Theory of Stellar Scintillation. 137 



value of 8/3 is given at once by the condition that Sy B = 0. 

 Thus 



^ 8vA= ^C y B^= 8 ^^, . . . (16) 



/A COS 2 Jo cos 



as before. The discussion, already given of (15), is thus 

 immediately applicable. 



Equation (16) solves the problem of determining the in- 

 clination of the bands seen in the spectra of stars not very 

 low (III.). It is only necessary to equate — Brj A to the 

 aperture of the telescope. 8/x, then gives the range of re- 

 frangibility covered by the bands as inclined. In practice h 

 would not be known beforehand ; but from the observed 

 inclination of the bands it would be possible to determine it. 



In a given state of the atmosphere h, so far as it is definite, 

 must be constant and then BfjL must be proportional to 

 cos 2 0/sin 0. This gives the relation between the altitude of 

 the star and the inclination of the bands. 



When is small, 8/x is large ; that is, the bands become 

 longitudinal. 



As a numerical example, let us suppose that the aperture 

 of the telescope is 10 centim., and that at an altitude of 10° the 

 obliquity of the bands is such that the vertical diameter of the 

 object-glass corresponds to the entire range from B to H. In 

 this case (15) gives 



indicating that the obstacles to which the bands are due are 

 situated at such a level that about ^ of the whole mass of 

 the atmosphere is below them. 



The next question to which (9) may be applied is to find 

 the angle 8a outside the atmosphere between two rays of 

 different colours which pass through the two points A and B. 

 Here 8n A =0, and thus 8/3=0. And further, since 8y B = } 

 we get 



. sin0 (K 8//, o Atan0 \ 



— ° u= i-fll s A"*y=— • • • • (17) 



s cos 2 Jo y K ' 



If the height of the obstacle above the ground be so small 

 that the density of the air below it is sensibly uniform, then 

 7i=y, and 



- 8a = fy4o tan (IS) 



In this case the angle is the same as that of the spectrum of 



