in the relative Situation of double Stars. 355 
been 86° 25' north-preceding. But this is quite inconsistent with 
the observations that have been given ; according to which, the 
small star, in the year 1803, was situated at x'. It is therefore 
proved, that the motion of x alone cannot account for the change 
which has taken place. 
( c ) If the motion of Castor should be only an apparent one, 
arising from the motion of the solar system, then the proper 
motion of the sun must be just the reverse of that which the 
new Tables assign to x Geminorum. This being admitted, let 
us examine what will be the result with regard to the relative 
situation of the small star, which, since only the sun is supposed 
to be in motion, must now remain at rest, as well as a. The 
effect of the parallax, which we are now considering, is inversely 
as the distances of the stars which are affected by it. Hence arise 
the three cases which have been examined in my first Paper, 
When a line from the sun to Castor, Ox,* is perpendicular to 
the line xx, joining the two stars, no change in their relative 
situation can take place, arising from parallax, which will 
act equally on both. For, let x, x° and x, in Fig. 2, be placed 
as they were in Fig. 1 ; and the real motion of the sun from O 
to O', will produce the parallactic motion of Castor from x to x". 
It will also occasion an apparent motion of x, equal to that of 
x, and in a parallel direction with it. This star will therefore 
appear to have moved from x to x', in the same time that the 
large star has moved from x to x", so that their relative situation 
will remain unchanged. 
( d ) If a; be placed beyond x, the effect of parallax, exerted in 
the direction xx" , parallel to xx", will be less upon this star 
than on Castor; and its apparent motion must fall short of the 
• See Figure i of the former Paper. 
