth was an oblong spheroid, the polar diameter being the longer; and as these different opinions were supposed to retard the general progress of science in France, the king resolved that the affair should be determined by actual admeasurment at his own expense. Accordingly, about the year 1735, two companies of the most abie mathematicians of that nation were appointed: the one to measure the degree of a meridian as near to the equator as possible, and the other company to perform a like operation as near the pole as could be conveniently attempted. The results of these admeasurements contradicted the assertions of Cassini, and of J. Bernoulli, (a celebrated methematician of Basil in Switzerland,. who warmly espoused his cause) and confirmed the calculations of Sir Isaac Newton.-In the year 1756, the Royal Academy of Sciences of Paris, appointed eight astronomers to measure the length of a degree between Paris and Amiens; the result of their admeasurement gave 57069 toises for the length of a degree.

The utility of finding the length of a degree in order to determine the magnitude and figure of the earth, may be rendered familiar to a learner thus; suppose I find the latitude of London to be 514° north, and travel due north till I find the latitude of a place to be 5210 north, I shall then have travelled a degree, and the distance between the two places, accurately measured, will be the length of a degree: now if the earth be a correct sphere, the length of a degree on a meridian, or a great circle, will be equal all over the world, after proper allowances are made for elevated ground, &c. the length of a degree multiplied by 360 will give the circumference of the earth, and hence its diameter, &c. will be easily found: but, if the earth be any other figure than that of a sphere, the length of a degree on the same meridian will be different in different latitudes, and if the figure of the earth resemble an oblate spheroid, the lengths of a degree will increase as the latitudes increase. The English translation of Maupertuis' figure of the earth, concludes with these words: " The degree of the meridian which cuts the polar circle being longer than a degree of the meridian in France, the earth