284 Mr. Ivory on the Theory of the Astronomical Refractions. 



lifrht after refraction to the velocity of the incident light; 

 ■which ratio, being independent of the direction of the incident 

 light, is constant for all light that falls upon the atmosphere 

 with the same velocity. 



What has been said of an atmosphere supposed homogene- 

 ous is next to be applied to the real atmosphere of the earth, 

 the density of which decreases continually in ascending. The 

 sphere M O N of which C is the centre, representing the 



earth, let S A B O be the trajectory described by light ema- 

 nating from the star S, in its passage through the atmosphere 

 to the earth's sui face at O ; through any two points of this 

 curve, A and B, draw spherical surfaces concentric to the 

 earth, the distances A C and D C from the common centre 

 being r + dr and r. Representing by p the density of the 

 air above the spherical surface at A, ]et § + d p stand for the 

 density, supposed uniform, of the stratum between the two 

 surfaces at A and B : and it is to be observed that, though 

 AD = rfr is an infinitesimal, it is nevertheless to be accounted 

 infinitely great when compared to the insensible distance at 

 which the molecular action of the air al A ceases to act : 

 from which it follows that the refractive power of the stratum 

 upon light which enters at A, is exactly equal to the refract- 

 ive power of a homogeneous atmosphere, supposing the den- 

 sity p + d p to extend unvaried to the earth's surface. Now 

 if denote the velocity with which the light moves in the 

 trajectory at A, the refractive power of the air above the stra- 

 tum will diminish y^ by the quantity 2 4: (p) ; for it is obvious 

 that the refractive power of the air above the spherical sur- 

 face at A, is equal and opposite to the refractive power of a 

 homogeneous atmosphere within the same surface and of the 



