Count Paul de Saint-Robert on Atmospheric Refraction. 415 



of the strata, as I am about to prove. But I will previously 

 make an observation with respect to the aqueous vapour mixed 

 with the air. 



Laplace was the first to observe that, if a mixture of vapour 

 with dry air diminishes the refractive power by making the den- 

 sity less, the greater action of the vapour upon light is found 

 almost exactly to compensate the defect. This was confirmed 

 experimentally by Biot and Arago. The consequence of this is, 

 that, as far as the refractive power of the air is concerned, we 

 may substitute dry air for moist at the same temperature and 

 pressure. 



According to this principle Table IV. was calculated, in place 

 of Table III., for all that concerns the optical effects of air. 



Table IV. — Showing the Decrease of Density of the Air, con- 

 sidered as dry, at different Altitudes, and the comparison of 

 various Laws of Decrease. 



Height. 



Density of the air. 



Ob- 

 served. 



Uniform 

 decrease. 



DiflFerence. 



Bessel. 



Difference. 



Laplace. 



Difference. 



Ivory. 



10000 

 0-8714 

 0-7514 

 0-6434 

 0-5515 

 0-4681 

 0-3939 



Difference. 



0-0000 

 -0 0001 

 + 0098 

 +00172 

 +00281 

 +00339 

 +00359 



feet. 

 



5,000 

 10,000 

 15,000 

 20,000 

 25,000 

 30,000 



10000 

 0-8715 

 0-7416 

 6262 

 05234 

 0-4342 

 0-3580 



1-0000 

 0-8862 

 0-7724 

 0-6587 

 0-5449 

 0-4311 

 0-3173 



00000 

 + 00147 

 +0-0308 

 +00325 

 +00215 

 -00031 

 -0 0407 



1-0000 

 08367 

 0-7000 

 0-5857 

 0-4900 

 0-4100 

 0-3430 



00000 

 -00348 

 -00416 

 -0 0405 

 -0 0334 

 -00242 

 -00150 



1-0000 

 0-8649 

 0-7366 

 0-6188 

 0-5131 

 0-4205 

 0-3411 



00000 

 - 0-0066 

 -00050 

 -00074 

 -00103 

 -00137 

 -00169 



Sum of the squares \ 

 of the diffeiences J 



0043 





0065 







00007 





00036 



The rate of the decrease deduced from the observed densities 

 by the method of least squares comes out 

 a = 0-00002276, 



which should be used whenever the optical effects are concerned, 

 reserving the value 



a= 000002266, 



previously found, for the conditions of equilibrium depending 

 on weight. 



We shall now proceed to the determination of the curve de- 

 scribed by light in its passage through the atmosphere. 



Let r denote the radius-vector conducted from the earth's 

 centre to any point of the luminous trajectory ; v the angle 

 which this radius-vector makes with a vertical line passing 

 through the observer ; 6 the angle made by the tangent to the 



