224 Proceedings of the Royal Irish Academy. 



lactic ellipse, the discrepancy between the two distances will be 27r cos 9, 

 and the discrepancy between the two position angles will be 27r sin 6. 

 These quantities cannot be both less than 7ry^2. If, therefore, we 

 retain for discussion every case in which the discrepancy in the two 

 distances, or the two position angles, amounts to a single second of 

 arc, every case in which the parallax could amount to 0"'70 will be 

 certainly included. On examining the list of observations, it will be 

 seen that in twenty-seven cases there is not a discrepancy, either in 

 the angle of position or in the distance, which amounts to a single 

 second of arc. In these cases there is, therefore, no suggestion that 

 the parallax reaches anything like the limit named : if any appreciable 

 parallax exists, it is masked in the errors of observation, which are, 

 of course, under little control when the number of observations is so 

 few. 



There are, however, fifteen cases in which the discrepancy does 

 amount to a second of arc. Thus, so far as the distance is concerned, 

 in 



XV. the discrepancy is !"• 

 xvm. ,, 1 



xxn. , , 1 



XXVI. , , 1 



1 



The following are the cases in which the discrepancy in the two 

 position angles is at least equivalent to a second of arc : — 



m., v., XI., xn., xin., xvm., xxiv., xxv., xxvi., xxvn., xxxi., xl. 



In the case of xvm. and xxvi., we have a discrepancy amounting to 

 over a second both in the distance and the position angle. 



It may be remarked, that of these fiiteen cases a large propor- 

 tion will be found where the observations have been more or 

 less incomplete, and where, consequently, the errors of observation 

 may reasonably be expected to be greater than in the cases where 

 the observations are complete. We shall, however, inquire as to how 

 far the discrepancies are capable of being subdued or removed by the 

 supposition of annual parallax. For this purpose it will be necessary 

 to examine the effect of annual parallax on each of the objects, sepa- 

 rately, by the well-kno^vn formulae. In order to reduce the observed 

 distance between a star which has parallax tt, and an adjacent star 

 which has no parallax, to the distance, as seen from the sun, a cor- 

 rection must be applied equal to 



- m-irR cos ( O - IP), 



where R is the distance from the sun to the earth, and where is 

 the sun's longitude, m, M being constants depending upon the object. 



