272 
Mr. Herschel on the 
star by great circles joining it and the north poles of the 
equinoctial and ecliptic respectively, <r being considered po- 
sitive for stars in the western hemisphere (or that whose pole 
is the point <Y>), and negative for stars in the eastern, whose 
pole is =£=. Let also o represent the sun’s longitude at any 
time, and call a the maximum semi-annual parallax or the 
angle (expressed in seconds), which the radius of the earth’s 
orbit would subtend if perpendicularly presented to an eye 
at the distance of the star. It is obvious then that a will re- 
present the major semi-axis of the star’s parallactic ellipse, and 
a . sin. X the minor, so that its excentricity = Va 2 — a 2 , sin. X 3 
= a . cos. X, which if we call a e, we have e = cos. X. The 
star will appear to describe this ellipse in the direction npsf. 
Its motion in it will however not be uniform, but equal areas 
will be described in equal times about its centre (or the star’s 
mean place) : this is evident, because the area described by 
the star in the parallactic ellipse round its centre is the 
orthographic projection on the surface of the heavens of that 
described by the earth round the sun in its orbit. This 
consideration gives us at once, the equation 
tan. 6 = — sin. / . cotan. (© — /); ( 1 ) 
where 6 represents the elongation of the star in its ellipse from 
the eastern extremity of its major axis reckoned in the direc- 
tion npsf. 
Let nr be the angle of position of the small star, nr being 
reckoned from a parallel to the equinoctial, in the same di- 
rection npsf and from the east, so that the nf quadrant shall 
line joining the two stars with the parallel, by this name, it becomes necessary to 
distinguish them, and the expression used in the text is perhaps also more correct 
than that in common use. 
