384 THE 8AYRE OBSERVATORY. 



Referring to the American Ephemeris, the reduction for aberration is 



Oc> + J)(V. 



Let us call this quantity k, and write for C, D, c', d' their values, 

 Then 



k = 20". 4451 [ — cos a cos Q (tau a cos (5 — sin a sin <V) — sin Q cos a sin 6], 



20".44r>l being Struve's value of the aberration constant;. 



Let v be the correction which this constant requires to satisfy the present series, Ak 

 the corresponding correction to k, 



Then 



20.4451 k . k 



an .... . =-5 — ; — 77 , IrOIll Which Mi = on aik< v. 



20.4451 -|- 1) k, -\- Ak' 20.4451 



e 



f our equation therefore equals 



k 

 20.4451' 



It will be convenient to modify this expression as follows: 



Ak: 



k _ 20 

 20' 20.4451 ' 



-. v = itt, v'. Where «' 



20 

 20.4451 



v' will be the unknown quantity of our equation. 



From a morning and evening observation on any pair, which observations will be 

 separated by an interval of several months, we have a pair of equations, 



</) -|- A -f a' x + ji' y + y> z + '!' U + <■;' »' + r> w --■ </>' 

 </)„ + A -\- a"x + li"y -I- y"z + 6"U -\- e"v' -| r"w = </<" 



By subtraction 



(a' — a") x + (ji' — ji") y -(- (7' — y") t + (<*' — >'>") U + (<■■' — '") v + (r» — r") w - </>' — ./>". 



For the purpose of illustrating the method of forming these equations the data for 

 one pair of stars will be given in full, viz. : 



o t 11 



h m 8 



B, A, 16 Mag 4.9 a 4 41! i 45 29 15 

 L L 220 7.5 11 4 85 58 25 



Difference of zenith distance approximately 10'. 



