Tlie motion of tlie stars 



00 



Til 



= cos(X"X) = 



sin a, 





= cos(X" Y) = 



sin 8 cos a, 





pn<s 1 X" 7\ 



— Oüö j — 







= cos(r'X) = 



— COS a, 



\ 



= cos ( Y" Y) ^ 



sin S sin c, 



Ï23 



= cos {Y"Z)^ 



cos S sin a, 



Thi 



= eos(Z"X) = 



0, 



T33 



= cos {Z" Y) = 



— cos S, 



Ï38 



= cos {Z"Z) = 



sin S. 



The riglit ascensions of the centres of the 48 squares are unequivocally deter- 

 mined by their definition (I p. 25). The dechnation of the »centre» of a square 

 may be defined in different manners. For practical purpose the difference in the 

 resulting values for 8 is, however, of little importance. The values here employed are: 



Squares A^- 



-A, : 



B = 



+ 80» 



B^- 



— -Sio 



: S = 



+ 4ô°6'.o 



C,- 



— 



: S = 



+ 14»28'6 



Dj 





: d = 



— 14"28'6 



E, 





: 8 = 



— 4ô"6'.o 



» 



—F 



: S = 



- 80°. 



The resulting values of '{.. for the different squares are given in tab. VII. 

 If the mean apparent motion of the stars in a certain square were dependent 

 only on the motion of the sun, then we should have 



M{V)^Y, = '^^ 



where and are given for each square (in tab. II). The equations (39*) then 

 should give, using for instance the method of least squares, the values of 



^^U'\ ^^V" and ^^W" 



from which the position of the apex can be found. 



If, however, the system is affected by a rotation about some instantaneous 

 axis, through which rotation the node of the X" F"-plan on a fixed plan of reference 

 (say the ecliptic 175Ü) retrogrades by the angle V and the inclination to that plan 

 be increased by the amount Ai, then, through this rotation, the coordinates a and 

 § of a stars, is increased by Aa and AS, where 



, cos s Aa = r (cos s cos S A- sin s sin S sin c.) — sin 8 cos a A^, 



(40) / . 



AS = r COS a sin s -|- A* sin a . 



