On the Motion of the Sun and Solar System. 241 



hiotion of Capella, in a direction 89<^ 54' 48" south-follow- 

 ing its parailel, amoumina; to 2-j8I25". In this calcula- 

 tion Capdla has been taken for a star of the first maonitudej 

 supposing Its distance from us to be equal to "ihat of 

 Arcturus. 



By cor.structii.g then a triangle, the three sides of which 

 Will represent the three motions which every star must have 

 that IS not at rest in space ,• we have one of the sides, re- 

 presenting the apparent motion of the star, equal to 0,4 63 7'"^ 

 the other side, being the parallactic motion of the star" 

 2,8125 'j and the included anele 18° 19' 27''. Fron> these 

 data v.e olitain the third 3ide,^-epresenting the real motion 

 ot the star, winch will be 2,375?". By the ffiven situation 

 ot t^his triangle with respect to the parallel ^of deciinatioii 

 01- l^apelia, the angle of the real motion will also be had. 

 which 15 86" 34' II" north-foilowu^g the parallel of this 

 star. A composition oi the paniilaclic and the real motion 

 in the directions we have assicrned, will produce the annu?! 

 apparent motion which has been established by obser- 

 vation. ■' 



But to apply what has been said to our present purpose, 

 It may be observed, that although we have accounted for 

 the proper motion of our third star by retaining the same 

 apex ot the solar motion, which has given us an explana- 

 tion of the apparent motions of the other two, yet in doino- 

 this we have been obliged to assion a sircat degree of real 

 motion to Capella ; and to this it may be objected, that we 

 can have no authority to deprive Arcturus and Sirius of 

 real motions, in order to give one of the same nature to our 

 third star : and indeed to every star that has a proper mo- 

 tion which does not tend to the same parallactic centre as 

 the niotions of Arcturus and Sirius. 



This objection is perfectly well founded, and I havej'iven 

 the above calculation on purpose to show that, wlien we 

 are in search of an apex for the solar motion, it ouoht to be 

 so fixed upon as to be equally favourable to cfeiy star 

 which is proper for directing our choice. Hence a pro- 

 blem will arise, in our present case, how to find a point 

 \vhose situation among three given apices shall be so that, 

 11 the sun's motion be directed towards it, there may be 

 taken away the greatest quantity of proper motion possible 

 from the given three stars. 'I>.e intricacy of the problem 

 IS greater than at first it may appear, because by a chaiK-e 

 ot the diBtanee of the apex from any one of the stars, its pt- 

 railactic motion, which is as the sine of that distance, will 

 be aflected j so that it is not the mere alteration of the anHe 



Vvl. 23. N®. 9J . Dtc 1805, (J V 



