Page:Baylee's Method of Finding the Longitude.djvu/7




 * —When two, or any number of fixed stars, which have the same right ascension, appear in a right line (or right circle), and perpendicular to the horizon of any observer, if a right line be drawn on the earth's surface, or on any plane parallel to that horizon, and perpendicular to the line of fixed stars which is then perpendicular to that horizon, the right line so drawn will give, accurately, the meridian line of that observer. For, let the right line (or right circle),, represent the meridian, and the right line (or right circle), , the horizon of any observer, 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, to which the sensible horizon is parallel; and as when any point in any right line (or right circle), , is perpendicular to any other right line (or right circle), , the whole of will be perpendicular to ; and, further, as any number of fixed stars, which have the same right ascension, must be all in the same right line (or right circle); it follows, that, if among any number of fixed stars, which have the same right ascension, any one of them coincide with any meridian, , 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 these fixed stars will be perpendicular to the