of the Orbits of Double Stars. 109 



t = 81°43' 6"-8 logtang(45°+ ?) = 0'127330„ 

 ^1 = 44. 1-5 log tang (45 + Kx) = 1-758266 

 ^ = 46 20 24 -0 log tang (45 + ti) = 1"630936„ 



From the above values of a the true one was readily to be 

 derived with a near approximation, and the smallness of the 

 divisor 2y giving rise to some uncertainty 1 preferred em- 

 ploying the equations (16). Hence I found that all the values 

 af reed^if the observations were assumed as follows : 



70 p Ophiuchi. 



1779-77 

 1803-38 

 1 820-20 

 1823-27085 



0° 0' 

 122 32 

 288 9 

 296 55 



4" '4 

 2-7 

 4 -17 

 4 -746 



For these data we obtain with perfect agreement 

 o,=-25° 40' 17"-9 ; ^ = +32° 47' 54"- 1 ; y = +92° 4'44"-0, 



\ogab= 1-066736; log k = 9-996494, 



whence by (41) U = 73-862 years; fj.' = 4° 52' 26"-2 mean 



annual motion. We now calculate first ^ = g cos p, 



Yi = g sin p for all four places. 



,,, = 0-000000 ^1 = +4-400000 



,,, = +2-276315 02 = -1-452033 



,3 = -3-962518 03= +1-298979 



Yi^ = -4-231850 04 = +2-148490 



Next follow the values of c, C, d, D, by (26) 



C = 51° 57' 13"-0 D = 118°57' 10"-0 



log c = 0-494393 log d = 0-648965. 



Next a, b, CO, by (28), 

 (a'-b^') sin 2co = —9*180268 «- + *"= +25-11 129 

 (a^-b-) cos2co = -1-542633 log ab = 1-066737- 

 The latter logarithm is the same as above. The values of 

 the individual quantities are : 

 log a = 0-617892; log 6 = 0-448845; co = 130° 13'50"-3 



Lastly, we find from the two formula? (29) 

 X = +1-47494 and +1-47495, Y = -0*638603, and 

 = -0-638616 log 11 = 0-206086 ; P = 336° 35' 19"-5. ' 



[To be continued.] 



XVI. On 



