®4^ Dr. Herschel on the Direction of the 
fix at once on the calculated apex, as well as on the relative 
distances that have been assigned to these stars, if other proper 
motions could with equal facility be resolved into similar paral- 
lactic appearances. But from the nature of proper motions, it 
follows, that when a third star does not lead us to the same 
apex as the other two, its apparent motion cannot be resolved 
by the effect of parallax alone. And to enhance our difficulties, 
the number of apices, that would be required to solve all proper 
motions into parallactic ones, increases not as the number of 
stars admitted to have proper motions, but, when their situa- 
tion happens to be favourable, as the sum of an arithmetical 
series of natural numbers, beginning at o, continued to as many 
terms as there are stars admitted : so that if two stars give 
only one apex, one star added to it will give three apices ; and 
ten, for instance, will give no less than 45, and so on. 
The method of reasoning which, on this subject, I have 
adopted, is so closely connected with astronomical observations 
that I shall keep them constantly in view ; and therefore shall 
illustrate what has been advanced, by taking in Capella as a 
third star. The three apices which then are pointed out will 
be that in the mouth of the Dragon, by Arcturus and Sirius ; 
a second under the northern wing of Cygnus, by Arcturus and 
Capella ; and a third in the following hand of Hercules, by 
Sirius and Capella. The calculation of them is in Table I. 
-The annual proper motions of our third star in Dr. Maske- 
lyne’s Tables are 4-o",2i in right ascension, and -j-o",44in 
north polar distance ; and by calculation these quantities give 
an annual motion of o", 46374 to Capella, in a direction which 
makes an angle of 71 0 35' 22", 4 south-following with the 
parallel of this star. 
