Count Paul de Saint-Robert on Atmospheric Refraction. 419 



the apparent zenith-distance and the true one, or the terres- 

 trial refraction 8, will be easily found by the resolution of the 

 triangle made by the radii r , r and the rectilinear chord. This 

 triangle gives 



r Q sin (0 O + 8) = r sin (0 O + 8—v), 

 whence 



cot (6 n -\-8) = — i tan — 



N u ' r smv 2 



Biot came to the same formulae by a different way in his 

 Memoire sur la Mesure Theorique et Experimentale de la Refrac- 

 tion Terrestre (1838). The reader is referred to that paper, which 

 contains likewise the formulae for a law of density expressed by the 

 first and second power of the height. Biot's three memoirs, 

 Memoire sur la vraie Constitution de V Atmosphere Terrestre de- 

 duite de V experience (1838), Memoire sur les Refractions Astro - 

 nomiques (1836), Memoire sur la Refraction Terrestre (1838), 

 which will be found in the Connaissance des Temps t are the most 

 complete writings that have hitherto appeared on the subject. 

 But the observations employed therein, derived from Gay-Lussac's 

 celebrated balloon-ascent, are contradicted by the latest experi- 

 ments. In fact the latter eminent physicist was led to the con- 

 clusion that the temperature varied less, for a given change of 

 elevation, near the earth than in the higher region. After Mr. 

 Glaisher's experiments this opinion is no longer tenable. 



In respect to the determination of the constants a and a, I may 

 make the following remarks. As we must admit that the state 

 of the atmosphere, especially in the inferior strata, is continually 

 changing, the parameters a and a entering into the above formulae 

 are to be in each particular case determined by means of direct 

 meteorological observations made at the moment in which the 

 value of the refraction is wanted. The value of a w T ill be given 

 by the barometer and thermometer of the observatory. The 

 value of a will depend on these data, and will require besides 

 the knowledge of the density of the air at a point sufficiently 

 elevated in the atmosphere. 



Supposing thus known by help of direct meteorological obser- 

 vations the densities p , p of the air at two stations situated at 

 different heights, the value of a will be given by the formula 



which is derived from the barometrical formula found above. 



The densities p , p should be calculated by means of the total 

 pressures p , p, as if the air were dry, because, as we said before, 

 moist air refracts light, sensiblv, as dry air under the same pressure 



2E2 



