Page:Baylee's Method of Finding the Longitude.djvu/19

Copy of the Outline, which I presented to the Board of Longitude on the 7th instant.

METHOD

 

OF

 

FINDING THE LONGITUDE,

 

THE MERIDIAN, THE CULMINATION OF THE FIXED STARS, THE VARIATION OF THE COMPASS, AND THE TIME, AT SEA, INDEPENDENTLY OF PARALLAX AND REFRACTION, BY ONE SIMPLE OBSERVATION.

 

To find the Longitude:—Assume any meridian, R, as a first meridian, and find the time of the culmination of any fixed star, for any day of any year, with respect to the meridian R: the difference between the time so found and the time of the culmination of the same fixed star, for the same day of any year, with respect to any other meridian, S, will give the difference of longitude between the two meridians, R and S. The times of the respective culminations should, for greater accuracy, be found by observation, and not by calculation only.

To find the Meridian:—Let the right line (or right circle), ${\begin{matrix}\mathrm {M} \\|\\\mathrm {E} \end{matrix}}$, represent the meridian, and the right line (or right circle), H—O, the horizon of any place at any parallel of latitude: now as all the parallels of latitude are parallel to the equator; and as the equator is the boundary of the rational horizon; and as when any point in any right line (or right circle) ${\begin{matrix}\mathrm {M} \\|\\\mathrm {E} \end{matrix}}$, is perpendicular to any right line (or right circle), H—O, the whole of ${\begin{matrix}\mathrm {M} \\|\\\mathrm {E} \end{matrix}}$ will be perpendicular to H—O and, further, as any number of fixed stars which have the same right ascension must be in the same right line (or right circle); it follows, that if among any number of fixed stars, having the same right ascension, any one of them coincide with any meridian, ${\begin{matrix}\mathrm {M} \\|\\\mathrm {E} \end{matrix}}$, the whole of them must coincide with that meridian; and hence, and also from the definition of a meridian, it follows, that the whole of them will be perpendicular to the horizon, H—O. When any fixed star, X, has not exactly the same right ascension as any other fixed star, Y, the time of the culmination of X can be found, by the method here presented, as if X had the same right ascension as Y; for let the fixed star X be on the meridian, and then will