To find the longitude:—Assume any meridian, A, as a first meridian, and find the time of the culmination of any fixed star, with respect to the meridian A: the dif-
- ↑ These two fixed stars are selected merely because the square of Pegasus is a remarkable constellation, which just now culminates at a convenient hour in the evening: the other two stars in this square may be taken, but at an earlier hour.
Algenib, γ, in the wing of Pegasus, be the fixed stars taken, suppose for the twelfth of next month[1]: now, if a good watch be set as to noon, or twelve o'clock, when those stars culminate, that is, when they are on the meridian, on the evening of the eleventh; that watch will on the evening of the twelfth, when those stars are again on the same meridian, indicate 24 hours, minus the motion of the sun (more properly speaking, the motion of the earth) in its orbit, converted into time, during the interval between those two observations: and if a meridian line be traced as directed by this method, and the sun's culmination, that is, his coming on that line, be observed; the same watch will indicate the difference in right ascension, converted into time, between the sun and those stars, minus the motion of the sun in its orbit, converted into time, during the interval between the observation of the stars and the time indicated by the watch at the culmination of the sun. As similar observations may be made on several lines of fixed stars during the same night, such a number of means present themselves as will reduce any error that may arise to a nullity, so far as respects the observation for the longitude.
The method heretofore in use for finding true time, by comparing the culmination of the sun with twelve o'clock, as indicated by a well-regulated clock, requires a correction which is compounded of two elements. The unequal motion of the earth in its orbit, and the obliquity of the earth's axis to the sphere of its orbit: the latter of these, the obliquity of the earth's axis, may be understood by viewing the relative position of the equinoctial and the ecliptic on a celestial globe; but the former, the unequal motion of the earth in its orbit, can be discovered only by observations on the sun, or, which is much better, by observations on the fixed stars.
The method now presented is materially different. With the orbits of the fixed stars we are wholly unacquainted; their distances mock human conception, and lay the pretensions of science in the dust. The distance between the sun and the earth is very great indeed; but brought into competition with the distance between the fixed stars and the sun, it becomes like the tiny mote, which we behold floating in the sun's beams, compared with the united bulk of all the vast globes which revolve about our sun; and we may include in the enormous bulk our sun itself, which is, at least, a million of times larger than our earth! In consequence of their distance their diameters are so minute, that in ob-
