( 23673} 
respectively, both of which evidently may be reduced to 
= SO? nnn). oon 
However, if it is true that the two components of the motus 
peculiaris may be treated as errors of observation, then there is 
evidently no reason why it should not be allowed, so far as possible, 
to base the determination of the elements of the solar motion on 
one of these components only. That this is the generally adopted 
view, is apparent from the fact that generally a result is derived 
both from the right ascensions and the declinations separately. 
Airy himself says expressly : (Mem. of the Roy. Astr. Soc. XX VIIT) 
„we must consider the elements of motion of the different stars as 
„being, to all intents, chance quantities, to be treated in the same 
„way as chance errors of observation,” and a little earlier (which 
also shows clearly which meaming is attached by Airy to the words 
elements of motion): ,in the instances in which evidence as to proper 
„motion in one element fails, it enables us to take account of.... the 
„evidence derived from the proper motion in the other element alone.” 
4. To this, however, Srrin does not object. The real point at 
issue is this, that, according to my contention, such a determination 
from one component alone may lead to an unacceptable solution, 
a solution which, for the particular case of stars situated at 
1) To avoid all mistakes, even at the risk of falling into repetitions I give here 
in extenso the reasoning by which the formulae (2) and (3) are derived. The reasoning 
is essentially the same as that which was used in $ 1 (a). Suppose for a moment that 
the Antapex is at the arbitrarily chosen point 4 (fig, 1), at a distance A from S, and 
h ee) 
take the arbitrary quantity — sin A= SB for the parallactic motion. In the supposition 
p 
that the Antapex is at 4, this parallactic motion is in the direction S4 and the motus 
peculiaris SD is such that the resultant of SD and SB is y. The projections of 
this motus peculiaris are, always in the same supposition, 
for my decomposition Da and Sa, 
for StEtn’s decomposition Dd and Sd. 
h 
If now we successively take other points for the Antapex and other values for —, 
P 
then also the direction of the parallactic motion and the amount of the motus pecu- 
liaris and its components will change. According to Atry that point 4 will be regarded 
as the most probable position of the Antapex, for which the minimum conditions (2) 
and (3) respectively are fulfilled. 
