Count Paul de Saint- Robert on Atmospheric Refraction. 421 



4k Po 

 or 



l+4kp 



=(?). 



l+4fy 



which expresses the relation between the density of the air and 

 the altitude involved in the hypothesis on which is grounded the 

 method used in computing terrestrial refraction. 

 We derive from it, putting, as before, 



1 + 4% 





7* 

 Substituting for — its value, 



-^ = 1-—, 

 r r 



and expanding, we shall find 



Po ~ a r o' 

 /^ 

 neglecting the higher powers of — , which is a very small quantity. 



r o 

 Assuming 



a = 0*00029 (at the temperature of melting ice, and m, 76 



pressure), 

 r =20,888,780 feet, 



we get £. =1 - (0-0000275)*. 



Instead of the coefficient 00000275 we had found 0*00002276. 

 The coefficient of terrestrial refraction corresponding to the latter 



value of a comes out 0*0689, or y-j— nearly*. 



* The following are the coefficients of refraction obtained experi- 

 mentally : — 



Bessel, from his operations in Prussia 0*0685 



Gauss, from his observations 0*0653 



Corabceuf 00642 



Struve 00618 



Mean derived from the survey in France 0*0665 



Mean derived from the survey in \ 00809 for rays crossing the sea. 



England | 00750 for rays not crossing the sea. 



(Ordnance Survey, London, 1858, pp. 512, 550.) 



