44 



Scientific Proceedings, Royal Dublin Society. 



or the moon appears to describe an ellipse round a point south of 

 its true position by the amount zs sin cos 8, the axes of the ellipse 

 being -& cos (f> and ct cos sin S, and the hour angle (6) being the 

 complement of the eccentric angle of the ellipse. 



If the true position of the moon's centre be represented by P 

 in Fig. 1, then the parallactic displacement will be Pa if 6 = 4 h , 

 half an hour later it will be Pb, and an hour later Pc ; so that 

 ab, ac, are the apparent motions of the moon due to this cause in 

 the two intervals. 



fig:l 



Iff 



flg:2. 



*S X 



The whole parallax is represented on the same scale (that of 

 1 mm. to 1 minute of arc) by the line PQ, and the ratios of Pa, 

 Pb, Pc to PQ are accurately known, so that any small error in the 



