of Ifw Places of the Stars. 23 



D. The apparent place of a star may, therefore, always be re- 

 ferred to a centre, situated between its true place, and its ap- 

 parent place, at the time of the earth's perihelium, the distance 

 being to the whole mean displacement, as the eccentricity to 

 the mean distance, that is nearly as 1 to 60 ; and this con- 

 stant aberration, referred to the plane of the ecliptic, will be 

 ",34 ; but since it has no effect on the relative places of the 

 stars at different times, its existence may be neglected in ail 

 common cases. 



E. The minute circle parallel to the ecliptic, projected on 

 the celestial vault, becomes obviously an ellipsis, of which the 

 semidiameter parallel to the ecliptic retains its original magni- 

 tude of 20 ",255, and the semidiameter perpendicular to it be- 

 comes 20",255 sin lat. 



F. The apparent place of the star in the circular orbit, as re- 

 ferred to its centre, being always 90° in advance of the earth's 

 place, and of course pointing to a place in the ecliptic 90° be- 

 fore the earth, or 90° behind the sun, the line on which the 

 star is found may be considered, from the principles of per- 

 spective, as a part of the great circle intersecting the ecliptic 

 in that point, and the angular magnitude of the aberration will 

 always be proportional to the sine of its distance from the star. 

 It is also obvious, that when this circle passes through the 

 pole of the heavens, the aberration will be only in decli- 

 nation, and the aberration in right ascension will vanish ; 

 and on the other hand, when the circle becomes perpen- 

 dicular to the circle of declination, the aberration in decli- 

 nation will vanish : and it follows from the properties of the 

 ellipsis, the ordinates of which are represented by the sines 

 and cosines of arcs of the circle from which it is derived, that 

 the maximum must belong to a point of the circle, at the dis- 

 tance of a quadrant from that which affords no aberration in 

 the respective direction ; so that by determining the magnitude 

 of the aberration in this point, we obtain the coefficient for 

 computing it in any other situation. 



G. The aberration in right ascension, tlierefore, will vanish 

 when the sun's longitude is =; 6 -t- 90°, 6 being the sun's 



