414 Count Paul de Saint-Robert on Atmospheric Refraction. 



of constitution of the inferior strata, and in no way upon that of 

 the remainder of the atmosphere. 



It might be objected to this explanation of Biot, that, in order 

 to reach the angle of 74°, it is necessary to ascend to a very great 

 elevation. For instance, the luminous trajectory which arrives 

 horizontally at the earth's surface must be retraced to the height 

 of 2- 5 th of the earth's radius in order to arrive at an angle of 

 incidence of 74°. Very likely the atmosphere does not extend 

 so far. But we must remark that, once arrived at a certain ele- 

 vation, the extreme tenuity of air renders the amount of refrac- 

 tion so small that it may be well supposed to depend only on the 

 density of the air at that place, though the angle of incidence 

 should not yet be reduced to the limit of 74°. 



To exemplify this, let us consider the luminous trajectory 

 arriving horizontally at the observer. By an easy calculation, 

 which I will explain hereafter, we find that at 30,000 feet, the 

 height actually reached by Mr. Glaisher, the angle of incidence 

 becomes reduced to 87° 8' 25", and that the angle at the earth's 

 centre comprised between the two radii vectores is 3° 18' 32". 

 It follows that the angle made by the tangent drawn to the 

 trajectory at 30,000 feet with the first tangent, that is to say, 

 the amount of refraction produced by the shell of air of the 

 depth of 30,000 feet, is 26' 57". 



Now, if we were to suppose the strata beyond 30,000 feet to 

 be plane and parallel, by the simple law of refraction, viz. of the 

 invariability of the ratio of the sines, we should find that the 

 light passing directly from vacuum into air of the density of 

 0*358, which it would be at 30,000 feet, would suffer a deflec- 

 tion of 7' 25". Adding this to the refraction due to the lower 

 shell of air, we should obtain 34' 22" for the total horizontal 

 refraction. 



Had we considered the whole atmosphere, we should have 

 found a refraction of 33' 37". The difference is only 45". 

 Going a little further, we should arrive at an altitude where the 

 consideration of the ulterior strata would be unnecessary. 



The consequence to be drawn from all this reasoning is, that, 

 for the determination of astronomical refraction, it is sufficient 

 to know the constitution of a shell of air of comparative thinness. 

 Mr. Glaisher's observations furnish us with that knowledge up 

 to 30,000 feet, which is quite sufficient for our purpose. As for 

 terrestrial refraction, we never have to observe terrestrial objects 

 beyond the strata explored by Mr. Glaisher. We are thus in 

 possession of sufficient data for calculating both refractions. 



When the law of equable decrease of density upwards from 

 the sea-level is admitted, the path followed by a ray of light is 

 an arc of an hyperbola whose interior focus occupies the centre 



