ference between the time so found, and the time of the culmination of the same fixed star for the same day of any
- ↑ In the case under consideration, finding the time, I take no greater liberty than what is universally assumed, namely, that in consequence of the distance of the sun from the earth, the excentricity of the earth's orbit may be neglected; in point of fact it can have no influence on my method.
servation for finding the times of their culminations an error in finding their centers becomes a nullity. Here then is one advantage which the method here presented possesses over all others; and another, and a still greater advantage, is, that the motion of the earth is no way affected by them; and, as they are quite beyond her orbit, her position compared with theirs may be depended on within very narrow limits; for it is only the precession of the equinoxes and the nutation of the earth's axis that can affect her position with respect to theirs; and the precession is known and amounts to only a small quantity in a year, while the nutation exhibits a progressive annual change, which experiences a progressive annual compensation. Again: the sun being the center round which the earth annually revolves, the sun and the earth are always at diameters[1] from each other, so far as respects their apparent relative positions with respect to the fixed stars; and as the fixed stars do not affect either the sun or the earth, so far as mortals have hitherto discovered, we may indifferently take the sun's place or the earth's place amongst the fixed stars; and, consequently, by finding the time of the culmination of a fixed star, the right ascension of which is known, we have the right ascension of the sun; and we have, also, the time of the culmination of the sun; for the difference of those right ascensions, in times plus or minus, according as the sun is in antecedentia, or in consequentia, with respect to the fixed star, applied to either of those culminations will give the time; and thus, as we can by observation ascertain the quantity of the earth's motion in its orbit, true time can be known, so as to give the longitude at sea or on land, within seven miles of absolute distance. Whereas the method now in use compares the culmination of the sun with twelve o'clock, as indicated by a good clock, which can never be exact, because the clock is itself regulated by the culmination of the sun, and must, of course, partake of the errors in finding that culmination; and as the motion of the sun is in reality nothing else than the motion of the earth, and as the earth is affected by the sun, as well as by other agents, the time found by the sun's culmination cannot be depended on for the longitude, particularly when we take into the account the errors which are inseparable from observations on refraction and parallax. The case is still worse with the lunar observations, as I shall probably have occasion to show hereafter.
