a Spherical Gaseous Nebula, 703 
the particular gas considered ; being its pressure at unit 
density. According to our units, as explained in §§ 10, 11, 
12, B is a linear quantity. The analytical expression of the 
hydrostatic equilibrium is 
dp = —gpdr (31), 
where [(16) repeated] 
m/r* 3 So drf9 P so*. 
Eliminating p from (34) by (33), and multiplying both 
members by r 2 , we find 
gfZloo-p 3 C r j 2 e 2 m . 
•^ o 
Differentiating this with reference to r, and then trans- 
forming from r to x as in equations (21) ... . (24) above, 
we find (32), with the following expression for a : — 
a 2 = '^B (37). 
o 
The equation of the first and third members of (36) gives 
§ 34. Let now /3 = F( t r) be any particular solution of (32); 
we find as a general solution with one disposable constant C, 
"= CF (vo) •■'■•• ( 39 )> 
which we may immediately verify by substitution in (32) 
(compare § 25 above). The particular solution F must 
belong to one or other of the two classes, class A and class B, 
defined in § 25 above. 
§ 35. AVe shall denote by ^(x) whatF(^) of § 34 becomes, 
when the particular solution of (32), denoted by F, is of 
class A, with units so adjusted as to make ^(00)=! ; that 
is to say, central density unity. Mr. Green in his Appendix 
