Mr. Ivory on the Theory of the Astronomical Refractions. 91 



305 905 _^\ 1 

 " 48 + 48 "" \^'^' 

 The next three terms are as follows : 



|-4a, + |^A, + ^(A3-2A0 + ^(A,-4A3 + 6A,) 



H,^(A,-6A..15A3-.OA0.-^^^^-^}.. 

 + {-4a3+^A3+^(A,-2A3 + A,) 



+ ^(A7-^A5+6A3-4AJ 



125 

 + i:s (Ag~6A7 + 15A5-20A3 + 15A0 



48 

 125 

 48 16 



125 125 -) „ 

 T^r- c-^ W . e^ 



r 91 * 215, . ^ . . , 



+ |- 4a5+ — A5+ — (A7-2 A5 + A3) 



+ 1^ (Ag-^A^ + SAg-iAg + Ai) 



125 



+ -4^(An-6A9 + 15A7-20A5 



+ I5A3-6AJ 

 125 125 , , 



+ "48 + — ^'"^-'- 



125 -1 



48 J 



On substituting the exact values of Aj, A3, &c., these three 

 terms will come out as follows : 



+ — - C-™ .e, or + '00239 . e 

 3 



348 



— c-^ . ^, or — '00316'. e^ 



5 



+ ^^ c-"* . ^^ or + -00538 . ^. 

 75 



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 



y/^l^t^x -00461 =/'x726"-7x -00461 =/'x3'''3, 



