22 Investigation of the Corrections 



Bessel's own very numerous observations on the pole star ; so 

 that he is far from wishing to depart from Delambre's co- 

 efficient, 



B. The ellipticity of the earth's motion causes the apparent 

 path of the star, in a plane parallel to the ecliptic, to be an 

 eccentric circle. 



See Vince's Principles of Astronomy, §291. The perpendi- 

 cular falling on the tangent from the remoter focus is always 

 proportional to the velocity, being always inversely as the per- 

 pendicular falling from the sun's centre ; its angular motion is 

 also equal to the angular motion of the tangent, or of the earth's 

 direction, which determines the displacement of the star, con- 

 sequently its extremity must describe a figure, similar to that 

 which is described by the apparent place of the star in the plane 

 parallel to the ecliptic : but this extremity describes, as is well 

 known, a circle circumscribing the ellipsis ; consequently the 

 apparent place of the star describes a circle situated in the same 

 manner with respect to the true place, as the circle circum- 

 scribing the ellipsis is situated with respect to the remoter focus, 

 except that the principal diameters are in transverse positions. 



C. The angular motion of the star, in its apparent orbit, is 

 always equal to the true heliocentric motion of the earth. ' 



The line C *, drawn from the 

 centre of the circle, to the apparent 

 place of the star, represented in the 

 circle circumscribing the earth's or- 

 bit, will always be parallel to S0, 

 drawn from the sun to the earth. 

 For if ST be perpendicular to the 

 tangent, and be continued beyond S 

 until SU become equal to * F, the U^ 



distance from the star's place to the remoter focus, the triangle 

 * T U will be similar to © T S, because * and F * or S U 

 are in the same proportion to each other, as © T and T S, conse- 

 quently the angle T * U is equal to T © S, and * U is parallel 

 to © S. But * U must pass through the centre C, since * and 

 U must be both in the circle, and * U is equal in length to a 

 diameter, being equal to S © + © F. 



