28 Ty-ans. Acad. Sci. of St. Louis. 



dl T n 



o 



a 



dr vR 



d*T T n da 



o 



dr 2 vR dr 



(48) 



(49) 



The relation between density and temperature can be 

 deduced from the celebrated equation of Poisson, 



P I 27 



3.44 



(50) 



which may be put in the form 



~ = (l) 



Substituting in (43) for a, y7and a their values given by 



equations (51), (49), and (48), we have 

 vi? d 2 T 2»R dT 



+ ^^ + A/Zf = o. (52) 

 ^ T n r dr ^ R<F\ TJ K } 



T dr* 



r T 



Putting -p = ? and yp = y, this equation may be written 



xi Z 



d 2 w 2 dri 3<7. / c o \ 

 L _) 1 _| L „244 _ o (53) 



dP ^ ^ d^ vd V ~ 



which is the form given by Ritter. We may determine 

 the three constants of this differential equation, as well as 

 the two constants of integration as follows. By the equation 



4 

 M — t, TTtrR 3 , the constant # is to be taken as known, when 

 o 



R and M are given, as we here assume; and the value r = R, 



£ = 1, corresponds to a = 1, and by equation (48 ) 



dT T Q d v 1 



— 7- - = — — 75-» or— p. = — — • 



dr vR dc v 



Thus the constant v is equivalent to the negative reciprocal 



dr) 

 value of -rg for 6=1. Moreover, T = 0, and ?; = 0, for 



