62 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



From the Pulkowa Tables we find : 



B, 



751.5 mm. 



9.31 C. 



f-' =271.05 C. 



R = r 1.332071 „,, ^^/ tanz 



Denoting the quantity enclosed in brackets by F and in- 

 troducing numerical values, we obtain : 



B F 



—_ tan z 



(A) 



log F = - (46.2 + 0.22 r) tan^z 



In the use of these formulfB B and r must be expressed 

 m millimeters and degrees C The formula gives log F in 

 units of the fifth decimal place. The number enclosed in 

 brackets is a logarithm. 



The corresponding formulae, when the pressures are ex- 

 pressed in English inches and the temperatures in degrees 



F., are: 



B F 



—^ fan z 



(B) 



R = [2.992151 



455.9 -[- r 

 log F = - (42.3 + 0.12 r) ian-z 

 The computation by these formulse is not more laborious 

 than the direct computation from the tables, and the fol- 

 lowing comparison shows that the differences between the 

 formulas and the tables are far less than the uncertainty in 

 the tabular numbers themselves. For zenith distances not 

 much exceeding 75° the formulse may be considered for 

 most purposes a complete equivalent for the tables: 



COMPARISON OF THE REFRACTIONS FURNISHED BY THE 

 FORMUL.^ AND BY THE PULKOWA TABLES. 



