ASCENSIONAL DIFFERENCE

ASCENSIONAL DIFFERENCE, is the Difference between the Right and Oblique Ascension. See ASCENSION. Or it is the Space of Time which the Sun rises or sets before or after six of the Clock. To find the Ascensional Difference trigonometrically, having the Latitude of the Place, and the Sun’s Declination given; say, As the Cotangent of the Latitude, is to the Tangent of the Sun’s Declination, so is the Radius to the Sine of the Ascensional Difference.
For Example, suppose the Latitude be 51°. 30'. and the Sun’s Declination 9°. 00'. Then, to the Arc co. of the Co-Tangent of 51°. 30' = 0.099395
Add the Tangent of 9°. 00' = 9.199712
Sum is the Sine of 11°. 29' = 9.299107
which is the ascensional Difference required; and being re- duced into Time, by allowing four Minutes of an Hour for every Degree, it will be 44’. 29”. See TIME. If the Sun be in any of the northern Signs, and the ascensional Difference, as D O, be subtracted from the Right Ascension D, in Tab. Astronomy, Fig. 63. the Remainder will be the Oblique Ascension O.—If he be in a southern Sign, the ascensional Difference being added to the Right Ascension, the Sum is the Oblique Ascension; and thus may Tables of Oblique Ascensions be constructed for the several Degrees of the Ecliptic, under the several Elevations of the Pole. See TABLE.

ASCENSIONAL DIFFERENCE