78 



H. JACOBT, 



Let us now assume that in the formation and solution of the equations 

 (8) etc., the annual aberration has been entirely disregarded, except for the 

 slight effect dealt with in equations (28). The refraction and diurnal aber- 

 ration will however be computed in the manner already explained. Now let : 

 Arc be the combined effect of precession, nutation, annual aberration and 

 proper motion on the polar distance, taken with the proper sign for turning 

 quantities' referred to the fundamental epoch into apparent quantities at the 

 time of observation. 



Aa be the same for the right ascension. 



Then, instead of the values u and v obtained from a solution of our 

 equations, we must use in our further discussion the corrected values: 



t . r 



u =w-f-Aa, v =#-t-A7r. 



In this way we shall have to determine only the small corrections re- 

 quired by the adopted values of the constants of aberration, etc., instead of 

 determining these constants themselves. 



Before proceeding to discuss u and v, it seems desirable to assemble 

 here the formulas of Fabritius, which are the most convenient for computing 



Aa and Ate 1 ). If we let: 



(a), (it), be the mean right ascension and polar distance of a star 

 referred to the equator and equinox of the fundamental epoch t 0i 



and compute the rectangular coordinates: 



(X) = cos (a) sin (tc) cosec 1 ", 

 (Y) = sin (a) sin _(ic) cosec l", 



(29) 



then the values of the rectaDgular coordinates referred to the mean equator 

 and equinox of the beginning of the year of observation, which we will call 

 (X ) and (T ), can be computed bx the formulas: 





(30). 



In these formulas, if m and n are the usual precession numbers for 

 the time t 0i 



-ji = — m ( J") gin i" — n cos ^ 



l) bee ABtr. Nach. 2072 and 2073; Von Oppolzer, Bahnbestimmung. 

 Elk in, Trans. Aatr. Obs. of Tale, Vol. 1, p. 181. 



