Group of the Pleiades. 317 



VIII. 



FINAL RESULTS. 



The final results of the photographic . measures have been ar- 

 ranged in two tables which will now be given. The Table op 

 mean results requires no explanation, except that in the column 

 of remarks, P refers to the Paris catalogue of the Pleiades ;* 

 Y, to the Yale catalogue ; and B, to Argelander's Bonn catalogue. 

 The magnitudes are those of Argelander. In the computation of 

 a — a and 8' — 5 from the distance and position angle, the follow- 

 ing formulae have been found very convenient and accurate : — 



Let a and 8 be the right ascension and declination of the central star, 

 a' and 8' the same quantities for any other star. 

 a the true distance between the two stars. 

 jt the true position angle, at the central star. 



Then if we put : 



m = a cos n n = cf sin rt 



we shall have :f 



8' — 8 = m — [4-384545] n 2 tan 5 



— [8.59300] n 2 m (1 -f 3 tan 2 8) 



-f- [2.67651] n 4 tan 5(i+3 tan 2 8) 



— [3.27875] n 2 m 2 tan 8 (2 -f- 3 tan 2 8) 



cos 8 (a — a) = n -\- [4.685575] n m tan 8 



— [8.89403] n 3 tan 2 8 



-f- [8.89403] n m 2 (1 -f- 3 tan 2 5) 



— [3.57960] n 3 m tan 8 (1 -f 3 tan 2 8) 

 ~h [3'5796 ] n m3 tan 8(24-3 tan 2 8) 



where the numbers in square brackets are logarithms. 



* Annales de l'Observatoire de Paris, Observations, t. 29, 1874. Catalogue 

 du Groupe des Pleiades, par M. C. Wolf. 



f For a demonstration of these formulae, see Jordan, Handbuch der Vermess- 

 ungskunde, dritte Auflage, 1890, vol. iii, p. 319. 



