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 + h tan*z h = 0.001362 



The following comparison shows the degree of accuracy 

 with which this formula represents the tabular numbers : 



z 50 60 70 75 



Tabular A 1.0022 1.0044 1.0103 1.0188 



Formula 1.0019 1.0040 1.0103 1.0190 



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 : ' 



, r I"* 



r * = [l + (r - r ) J 



Developing this expression by means of the exponential 

 series it becomes, when the terms of the order s* are neg- 

 lected, 



-j- E (r r \ h tan*z 



1 E h tan 2 z (T r ( 



For zenith distances less than 75 the exponent A does 

 not sensibly differ from unity, and we have 



where B is the normal barometric pressure of the tables 

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

 of the barometer "reduced to the freezing point." 



Collecting the expressions for the several factors above 

 developed, we obtain: 



r 



R = #! -g- _ 1 ]jr ro tan z \ 1 f^ + h (r rj\tan*z 

 i Chauvenet, Vol. II, p. 165. 



