Terrestrial Refraction . 



551 



Substituting in (13) this value, and the value of a given 

 by (16), we have for \ = 5000 A.U. 



n = 1-0002839--00002646A + -000000696A 5 



(17) 



To compare the merits of (14) and (16), curves have been 

 drawn in fig. 2 representing (i.) the observed data in the 



Ficr. 2. 



•00115 



(1) Observed values of cr 



(2) Empirical curve for cr 



(3) Curve for K= -1796 ) Radius of 



[Curvature 

 (4) Curve for K= -1420 ) ofany r3y 



(5) Curve for K=- JO 20 



I Constant. 



•00015 



HEIGHT IN KM. = h. 



second column of Table I. ; (ii.) the empirical expression (16) ; 

 (iii.) three of the straight lines (14) corresponding to the 

 three selected values of g '1796, *1420, and '1020. These three 

 values are determined, respectively, by the observed values 

 of <t at heights of 1, 6, and 15 km. From the curves, it is 

 seen that the empirical formula (16) gives a much better 

 representation of the density, than any of the curves which 

 are based on the assumption of a constant radius of curvature 

 for a given ray. This we would naturally expect since (16) 

 has one more available constant than (14). 



3. -Refractions. 



Along a ray which traverses a continuous atmosphere, 

 which has a constant density over the surface of the sphere 

 r = constant, the relation nr siiKjb = k holds. At a definite 

 point on the ray, the slight deviation of the ray due to the 



2 Q 2 



