fi-10 On the Mollonqf llie Sun and Solar System. 



been ascertained bv observation as the proper motion of 

 Sirius. 



Now since, according to the rules of philosophizing, we 

 ought not to admit more motions than will account for the 

 observed changes in the situation of the star^;, it would be 

 ■wrona; to have recourse to the motions of Arciurus and Si- 

 rius, when that of the sun alone will account tor them both ; 

 a.nd this consideration would be a sufficient inducement for 

 us to 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 parallactic 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 situation happens to be 

 favourable, as the sum of an arithmetical series of natural 

 numbers, beginning at 0, continued to as many terms as 

 there are stai-s 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 closelv connected with astronomical observa- 

 tions that I shall keep them constantly in view ; and there- 

 lore 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 fol- 

 lowing hand of Hercules, by Sirius and Capella. The cal- 

 culation of them is in Table I. 



The annual proper motions of our third star in Dr. Mas- 

 kelyne's Tables are +0",21 in right ascension, and -|-0'',44 

 in north polar distance; and by calculation these quantities 

 give an annual motion of O", ±5374 to Capella, in a direc- 

 tion which makes an angle of 71° 33' 22",4 south-follow- 

 ing with the parallel of this star. 



The distance of Capella from the same calculated apex 

 of the solar motion, by which we have already explained 

 the apparent motions of the other two stars, is 80'' 34' 46''; 

 and, admitting again the velocity of the sun towards the 

 same point as stated betorc, it will occasion a parallactic 



motion 



