28 Trans. Acad. Sci. of St. Louis. 



dr vR 



d^T T. da 



(48) 







dr^ vR dr 



(49) 



The relation between density and temperature can be 

 deduced from the celebrated equation of Poisson, 



which may be put in the form 



T\2.44 



(51) 





Substituting in (43) for a, T~and a their values given by 



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



vR d'T . 2uR dT . 3<7„ / TV-^ 



r ^ "^ 



> = c and 7j 









Putting ~p = c and yr = ^, this equation may be written 



^^^ 4.^^+^^ ^244^0 (53) 



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 

 3/ = ^ TT^ri?^, the constant a is to be taken as known, when 

 6 



R and 31 are given, as we here assume; and the value r = R, 



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



dT _ T, ^ _ l_ 



dr vR' ^^ d^ v' 



Thus the constant v is equivalent to the negative reciprocal 



dri 

 value of -T^ for ^ = 1. Moreover, T = 0, and 77 = 0, for 



