354 Dr. Herschel's Account of the Changes 
(b) As the observations of the Astronomer Royal have ascer- 
tained the motion of Castor, so it is no less evident, from the 
series of observations which has been given in my Paper, that 
its smaller companion has also changed, if not its real situation, 
at least its relative one with respect to the large star. Let us 
therefore examine, whether the motion of u can be the cause of 
the apparent change that has taken place in the relative situa- 
tion of these two stars. 
The annual proper motion of a Geminorum, in right ascension, 
by the new Tables, is o",i5; which, in years, will amount 
to 3", 525. The annual proper motion in polar distance, by the 
same Tables, is o ,, ,04; which, in the same time, will amount to 
o",94 ; the former motion being retrograde, and the latter to- 
wards the south. Let FP, in Figure 1, (Plate IX.) be the parallel 
of Castor, and make a a! equal to 2978,5; which will be the 
quantity of its motion in right ascension in the parallel, when it 
is 3525 in the equator. At right angles to «P, make a! a," equal 
to 940 ; and this will represent the motion of the star in polar 
distance towards the south. Draw the line a,x so as to make 
an angle of 32°47' with the parallel FaP on the north preceding 
side, and place x at the distance of 37 65 from «. Then will « 
and x be the situation in which these two stars were observed 
in the year 17 79; their apparent distance, estimated in diame- 
ters of the large star, being i£ ; and the angle of position, as 
has been stated, 32 0 47' north-preceding. 
If the star x had been at rest while « moved towards u", the 
relative situation of the two stars in the year 1803 would have 
been represented by a." x ; that is to say, the apparent disks of 
these two stars would have been hardly diameter of the 
largest asunder, and the angle of position xotl'P' must have 
