About the Book
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1834 Excerpt: ...figure 92, represents a portion of the concave surface of the starry heavens, the sun S, being the centre of this surface; & AA'A"G the ecliptic; SI CC" C'G' the heliocentric orbit of the planet or comet, whose elements are to be computed. A, A', A," the heliocentric places of the earth, at the times of the three observations; C, C, C," the corresponding (S) heliocentric places of the planet; B, B1, B," the geocentric places; the arcs AB, A'B', A"B," being always less than 180'. Then as the sun, earth, and planet are situated in a plane, which is projected in the heavens, in a great circle, it is evident that the arcs A CB, A' CB', A" C" B', are portions of great circles, and we shall suppose them to be continued, till they intersect each other, in the points E, E', E." Lastly, we shall suppose the points B', B, to be connected, by a great circle, which intersects A'B1 in the point B, and the orbit XG', in the point M. From this construction, it is manifest, that the situation of the point B, will be indeterminate, if the arcs BB," A'B" coincide; or, in other words, if the points A', B, B', B', fall in the same great circle. This case we shall exclude from our calculations, pie" with the remark, that we must select such observations as vary considerably from this situation; so that the slight errors of the observations may not materially effect the position of the point B, which is an object of importance in these calculations. Moreover, the situation of the point B, or of the arc B B" is indeterminate, when the points B, B," coincide; or are in opposite parts of the spherical surface; we must therefore, for the same reason, avoid the use of observations, where the geocentric pos...
