Physical Constitution of the Sun. 295 



If a x denotes the density of a volume-element of the chromo- 

 sphere which on the visual line g x g v is at the distance x from 

 the maximum of density a lt the quantity ra, of gas contained in 

 a space of the length 2x and the unit of surface as cross section 

 is expressed by 





m i = 2\ * x dx (4) 



With an unlimited atmosphere this integral, taken strictly, 

 would have to be extended to the entire visual line — that is, as 

 far as to the eye of the observer ; but in the present case, consider- 

 ing partly what has been remarked, and partly the inexactness 

 of the empiric data, we have a right to extend the integral only 

 to such a length of the line x as makes it permissible, in view of 

 the approximative character of the entire determination of value, 

 to neglect the altitude h x in comparison with r. 



On this hypothesis we have 



a x =a L e aai, (5) 



x* 

 or, putting for h x the value ~-, which results from the equation 



(r-f^)* = r 2 + ^ 

 by neglecting h 2 v , 



in- 



putting herein 



a x = a l e &<*?** (6) 



*h= c > ■ ■ • • w 



and substituting in expression (4) the value then resulting for 

 cr„, it becomes 



*/ 



m x = 2aA e~ c * 2 dx. .... . (8) 



n) 



Without previously entering more closely into the determina- 

 tion of the value of this integral, it is readily seen that, with the 

 smallness of the distance between the two lines g x g x and g^g^ 

 the following expression results for the number of gas particles 

 situated on the upper line g 2 g 2 : — 



m 



By division we get 





2a A e' cx dx ■ (9) 



2~* u 2 





9 "2 



