Physical Constitution of the Sun, 317 



a simplification and alteration of the above formula rendering 

 them more suitable for the question under consideration. 



If H represent the height to which a body possessing the 

 initial velocity v can be thrown up vertically from the sun's sur- 

 face, we have 



2 O XT r V<2 rH 



v z = 2qil — -yy, or — = , TT * 



This value, substituted for =~ in equation (1), gives 



rHA 

 fi ~ K c{r+U) + ta ' J 



rHA 



or when — -. rx =« and, according to our hypothesis, t a =t, we 



KCVr ~j" ■£*■) 



have for equation (1), 



ti=a + t (I.) 



If, further, we place' 



k—1 __ 1 p _, g __ 

 the equations (2), (3), and (4) will read as follows : 



(no 



<r=b^, (III.) 



Pa=pJ'™ (IV.) 



By elimination the following equation is obtained : 



=s-,m>™- ■ • • •>•> 



This equation therefore expresses the density a of the com- 

 pressed gas as a function of the three values p h , h, and t. If, 

 therefore, three of these four magnitudes can be ascertained by 

 observation, or if certain limits can be assigned to their values, 

 the fourth can be determined. In fact it is possible, partly by 

 spectroscopic and partly by other means of observation, to deter- 

 mine certain limiting values for a, p h) and h ; so that a limit 

 can also be obtained for the value of t — that is, for the tempera- 

 ture of the outer atmosphere of hydrogen in the neighbourhood 

 of the glowing liquid layer of separation. This value, substituted 

 in equation (I.), then gives, when H is known, a value for the in- 

 ternal temperature /,- ; and in the same way the values of p { and 

 /? a canbe obtained from equations (III.) and (IV.). 



U 7M« 



a 



