216 Proceedings of the Royal Irish Academy. 



The question then arises as to whether there are any additional 

 presumptions which may guide the parallax seeker in choosing the 

 stars to obserye. I will mention two. 



In Mr. G. J. Stoney's memoir on the " Physical Constitution of 

 the Sun and Stars," Proceedings of the Royal Society, IS'o. 105, 1868, 

 p. 49, is the following passage : — 



" The minute crimson stars which are met with here and there in 

 the sky seem to be either very small stars or stars enormously 

 distended by heat. It is very desirable that the proper motion and 

 parallax of these bodies should be inquired into when practicable, on 

 the chance that some of them may be found to owe their colour to 

 being very small, and therefore very close to us." 



There is also a certain presumption that some of the variable stars 

 are really small, and that therefore, as we see them, they must 

 be comparatively near us. 



Before commencing the observations now about to be described, a 

 working list was formed, containing Red Stars, variable stars, stars 

 with large proper motion, and several other stars which were chosen 

 on different grounds. The observations of these stars are directed with 

 the special object of seeing whether any of them have a large 

 parallax. My present purpose is to place on record the observations 

 of forty-two different objects selected from this working list. In 

 almost every case here described the observations have been sufficient 

 to convince me that the parallax is certainly less than one second of arc, 

 and most prolahly does not exceed half a second. It will, therefore, bo 

 understood that the results of the reconnoitring observations which 

 are here set forth are merely negative so far as the immediate object 

 in view is concerned ; and as they do not suggest the existence of any 

 parallax worth following up, I do not intend to observe the objects 

 herein named any further. The time, therefore, seems to have arrived 

 when these observations may be published. 



We have now to describe the principle upon which the recon- 

 noitring observations have been conducted. The effect of annual 

 parallax upon a star is to make the apparent place of the star describe 

 a minute ellipse, of which the mean place of the star occupies the 

 centre. In the reconnoitring observations the star is observed twice ; 

 at the first observation the star is at one of the extremities of the 

 major axis of the ellipse. The second observation is made after an 

 interval of six months, during which time the star has moved to that 

 part of the ellipse which is at the other extremity of the major axis. 

 It thus appears that the two observations are so arranged that in 

 each case parallax shall have the greatest effect it is capable of 

 producing. 



"When a star undergoes the greatest displacement from parallax it 

 must be at a distance of 90° from the sun. If, therefore, a, a', and 

 8, 8', be the right ascension and declension of the star and the sun,- 

 respectively, then, at the time of greatest parallactic displacement, 



tan 8 tan S' = - cos (a' - a). 



