COMSTOCK — STUDIES IN ASTRONOMY 61 



distance, z, but for values of z less than 75° it may be rep- 

 resented by the empirical formula : 



A = 1 4- /i tan-z h -= 0.001362 



The following comparison shows the degree of accuracy 

 with which this formula represents the tabular numbers: 



If we represent by e the adopted coefficient of expansion 

 of air per degree C, by r^, the normal temperature of the 

 refraction tables, and by r any other temperature, we shall 

 have : ' 



A - - -^ 



r^ = [l + f(r- r^)] 



Developing this expression by means of the exponential 

 series it becomes, when the terms of the order £» are neg- 

 lected. 



A 

 r 



£-' 4- r„ ^ ^ 



= .; il- eh tan^z (r - rj )■ 

 £-'-t-r [ "'J 



For zenith distances less than 75° the exponent A does 

 not sensibly differ from unity, and we have 



Bo 



where ^o is the normal barometric pressure of the tables 

 and B is the actual pressure at any time, /. e. the reading 

 of the barometer " reduced to the freezing point. " 



Collecting the expressions for the several factors above 

 developed, we obtain: 



' Chauvenet, V"ol, II, p. 165. 



