DETERMINATION OF ASTRONOMICAJL REFRACTION. 79 



at stated times during the evening's work, the indications 

 showing that the observing room was generally between 

 three and five degrees higher in temperature than that 

 denoted by the external thermometer. 



5. Method of Determining the Refractions. 



Notation. 



3 = Apparent zenith distance. 



8' = Distance, in arc, from the equator, measured on a 



great circle at right angles thereto, positive towards 



the north. 

 <£ = Latitude 

 r = Refraction observed 

 r = Refraction calculated from tables. 

 The suffixes n and s refer to north and south. 



If we put 



«'n = </> + (S'n + r„) 1 



S's = <f> - &. + r.) 2 



and subtract equation (2) from (1) then 



8'n — s 's •— s'n + «'■ + r u + r s 

 Put X = 8 f n - 8' s 



Y = z\ + z\ 

 then X - Y = r n + r s 



2 r n - r a + r B = X - Y 

 or r n = i(X - Y) + \ (r' n - r\) 3 



In a similar manner 



r n = i(X - T) + i (r' s - r' n ) 4 



It will be noted from the above deductions, that if the 

 northern and southern zenith distances were the same, and 

 the meteorological data similar, then the refraction for 

 each would be the same, that is, we should have 



r„ — r s 

 in which case 2 r = X - Y 



