220 MR. IVORY ON THE THEORY OF ASTRONOMICAL REFRACTIONS, 



and, having computed the differences in the following table, 



we shall have 



H, =-4a, + §iA; + ^*A2A5 + ^A4A3 + ^'A«A, = -04861 



01 01 'S 1 T*! 10.^ 



H, =-4a, + 2j5A3 + ^'A2A, + i^^A<A5+^A«A3 = -07091 



H„=-4a„+fiA„+^*A2A, + ^'A*A; + ^A«A, = -04469 



01 oi'i 175 125 



H,3 = - 4 a,3 + ^ A,3 + ^ A2 An + -j^ A4 As + ^ A6 A; = -00249 

 H,5 = - 4 a„ + ?^ A„ + ^ A^ A,3 + ^* A* A„ + ^'a« A,= - -02230 



01 215 175 125 



Hi; = - 4 ai; + f^ Ai7 + -Tfi A2 Ai5 + 4 A4 Ai3 + lo- A6 A^ = - -02558 



01 215 175 125 



H,9=-4a„ + fgAi<, + ^A2A„ + ^A«A,5 + ^'A6A,3=--01835 



01 215 175 125 



Hji = - 4 a^i + ffi A^i + -^ A2 A,., + 4 A4 Ai; + -^ A" A,5 = - -01023 



01 215 175 125 



H23 = - 4 a23 + 16 A,3 + -jg A2 A21 -4- ^ A4 Ai9 + -^ A6 A,; = - -00487. 



The coefficients of the assumed series being found, and being expressed in seconds of 

 a degree, the part of the refractions depending on Q3 will be as follows : 



f X sin ^ X -^7=7^ X Q3 =/' X sin ^ X |e7 X 35-324, 1-54807 



-f e9 X 51-529, 1.71205 



+ eii X 32-476, 1-51156 



-f e»3 X 1-809, 0-25755 



— e^5 X 16-205, 1-20965 



— e^7 X 18-588, 1*26925 



