Count Paul de Saint-Robert on Atmospheric Refraction. 413 



ray, whatever might be the constitution of the interposed strata. 

 By the simple law of the constancy of the ratio of the sines of 

 incidence and refraction, the amount of astronomical refraction 

 would be immediately known when the density of the air at the 

 place of observation was given by the indications of the barometer 

 and thermometer. The determination of terrestrial refraction 

 would require besides the knowledge of the state of the air at 

 the object. 



Owing to the greatness of the earth's radius, its surface is 

 sensibly a plane to a certain extent round the observer, and the 

 layers of air are likewise sensibly plane and parallel to a certain 

 extent round a vertical line passing through the observer ; this 

 is the reason why the astronomical refraction, down to about 74° 

 zenith-distance, is hardly affected in a perceptible degree by the 

 peculiar constitution of the atmosphere. 



Near the horizon the same ray of light encounters the several 

 concentric strata of air in parts which are far from being paral- 

 lel ; hence we cannot determine the deflections caused by them 

 without knowing the arrangement of their density. But hap- 

 pily refraction depends almost entirely upon the lower portion 

 of the atmosphere (which is accessible to exploration), and is not 

 sensibly affected by the higher regions. 



Ivory, in a memoir on refraction published in the Philoso- 

 phical Transactions of the Royal Society of London for 1823, 

 first pointed out, as a consequence of his calculations, the sin- 

 gular fact that " the refractions undergo hardly any change in 

 all the atmospheres comprehended in the formula " which he 

 assumed for representing the decrease of density; "although 

 their height increases from about twenty-five miles to be in- 

 finitely great"*. 



The physical cause of this fact was afterwards shown by Biot, 

 in a paper on astronomical refraction published in the Connais- 

 sance des Temps for 1839, to be the following. 



Let us consider any luminous trajectory whatever, arriving 

 at the observer at a given zenith-distance; and let us retrace it 

 in our mind, ascending with it into the different strata of air. 

 As we recede from the earth's surface, the angle between the 

 curve and the radius-vector, directed to the centre of the earth, 

 will progressively decrease. It is obvious that in continuing to 

 ascend we must come to an altitude where this angle will not be 

 greater than 74°, or whatever other zenith-distance beyond which 

 refraction is no longer influenced by the superincumbent atmo- 

 sphere, and depends only upon the density at such altitude. 

 Whence we see that refraction will depend only upon the mode 



* Philosophical Transactions of the Royal Society of London for 1823, 

 part 2, p. 451. 



