Translated by E C Otte
from the 1858 Harper & Brothers edition of Cosmos, volume 1 —————————————————————————
The manifold translatory changes of the stars, not those produced by the parallaxes at which they are seen from the changing position of the spectator, but the true changes constantly going on in the regions of space, afford us incontrovertible evidence of the 'dominion of the laws of attraction' in the remotest regions of space, beyond the limits of our solar system. The existence of these laws is revealed to us by many phenomena, as, for instance, by the motion of double stars, and by the amount of retarded or accelerated motion in different parts of their elliptic orbits. Human inquiry need no longer pursue this subject in the domain of vague conjecture, or amid the undefined analogies of the ideal world; for even here the progress made in the method of astronomical observations and calculations has enabled astronomy to take up its position on a firm basis. It is not only the discovery of the astounding numbers of double and multiple stars revolving round a center of gravity lying 'without' their system (2800 such systems having been discovered up to 1837), but rather the extension of our knowledge regarding the fundamental forces of the whole material world, and the proofs we have obtained of the universal empire of the laws of attraction, that must be ranked among the most brilliant discoveries of the age. The periods of revolution of colored stars present the greatest differences; thus, in some instances, the period extends to 43 years, as in πpi of Corona, and in others to several thousands,, as in 66 of Cetus, 38 of Gemini, and 100 of Pisces. Since Herschel's measurements in 1782, the satellite of the nearest star in the triple system of [Greek letter] of Cancer has completed more than one entire revolution. By a skillful combination of the altered distances and angles of position,* the elements of these orbits may be found, conclusions drawn regarding the absolute distance of the double stars from the Earth, and comparisons made between their mass and that of the Sun.
[footnote] *Savary, in the 'Connaissance des Tems', 1830, p. 56 and 163. Encke, 'Berl. Jahrb.', 1832, s. 253, etc. Arago, in the 'Annuaire' 1834, p. 260, 295. John Herschel, in the 'Memoirs of the Astronom. Soc.', vol. v., p. 171.
Whether, however, here and in our solar system, quantity of matter is the only standard of the amount of attractive force, or whether 'specific' forces of attraction proportionate to the mass may not at the same time come into operation, as Bessel was the first to conjecture, are questions p 148 whose practical solution must be left to future ages.*
[footnote] * Bessel, 'Untersuchung. des Theils der planetarischen Storungen, welche aus der Bewegung der Sonne entstchen' (An Investigation of the portion of the Planetary Disturbances depending on the motion of the Sun) in 'Abh. der Berl. Akad. der Wissensch.', 1824 (Mathem. Classe), s. 2-6. The question has been raised by John Tobias Mayer, in 'Comment. Soc. Reg. Gotting.', 1804-1808, vol. xvi., p. 31-68.
When we compare our Sun with the other fixed stars, that is, with other self-luminous Suns in the lenticular starry stratum of which our system forms a part, we find, at least in the case of some, that channels are opened to us, which may lead, at all events, to an 'approximate' and limited knowledge of their relative distances, volumes, and masses, and of the velocities of their translatory motion. If we assume the distance of Uranus from the Sun to be nineteen times that of the Earth, that is to say, nineteen times as great as that of the Sun from the Earth, the central body of our planetary system will be 11,900 times the distance of Uranus from the star 'a' in the constellation Centaur, almost 31,300 from 61 Cygni, and 41,600 from Vega in the constellation Lyra. The comparison of the volume of the Sun with that of the fixed stars of the first magnitude is dependent upon the apparent diameter of the latter bodies — an extremely undertain optical element. If even we assume, with Herschel, that the apparent diameter of Arcturus is only a tenth part of a second, it still follows that the true diameter of this star is eleven times greater than that of the Sun.*
[footnote] *'Philos. Trans.' for 1803, p. 225. Arago, in the 'Annuaire', 1842, p. 375. In order to obtain a clearer idea of the distances ascribed in a rather earlier part of the text to the fixed stars, let us assume that the Earth is a distance of one foot from the Sun; Uranus is then 19 feet, and Vega Lyrae is 158 geographical miles from it.
The distance of the star 61 Cygni, made known by Bessel, has led approximately to a knowledge of the quantity of matter contained in this body as a double star. Notwithstanding that, since Bradley's observations, the portion of the apparent orbit traversed by this star is not sufficiently great to admit of our arriving with perfect exactness at the true orbit nd the major axis of this star, it has been conjectured with much probability by the great Konigsberg astronomer,* "that the mass of this double star can not be very considerably larger or smaller than half of the mass of the Sun."
[footnote] *Bessel, in Schum., 'Jahrb.', 1839, s. 53.