296 M. F. Zbllner on the Temperature and 



or, expressed in words : — 



The quantities of luminous gas particles which at the lower and 

 upper limits of the chromosphere lie on the line of sight of the ob- 

 server, have approximately the same ratio as the densities or pres- 

 sure-values in the strata in question of the chromosphere. Q. E. D. 



§4. 



The application of the hitherto developed formulae to the tem- 

 perature ratios on the surface of the sun presupposed in reality 

 only the knowledge of the ratio of the pressure or density in two 

 strata at different altitudes of the chromosphere, the distance 

 between which is known ; the pressure or the density itself at 

 those altitudes remained undetermined. It shall now be shown 

 how_, with the aid of the above formulae, this quantity also can 

 be approximately calculated. 



Formula (8) expressed the quantity m x of the incandescent 

 gas contained in a space whose length is formed by the extent 

 passed through at the lower limit of the chromosphere by the 

 line of sight, and whose cross section is the unit of surface. 



Putting herein 



cocP—y*, 



the expression for m l changes into the following s — 



y 



■■-m; 



e-y*dy (II) 



The integral which here enters cannot be presented in a definite 

 form ; on the contrary, it is known from a formula which ex- 

 presses the probability that a designated error of observation does 

 not exceed a certain amount. For constantly increasing values 



v- 



of y, the integral converges towards the value _ — , so that we 

 have 2 



i 



•y'dy^^l 



From the Tables which contain the numerical values of the 

 above integral for increasing values of y it is evident that the 

 convergence is rapid, so that e. g. for y=2 . 4 the value of the 

 integral differs by less than a thousandth part of its quantity 



from ^_ We shall therefore in the present case be justified 



in substituting this value as sufficiently approximate for the 

 above integral and obtaining 



