INVESTIGATION OF THE ABERRATION, &c. 85 

 But cos QT= cos TN. cos QN+ sin TN. sin QN. sin TNr , 



and cos TN= cos Tnr . cos nr JV+ sin TV . sin or JV. cos T<r N, 



= sin O cos a cos O sin a cos o>. 



Also, sin TN. sin 2Wv = sin TV . sin TT JV= cos sin . 

 Substituting these values, and putting 90 S for QN, we find 

 "' A8 = ^t{sinS(sinO cos a cos O sin a cos w) + cos S cos Q sinw}. 



2nd. For the Aberration in Right Ascension : produce 

 to a point B, such that ^B = 90, and join R8, RT. Then, 

 if Aa be the aberration in right ascension, 



A A 



Aa = - - K sin ST. cos TSR = - ^ cosET. 



COS COS 



But cos ^T= cos JV . cos R <r + sin TV . sin .5 nn cos R v T, 

 = sin sin a + cos a sin Q cos w. 



Consequently, 







Aa = -- ^ {sin sin a + cos a sin O cos &>]. 

 coso c 



