Terrestrial Refraction, 



557 



P and Q respectively. If there were no refraction, we 

 should have 



'R + 7* 



Fia-. 3. 



But owing to refraction, we must add the Lending of the 

 tangent along the ray PQ. This is found by taking first 

 differences of the refractions in Table II. Writing the 

 first differences in the form A 2( £?, we have, very nearly, 



<f>i = sin 1 ( tt^— r sin </>;-i) + A 2 ^> 



7i = <fc_i — sin ~ 1 U|, | sinifc.A 

 For the length U we have, approximately, 



Zi s = 4(R + ;, i _ 1 )(R + ''.)sin 2 ('|') +-1. 



(30) 

 (31) 



or 



SSUl 



R/wi, we have 



(32) 



If we assume that PQ is an arc of a circle of radius 



iA'-'4>, 



(33) 



