WHICH REFLECT LIGHT. 323 



In the passage from a vacuum into atmospheric air ?i= 1*000294 

 In the passage from a vacuum into oxygen . . w= 1*000272 

 In the passage from a vacuum into nitrogen . . w= 1*000300 

 and from the two last it follows that 

 In the passage from oxygen to nitrogen . . . 71=1*000028 



k 

 In the following table are set down the values of -r obtained 



from equation (18) for the first and last of these quantities, 

 or rather, for the sake of simplicity, for n — 1*0003 and 

 w= 1*00003; and to be certain that we embrace all refractive 

 indices conceivable in the case, the same calculation is extended 

 to a series of much smaller indices : — 



n I 1-0003 I 1-00003 I 1-00001 I I'OOOOOl { 1-0000001 I 1-00000001 

 -^ I 0-0034 I 0-00046 | 0-00017 | 0-000021 | 0-0000025 [ 0-00000029 



The value of the coefficient of reflexion h is found as men- 

 tioned above, independent of the index of refraction n^ from 

 the experiments of Bouguer and Lambert. According to the 

 signification of this coefficient, taking no account of the disper- 

 sion of the light in the atmosphere, regarding its weakening by 

 reflexion alone, and denoting the intensity with which a star 

 appears after it has passed over the path s in the atmosphere by 



v^ we have 



dv= —hvdsy 



and hence 



Now as a star in the zenith sends only 0*75 of its original light 

 to the earth's surface, if we take the perpendicular path through 

 the atmosphere as the unit of the path s, we obtain 



0*75 =e-*, 

 from which it follows that 



^=0*28768 (19) 



It might be objected here, with reference to the use made of 

 the number 0*75, that it is not proved that the entire loss, 0*25, 

 is due to reflexion ; a portion of it may perhaps be due to an 

 unknown absorption. At all events, the reflexion must however 

 have much to do with it, inasmuch as the firmament sends us 



