LIMIT OF THE ATMOSPHERE KERBER 



55 



which is deduced in a manner similar to that of Bunsen's law of 

 absorption. After substituting this value then the solution of the 

 differential equation offers no difficulty and the equation of the 

 curve of the pencil of light is easy to find. 



As to the constant exponent m, that is best found from one 

 accurate determination of the refraction. I will hereafter check 

 the value of m thus found against the diminution of temperature 

 with the altitude, since I hope to be put in possession of the neces- 

 sary observational material through the kindness of a physicist, 

 a relative, who expects to remain several years in the tropics. 



In accord with my previous efforts I also believe that I shall suc- 

 ceed in obtaining from the observation of the twilight colors material 

 for the direct demonstration of the diminution of the refracting 

 power and the determination of the constants. 



Let cm in fig. 7 be the earth's radius and ca the horizon of the 

 observer at c. At t' and /" hours after sunset the sun is at s' ami 



FIG. 7. 



s" \ the altitudes of the reflecting strata of air are a' c' = h' and 

 a" c" = h" \ the corresponding angles of incidence and reflection 

 are e' and e" . We easily find 



1 



,-fl-?- 



h' 



24 / v > 2 24 



(1 - sin e') R h" = (1 - sin e") R 



