On the J\[olion of the Sun and Solar System. 23-9 



changes, arising from sidereal parallax, the stars remaining 

 pertecllv at rest. 



Let the stars be Arcturus and Sirius, and tlieir an-nual pro- 

 per motions as givt'n in the Astronomer Royal's Tables. 



When the annual proper motion of Areturus, which vs 

 — 1",26 in right ascension, and+ l",72 in north polar di- 

 stance, is reduced bv a composition of motions to a sincle 

 one, it will be in a direction which makes an angle of 

 55° 29' 42" south-preceding with the parallel of Arcturus, 

 and of a velocity so as to describe annually 2''j08718 of a 

 great circle. 



The annual proper motion of Sirii;?,— o",42 in right 

 ascension, and-h 1^,04 in north polar distance, by the sairie 

 method of composition, becomes a motion of l'',l 1528, in 

 a direction which makes an angle of 6S"' 4 9"" 41 " south- 

 preceding with the parallel of Sirius. 



By calculation., the arches in which these two stars 

 move, when continued, will meet in what I have called 

 tlieir parallactic centre, whose right ascension is 73" 39' 50'', 

 and south polar distance is 36° 41' 34'^ The opposite of 

 this, or right aicension 255° 39' 50", and north polar di- 

 stance 36" 4 1' 34", is what we arc to assume for the re- 

 quired apex of the solar motion. 



When a star is situated at a certain distance from the 

 sun, which we shall call 1; and 90" from the apex of the 

 solar motion, its parallactic motion will be a maxinium. 

 Let us now suppose the velocity of the sun to be such that 

 its motion, to a person situated on this star, would appear to 

 describe annually an arch of 2",84825, or, which is the 

 same thino-, that the star would appear to us, from the 

 effect of parallax, to move over the above-mentioned arch 

 in the same time. 



To apply this to Arcturus, we find by calculation that its 

 distance from the apex of the solar motion is 47° 7' 6"; its 

 parallactic motion therefore, which is as the sine of that 

 distance, will be 2",(j8718 ; and this, as has been shown, 

 is the ajiparenl motion which observation has established as 

 the proper motion of Arcturus. 



In the next place, if we admit Sirius to be a very large 

 star situated at the distance l,6S0;j from us, and compute 

 its elongation from the apex of the i-olar mention, we shall 

 find it 136" 50' 14",5. W^ith these two data wc calculate 



♦ . s 

 that its parallactic rtiotion will be -— ^^ =,-^/^ = r',11528 ; 



and this also agrees with the apparent motion whiuh has 



bcea 



