Group of the Pleiades. 26? 



IV. 



CORRECTION FOR PRECESSION, NOTATION, AND ABERRATION. 



Precession and nutation affect all the position angles at the 

 central star equally. For they change only the position of the 

 celestial equator ; and this changes nothing but the direction of the 

 zero of position angles on the plate. They produce no effect what- 

 ever on the distances. Moreover, it has been shown by Bessel* 

 that if a very small circle be supposed drawn upon the sky, the 

 effect of aberration will be to transform it into another small circle, 

 concentric with the first, but having a slightly different radius, and 

 also slightly revolved about the common centre. It follows from 

 this that the aberration correction of the position angles, like that 

 for precession and nutation, is a constant for the whole plate ; while 

 the aberration correction of the distances is entirely independent of 

 the direction in which they are measured. This makes the applica- 

 tion of all these corrections a very simple matter. If we adopt the 

 usual designations of the American Ephemeris, as well as the 

 customary Besselian formulae, we have for the position angles : 

 a! = 20". 06 sin a sec 8 y f = cos a tan 8 



j3 r = cos a sec 8 5'= sin a tan 5 



±p = —Aa f — B(3' —Gy f — D8' 



which is additive to observed position angles. The annual increase 

 of position angles is: 



20". 06 sin a sec 8. 



For the distances, the aberration correction is given by : 

 r = (tan s sin 8 -j- sin a cos 8) sin 1" 

 8 = — cos a cos 8 sin 1" 



AS = (Cy + D8)s 



* Bessel, Astronomische Untersuclmngen, vol. i, p. 207. 



