358 Dr. Herschei/s Account of the Changes 
a supposition which ascribes all the observed phenomena to three 
real motions, will not be affected by the given alteration in the 
proper motion of Castor. Without repeating any part of the 
discussion of the former paragraph (z), it will be sufficient if I 
point out three motions, such as will answer the required purpose. 
Let the solar motion, as before, be towards A Herculis, with 
such a velocity as will in 23^- years produce a parallactic 
motion, at the distance and situation of » Geminorum, amounting 
to 2",28 o 5, in a direction of 6 o° 3 6' 57" south-preceding the 
parallel of that star. Let Castor have a real motion, which in 
234- years would carry it over an arch of 2", 1341, in a direction 
of 29 0 23' 3" north-preceding its parallel ; and let the real motion 
of the small star be such that in 23-E years, at its distance from 
us, supposed to be to that of Castor as 3 to 2, it would describe an 
arch of 2", 921 2, in a direction of 18 0 50' 13'' south preceding. 
Then would the parallactic motion of «,= 2", 2805, compounded 
with the real motion we have mentioned, give us an apparent 
annual motion equal to that which, in Dr. Maskelyne’s Table, 
is called the proper motion in right ascension and polar distance 
of this star. And the parallactic motion of x,= i",5203, com- 
pounded with the real motion we have assigned, would also 
produce an apparent annual motion which would correspond 
with my series of observed situations of this small star. But, for 
the high improbability of such an hypothesis, I refer to the para- 
graph (z) of my former Paper. 
What has been said of Castor, will apply to every other 
double star of which the proper motion may hereafter be assigned; 
for, unless the parallactic motion arising from the motion of the 
solar system should completely explain the observed changes, 
the same arguments will still remain in full force. 
