One of a set of numbers and a system of coordinates, introduced by Bessel, for predicting the progress of solar eclipses and of occultations. The coordinate system has its origin at the center of mass of the Earth. The z-axis is drawn in the direction of the Moon and parallel to the line joining the centers of the Sun (or other star) and the Moon. The y-axis lies in the plane of the z-axis and the North Pole and is positive northwards. The x-axis is drawn to complete a right handed, rectangular Cartesian coordinate system. The Besselian elements are then the following: (a) the coordinates (x,y) of the center of the Moon's shadow on the (x,y) plane (eclipse) or the right ascension and declination (áα*, δ*) of the star (an occulation); (b) the rates of change (x',y') of x and y per hour; (c) the Universal Time or Ephemeris Time To of conjunction in right ascension of the Moon and star (occultations only); (d) the hour angle μ of the z-axis at the Greenwich meridian (eclipses) or the hour angle H of the star at Greenwich at the instant To (occultations); (e) the declination d of the z-axis (eclipses) or the value Y of the y coordinate at the instant To (occultations). The quantities α*, δ*, x', y', To, H and Y are the Besselian elements of an occultation. The quantities x, y, x', y', μ, sin d and cos d, together with the following quantities peculiar to eclipses, are the Besselian elements of an eclipse; (f) the quantity dμ/dt (μ'); (g) the radii l₁ and l₂ of the umbral and penumbral cones on the (x,y) plane; (h) the angles f₁ and f₂ (half the vertex angles of the penumbral and umbral cones, respectively. The Besselian elements both for eclipses and for occultations are usually given in astronomical almanacs. However, many almanacs, because interest in eclipses and occultations has decreased and because calculating machines can easily calculate some of the elements, no longer list all the elements. (Some authors consider only x, y, x', y', μ, sin d and cos d to be Besselian elements of an eclipse. )