MR. IVORY ON THE THEORY OP ASTRONOMICAL REFRACTIONS. 219 



+ {^'A. + i^^(A3-4A,) + ^^A,-6A3 + 15A.)-^^ + fc-}x^ 

 The next three terms are as follows : 



r 01215 175 



|-4a. + ZgA, + -j6(A3-2Ai)+^(A,-4A3 + 6A,) 

 + ^'(A;-6A5+15A3-20A,)+^' + ^%-«}-e 

 + { - 4 aj + j^ A3 + ^ (As - 2 A3 + A,) 



+ ^(A7-4A5 + 6A3-4A,) 



125 

 + l8 (^ -^ 6 ^7 + 15 A5 - 20 A3 + 15 Ai) 



125_ 125 _„■) 



48 16 ^ J -^ ^ 



+ { - 4 a, + ?i As + ^ ( A; - 2 As + A3) 



+ ^ (A9 -- 4 A7 + 6 As - 4 A3 + Ai) 



125 

 + -48 (^11 - 6 A9 + 15 A; - 20 As + 15 A3 - 6 Ai) 



125 J125 _^\ 

 + 48 + 48 ^ ]'^' 



On substituting the exact values of Aj, A3, &c., these three terms will come out as 

 follows : 



158 

 + -^ c-"» , e, or 4- -00239 . e 



3 



348 

 5 



c-"*.e3, or - -00316. e* 



+ ^c-«.e5, or + -00538 . e^. 



These three terms are the part of the refraction that depends on the height of the 

 atmosphere : at the horizon, or when e = 1, their amount is greatest and equal to 



/ X ^^^7=7^ X 00461 =/ X 726"-7 X -00461 =/ X 3"-3, 



which, on account of the smallness ofy, will be a minute fraction of a second. 

 Rejecting the six foregoing terms, we may assume 



Q3 = H7 e7 + H9 e9 + Hii ell + &c. : 

 2 f2 



