Sixty-five Stars near 61 Cygni. 59 



a' = 20. "06 sin a see S . -. 7' = cos a tan ^ 



/3' = cos a sec rf <?' = sin a tan (5 



Ap = ( T— t) a' — Aa' — Bp> — Cy> — Dd>. 



■ The epoch T= 1873.0 has been selected to which to reduce all 

 the observations. The substitution of the coordinates of 61 1 Cygni 

 for this epoch gives : 



4fci = — 36"+ [1.254] A + [9-956n] 5+ [9-746n] 0+ [9.742] D. 

 Ap n = —i8 + [1.254] A + [9-956n] 5+ [ 9 .746n] C+ [9.742] Z>. 

 A i>73= o + [1.254] J + [9-956n] B+ [9-746n] C+ [9.742] I). 

 4^= +18 + [r.254] 4 + [9-956 Q ] B+ [9.746J C+ [9.742] D. 



Where dp 71 denotes the correction to be applied to the posi- 

 tion-angle for the plates made in 1871, and so on in the other years 

 as denoted by the subscripts. 



5. Precession and nutation have no effect upon the distances ; 

 but aberration does have, and its amount is given by : 



y /f = (tan e sin 6 -f- sin a cos 6) sin 1" 

 d"= — cos a cos<5 sin 1" 

 As =(Oy"+DS")s 



For 61 x Cygni this becomes 



As =j [4.141JC + [4-433n] -D|s for all years, 



and is additive to the distances to reduce them to 1873.0. This 

 factor of s is given in column three of Table III. 



6. The logarithms of the Besselian day-numbers, taken from 

 the American Ephemeris, are : 



Plates. log A. log B. log C. log D. 



1, 9-692 0.035,! 1. 104 1. 178 



2, 3, 9-699 o.o22 Q 1-077 1. 198 



4, 9-774 0.583,! 0.840 1.279 



5, 6, 9.816 0.580,! 0.244 1.309 



7, 9.821 0.582,1 0.038 i-3- 10 



8, 9, 9.788 0.807,! 1.043 I - 2lS 



10, 9.80O 0.802 n O.985 1.244 



11, 12, 13, 9.805 O.Soin O.958 1.253 



15, 9-336 0.857 n 0.776 a I.287n 



16, 17, 9.4II 0.854a O.41811 L306u 



18, 19, 20. 9.417 0.854,1 0.364,1 I-3°7n 



7. In the second portion of Table III. is given the mean of the 



