24 



Investigation of the Corrections 



longitude when his right ascension is equal to that of the 

 star; and if a be the right ascension, and « the obliquity 

 of the ecHptic, tang, b — tang, a sec. v. The maximum of 

 aberration in right ascension will be when the sun is at 

 the distance A B r: 90° from the circle of dechnation A P, 

 and if B E be perpendicular to A P, the hypotenuse A B 

 being a quadrant, A E will be also a quadrant, and sin. 

 BE will be sin. SB sin. BSE, which is the cosine of 

 the angle made by the line of aberration S B with the 

 parallel of declination, so that sin. B E will represent the true 

 magnitude of the aberration reduced to the latter direction. 

 Now B E is the measure of the angle BAEorFAG=c, and 

 cos. c =: cos. F G sin. A F G n cos. a sin. u. While the sun 

 is between A and B, the aberration being directed to a 

 point behind A, will, of course, be negative with respect to 

 the right ascension ; and its complete expression will be 20", 255 

 sec. ^ sin. (O — b — 90°) sin. c; the secant of the declina- 

 tion i reducing the direct measure of the aberration to the an- 

 gular right ascension subtended by it at the pole. 



H. For the aberration in declination, if we draw a great 

 circle S C perpendicular to the circle of declination, and let 

 fall on it a perpendicular Q R D from the pole of the ecliptic, 

 it is obvious that C will be the pole of Q R, in the same man- 

 ner as A is the pole at E B, so that D will be the sun's place 

 when there is no aberration in declination, and the sine of S D 



