[ 175 ] 



XXII. On the Calculation of the Orbits of Double Stars. By 

 Professor Encke. 



[Continued from p. 109.] 



TN making the transition to the true ellipsis, we may now 

 *- first apply the formulae (46) 



-^ sin F = -^ sin (P-6.) /' sin(Q-P) = - ^^^^^^sin 2F 



i-cosF = -i-cos(P-«;) /'cos(Q-P) = — -^, 



whence 



log I = 0-572544; F = 216° 10' 38"-4 

 log V — 0-523534; Q = 177 24 50 -8 

 The three formulae 



V- sin z'^ sin 2ft = (d^—b"-) sin 2 w — R- sin 2 P 

 V^ sin f'^ cos 2 ft = {cr — b') cos 2 w — R- cos 2 P 

 6'2 + J'^cos r- = a* + 6--R2 give 



log b' = 0-591921, ft = 122° 47' 54"-7, i' 46=24' 56"-9. 

 Lastly, the formulae (39) and (40) give with perfect agree- 

 ment of sin ^' and cos $' ... log a' = 0-636332 



TT = 166° 56' 44"-5, <p' = 25° 28' 19"-8. 

 For determining the epoch, we have 



sin E' = § [9-505808] sin {336° 35' 19"'5-p} 

 cos E'= §[9-456798] cos{ 177 24 50 -8 -p} +0-430073, 

 whence applying the preceding value of ju.', we obtain 



T = 1806-877706; 1806-87695; 1806-87697; 1806-87700; 

 the mean of which is T = 1806-877. We obtain 



k' = 0-158010, and consequently we have the followino- 

 elements : 



T = 1806-877 



ff = 166°56'44"-5) . j r i. 



8 = 122 47 54 -7 r counted from the eastern parallel. 



i' = 46 24 56 '9 



^' = 25 28 19 -8; log a' = 0-636332; /a' = 4° 52' 26"-2 

 mean annual motion. Motion westerly. 



Calculating with these values the constants v, V, v', V, by 

 (47) we obtain the following equations for the computation 

 of the place: 



E'-{24°38' 28"-8} sin E'= (/;-1806-877){4° 52' 26"-2} 

 g sin;) = [0-5623641 sin (E'+ 155° 59' 57"-2) -0-638606 

 J cosp = [0-535651 J sin (E'-f 267 29 6 -9) + 1-474941. 



For 



