82 " 



perature. The mean also serves as a criterion of the accu- 

 racy of the French and of other tables at this zenith distance. 



Investigation of the Jluxional equation for refraction. 



Let V RP T be the path of a ray of light refracted at 

 P and R, and let CO be perpendicular to TP produced. 



(Fig.) 



Let the apparent zenith distance HVR =6* 



C V the radius of the earth = a 



CR = r' 

 CP = r 

 The density of the air at P = § 

 The density at the surface V =(f) 

 The height of an uniform atmosphere at F = I 

 Let m : 1 represent the ratio of the sine of incidence to 

 the sine of refraction, when light passes from a vacuum into 

 air of the same density as that in VR. 



k' : 1 the same ratio for air of the density of that in PR, 

 and k : 1 the same ratio for air of the density of that in TP 

 Then it readily appears that 

 sin. VRC : sin. CRP:: k' :m 

 sm. C PR : sm. CPT ::k:k' 



• The same quantities are denoted by the same' letters which Laplace has used (chap. 

 I. liv. 10. torn. 4. M6c, c^l.) 



