POSITION OF DOUBLE STARS. 22^ 



direQions ; that the velocities of their motions fliould be in a Obfervations 

 given ratio to each other ; and that this ratio fliould be com- ^"^ *"^f ^^°*i^' 

 pounded with the ratio of their diftances from O ; a fuppofi- changes of rela- 

 tion which muft certainly be highly improbable. To ftiew this tive fituation ia 

 with fufficient evidence, let us admit that, according to the j^^^^ each othcrji 

 beft authorities, the annual proper motion of Caftor is — 0'^ 105 

 in right afcenfion, and 0'',12 in declination towards the 

 north. Then, as the fmall ftar, without changing its diftance, 

 has moved through an angle of 2 1'* 54', the only difference in 

 the two motions of thefe ftars, will be exprefled by the extent 

 of the chord of that angle. To produce the required effeft, 

 it is therefore neceffary that the motion of a, which is given, 

 fliould regulate that of the fmall ftar, whofe relative place at 

 the end of 23^ years is alfo given. Then, as a moves in an^ 

 gle of 53'' 31' north preceding, and with a velocity which, 

 being exprefled by the fpace it would defcribe in 23f years, 

 will be 3''',51, it ijf required that x (hall move in an angle of 

 29 '^ 25', like wife north preceding, and with a velocity of 

 3''',02. The ratio of the velocities, therefore, and the direc- 

 tions of the motions, are equally given. But this will not be 

 fufficient for the purpofe : their diflance from O muft alfo be , 

 taken into conlideration. It has been fhown, that the two 

 ftars cannot be at an equal diftance from us, without an evi- 

 dent connexion ; it will therefore be necefTary for thofe who 

 will not allow this connexion, to place one of them nearer to 

 us than the other. But, as the motions which have been af- 

 fumed, when feen from different diftances, will fubtend lines 

 whofe apparent magnitudes will be in the inverfe ratio of the 

 affumed diftances, it is evident that this ratio, if the motions 

 are given, muft alfo be a given one ; or that, if the diftances 

 be affumed, the ratio of the motions muft be compounded with 

 the ratio of the diftances. How then can it be expected that 

 fuch precife conditions fliould be made good, by a concurrence 

 of circumftances owing to mere chance ? Indeed, if we were 

 inclined to pafs by the difficulties we have conjfidered, there 

 is ftill a point left which cannot be fet aflde. The motion of 

 the folar fyftem, although its precife direction and velocity 

 may ftill be unknown, can hardly admit of a doubt ; we have 

 therefore a third motion to add to the former two, which con- 

 fequently will bring the cafe under the ftatement contained in 

 our 7th number, and will be coniidered hereafter. 



