The estimation of distances among the stars by the eye, is an extremely inexact process. In some of the ancient observations, however, this appears to have been the method employed; and stars are described as being a cubit or two cubits from other stars. We may form some notion of the scale of this kind of measurement, from what Cleomedes remarks,[80] that the sun appears to be about a foot broad; an opinion which he confutes at length.
[80] Del. A. A. i. 222.
A method of determining the positions of the stars, susceptible of a little more exactness than the former, is the use of alineations, [already] noticed in speaking of Hipparchus’s catalogue. Thus, a straight line passing through two stars of the Great Bear passes also through the pole-star; this is, indeed, even now a method usually employed to enable us readily to fix on the pole-star; and the two stars β and α of Ursa Major, are hence often called “the pointers.” [162]
But nothing like accurate measurements of any portions of the sky were obtained, till astronomers adopted the method of making visual coincidences of the objects with the instruments, either by means of shadows or of sights.
Probably the oldest and most obvious measurements of the positions of the heavenly bodies were those in which the elevation of the sun was determined by comparing the length of the shadow of an upright staff or gnomon, with the length of the staff itself. It appears,[81] from a memoir of Gautil, first printed in the Connaissance des Temps for 1809, that, at the lower town of Loyang, now called Hon-anfou, Tchon-kong found the length of the shadow of the gnomon, at the summer solstice, equal to one foot and a half, the gnomon itself being eight feet in length. This was about 1100 b. c. The Greeks, at an early period, used the same method. Strabo says[82] that “Byzantium and Marseilles are on the same parallel of latitude, because the shadows at those places have the same proportion to the gnomon, according to the statement of Hipparchus, who follows Pytheas.”
[81] Lib. U. K. Hist. Ast. p. 5.
[82] Del. A. A. i. 257.
But the relations of position which astronomy considers, are, for the most part, angular distances; and these are most simply expressed by the intercepted portion of a circumference described about the angular point. The use of the gnomon might lead to the determination of the angle by the graphical methods of geometry; but the numerical expression of the circumference required some progress in trigonometry; for instance, a table of the tangents of angles.
Instruments were soon invented for measuring angles, by means of circles, which had a border or limb, divided into equal parts. The whole circumference was divided into 360 degrees: perhaps because the circles, first so divided, were those which represented the sun’s annual path; one such degree would be the sun’s daily advance, more nearly than any other convenient aliquot part which could be taken. The position of the sun was determined by means of the shadow of one part of the instrument upon the other. The most ancient instrument of this kind appears to be the Hemisphere of Berosus. A hollow hemisphere was placed with its rim horizontal, and a style was erected in such a manner that the extremity of the style was exactly at the centre of the sphere. The shadow of this extremity, on the concave surface, had the same position with regard to the lowest point of the sphere which the sun had with regard to the highest point of the heavens. [163] But this instrument was in fact used rather for dividing the day into portions of time than for determining position.
Eratosthenes[83] observed the amount of the obliquity of the sun’s path to the equator: we are not informed what instruments he used for this purpose; but he is said to have obtained, from the munificence of Ptolemy Euergetes, two Armils, or instruments composed of circles, which were placed in the portico at Alexandria, and long used for observations. If a circular rim or hoop were placed so as to coincide with the plane of the equator, the inner concave edge would be enlightened by the sun’s rays which came under the front edge, when the sun was south of the equator, and by the rays which came over the front edge, when the sun was north of the equator: the moment of the transition would be the time of the equinox. Such an instrument appears to be referred to by Hipparchus, as quoted by Ptolemy.[84] “The circle of copper, which stands at Alexandria in what is called the Square Porch, appears to mark, as the day of the equinox, that on which the concave surface begins to be enlightened from the other side.” Such an instrument was called an equinoctial armil.