295 
1907-8.] The Problem of a Spherical Gaseous Nebula. 
§ 12. In the particular case of equation (1) for which k = oo (1c = 1), and 
which corresponds to an ideal gas which obeys Boyle’s Law for all pressures, 
the differential equation becomes 
d 2 log p _ p 
dx 2 £C 4 
• (16). 
Assume as the solution of this equation which gives p = 1, when x—cc, 
1 
T'G) 4 
l+fh + ^+fl + etc. xw 
ry*A /y»4: ry* O 
tAj tAs *Aj 
• (17). 
oft log "SPhc) 
We may, in this case also, write 1—9 ~ in the two forms 
J ’ 5 dbx A 
/2.3.a 1 4. 5.a 9 
n[ — t — 1 a. — I - etc. 
V £C 4 x° 
2.3.a pn 
„ a-, Oo a, 
1 + J + J + J + etc - 
- 2 + etc. ) 4- n( 4- 
4a 0 
etc. 
4. 5. Or, 
4- 
f+-2 
a 9 
+ -f 
a, 
+ — [• 
4- etc.^ 
2 
X L 
£C 4 
X b 
6. 7. a. 
a i 
a 9 , \ 
a 8 
- + etc.Jj^ 
1 + 52‘ 
f a? + et °7 
( 
'l + 
a l a 2 
/^2 yA 
Or. \ 2 
+ J + etc.) 
/2aj 4tt2 
\ a 3 + ^ 
\ 2 
By taking n — 2 in the first of these forms, and n — 1 in the second, and 
proceeding exactly as in § 11, we obtain two expressions for Tf x ) in the 
form (17), the coefficients cq, a 2 , a 3 , etc. being again determined from the 
series of equations (14), when n = 2, and from equations (15), when n = 1. 
§ 13. At present only the numerical values given by the above solutions 
2 
are of importance; and for this purpose, the expression (13) with n = - — ^ 
has been used to calculate the Homer Lane Functions, and the expression 
(17) with n = 2 to calculate the Boylean Function. The following table 
gives the logarithms of several of the coefficients cq, a 2 , etc. for the func- 
tions given in Tables I. . . . V. ; the letter n indicating that the term is 
negative : — 
