As the celestial sphere, in its apparent revolution, may present itself under three different aspects, according to the situation of the observer, it becomes necessary to dis tinguish them by particular names. Accordingly, to an observer at the equator, the celestial sphere is said to be right, because the equinoctial and parallels of declination, or circles described by the heavenly bodies, are at right angles to the horizon, and divided by it into two equal parts. To an observer between the equator and the pole, the sphere is oblique, because the equinoctial and parallels of declination are inclined to the horizon, so that all hea venly bodies not in the equator, are above and below the horizon during unequal periods. And from the pole the sphere appears paraild, the equinoctial coinciding with the horizon, and the heavenly bodies revolving in circles pa rallel to it.
In the view that we have hitherto taken of the earth, we have considered it merely as a spherical body, without any regard to its actual magnitude and dimensions. All the phenomena, indeed, which we have yet noticed, depend en tirely on the Figure and situation of the earth ; and there fore, in the explanation of these phenomena, it is not ne cessary to take the volume of the globe into the account. In practical geography, however, it is frequently an impor tant question to express the distance between different points on the surface of the earth, in terms of some known measure, as miles, yards, feet, Sze. ; and as these distances cannot always be subjected to actual measurement, it be comes necessary to determine the dimensions of the globe itself. Various attempts have accordingly been made by astronomers to solve this problem, though it is only from the perfection of modern instruments, that they have been able to accomplish it with any degree of accuracy.
If the earth were perfectly spherical, it is obvious that, to determine its circumference, nothing more would be necessary, than to find the length of a degree of the terres trial meridian, that is, the distance between two places ly ing under the same meridian, but differing 1° in latitude, and multiply that distance by 360. It was upon this prin ciple that Eratosthenes, computing the difference of lati tude between Alexandria and Syene to be 7° 8' 45", and es timating the distance between them at 5000 stadia. deter mined the circumference'of the earth to be about 252,000 stadia. This estimate is valuable, as being the result of the first attempt to ascertain the dimensions of the globe on correct principles. In point of accuracy, however, as might be expected, it is very deficient. Independent of the uncertainty with regard to the length of the stadium which Eratosthenes employed, he committed a considerable error in supposing Alexandria and Syene to be under the same meridian, and his calculation was also affected by an irre gularity, of which he was not perhaps aware. It has been
found, from actual measurement, that the degrees of a me ridian on the earth increase in length from the equator to wards the poles ; that is, if two points be taken in a terres trial meridian, at such a distance from each other that per pendiculars at these points, or lines in the direction of gra vity, when produced to the heavens, include between them 1° of a celestial meridian; and if other two points be-taken on the same meridian, but nearer the pole, such that per pendiculars from them also include between them 1° of the celestial meridian, then it is found, that the distance be tween the two first points, measured on the surface of the earth, is less than the distance between the two last. This difference, indeed, is the necessary consequence of the spheroidal figure of the earth, which we formerly men tioned ; and though, in geographical problems in general, the irregularity may be safely neglected, yet it is of impor tance to take it into account, in determining the dimensions of the earth. At the equator, a degree of latitude has been found to measure 60480.247 fathoms ; at the parallel of 45°, 60759.473 ; and in latitude 66° 20' 10", 60952.374. Taking the second of these as nearly a mean for all latitudes, and multiplying by 360, we have for the whole circumference of the meridian 21873410.28 fathoms, or 24356.148 Eng lish miles. The circumference of the equator is found to be 24896.16 miles, or 40 miles greater than that of the me ridian.
As all the meridians on the globe intersect one another in the poles, the distance between any two of them dimi nishes as the latitude increases. In many cases, it is of importance to know the law of this diminution, that is, to determine the length of a degree of longitude on any paral lel of latitude, the degree on the equator being given. In order to solve this problem with the greatest possible ac curacy, it is necessary to make allowances for the spheroi dal figure of the earth, or the difference in the length of de grees of latitude at different distances from the equator. But as there are irregularities in these differences, that have led to doubt whether the earth be a regular spheroid, and as for ordinary purposes it is not necessary to aim at a degree of accuracy, which is after all perhaps a mere waste of calculation, we shall suppose the earth to be a sphere, and on this principle exhibit in a Table the diminution of the degrees of longitude for every degree of latitude. In such tables, it is usual to express the degree of the equa tor in terms of English Miles ; hut as the length of this de gree is estimated differently by different writers, we shall, in the following Table, assume it equal to unity, and exhi bit the corresponding arches of the parallels in decimal fractions.