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



which, on account of the smallness ofy, will he a minute 

 fraction of a second. 



Rejecting the six foregoing terms, we may assume 



Qe = H^e^ + HggS + Hii e" + &c.: 

 and, having computed the differences in the following table, 





A2 



A4 



A6 



A. 

 A3 

 A, 

 Av 



A. 



Ah 



Al3 

 A,3 



A., 



Al9 



A., 



+ •0873930 

 + •0748672 

 + •0446024 

 + •0209241 

 + •0081714 

 + •0027438 

 + •0008096 

 + •0002133 

 + •0000509 



- ^0595755 

 -•0177390 

 + •0065865 

 + •0109256 

 + •0073251 

 + •0034934 

 + •0013379 

 + •0004339 

 + •0001224 



+ •0278859 

 -•0175110 

 -•0199864 

 — CO79396 

 — •0002312 

 + •0016762 

 + •0012515 

 + •0005925 

 + •0001891 



we shall have 



H7 = -4a7+|^A7+?^A2A,+ I^A4A3+^A6Ai =-04861 



Ql 21^1 \1^ 12^1 



Ha = -4a9+|gAyf ^A^Ay +-^ A^ A5+-| A" A, =-07091 



Hn = -4an+YjAu+^ A^ A9+^^ A4 A7+^| A6 A5 =-04469 

 Hi3= -4ai3+j4Ai3+^^^Ai,+^A*A,+ -^A«A7 =-00249 



Hi5= -4 ai,+^g A,3 +^A» A ,3+1^ A4 Ai,+ ^^ A' A, = —02230 



Ql 2n l?"! 12^; 

 Hi7=-4an+^A,-+^A«Aj5+^A4A,3+'^| A6A„= -02558 



Ql ' 21^^ l?'* \1^ 

 Hi,= -4a,n+^ Ai:,+ ^A"- k,T\- -^ A*A,,+ ^^A" A13 = —01835 



Ho,= -4a2.+^A„i+"^A3A,9+^A<Ai7+^A''Ai5 = —01023 



91 2K 175 12'^ 

 H23= -4a.3+Y6 A23+^A2A„+-j^A4A„+^A6Ai7 =--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: 



