362 Proceedings of the Royal Irish Academy. 



According to 0. Struve {Joe. cit.), the annual proper motion in right 

 ascension is + 0'-0167, and the declination - 0"-152. It hence appears 

 that the arc moved over in one year by P rn 242 is 0"*2497, while 

 the position angle of the star, in the position it will occupy next year, 

 measured from the present position, is 127°* 5. The correction to be 

 applied to the observed distance, in order to reduce the observed dis- 

 tance to that between the places at the epoch, is 0"-04407 per annum, 

 while the corresponding correction to the observed position angle is 

 - 3'-565, or in arc - 0"-2457. 



The adopted mean distance at the epoch is 237"*320, and the 

 adopted mean position is 207° 13'-86. 



From the usual formulae it is found that when is the sun's lon- 

 gitude, R the sun's radius vector, and it the annual parallax of P iii 

 242, the correction to be applied to the observed distance to clear it 

 from the effects of parallax is 



- [9-82787] z;R cos(0 - 174° 56' 0"), 



while the corresponding correction for the observed position angle is 



- [9-90007] zsR cos (0 - 142° 8' 29"). 



Assuming that x is the correction to be applied to the annual mean 

 distance, while x' is the correction to the assumed value of the proper 

 motion in distance, and k is a probable difference in the coefficients of 

 aberration of the stars, then we have from the observations of the dis- 

 tance the usual eq[uations of condition. 



Solving these, we deduce in the usual way 



X =-0"-1459 ± 0"-08, 

 ;^;' = + 0"-3009 ± 0"-15, 

 OT = + 0"-0163 ± 0"-09, 

 K = + 0"-1405 ± 0"-12. 



The sum of the squares of the residuals is 1-2732, from which the 

 probable error of one complete observation is + 0"-15. The sum of the 

 squares of the absolute terms is 1-4638. 



"We next proceed to form the equations of condition from the ob- 

 servations of the position angle. In a complete series of measures, 

 four observations of the parallel and four of the position angle have 

 been made. Owing to the great distance of the stars, the measure- 

 ments of the position angle (estimated in arc) are not very satisfactory ; 

 and on two occasions (3rd December and 5th December, 1879) the 

 discrepancies have attained to very undesirable dimensions. The resi- 

 dual on 3rd December is no less than - l"-332, but only a weight of 

 one-half attaches to this result because it was based on but two observa- 

 tions of the parallel and two of the position. The notes at the time of 



