1907-8.] The Problem of a Spherical Gaseous Nebula. 
275 
< T 
r 
OO 
P 
1 
e 2 
EB < r m 
0 
P 
1-21 
1 
e 2 
EBo- m 
o 
•275 
' -2491 
6-697 
•2511 
7-19 
•250 
•2076 
7-905 
•2069 
8-39 
•225 
•1673 
9-38 
•1647 
9-86 j 
•200 
•1295 
11-20 
•1260 
11-64 
•195 
•] 223 
11-61 
•1189 
12-03 
•190 
•1153 
12-04 
■1118 
12-46 
•185 
•1084 
1250 
•1048 
12-89 
•180 
•1017 
12-97 
•0982 
13-35 
•175 
•0952 
13-47 
•0918 
13-83 
•170 
•0889 
13-99 
•0855 
14-34 
•165 
•0828 
14-53 
•0795 
14-86 
•160 
•0769 
15-10 
•0738 
15-40 
•155 
•0712 
15-71 
•0681 
16-10 
•150 
•0657 
16-34 
•0628 
16-59 
•145 
•0605 
17*01 
•0577 
17-22 
•140 
•0554 
17-71 
•0529 
18-04 
•135 
•0506 
18*45 
•0483 
18-61 
•130 
•0461 
19-23 
•0439 
19-35 
•125 
•0418 
20-06 
•0398 
20-14 
•120 
•0377 
20-95 
•0359 
20*98 
•115 
•0339 
21-89 
•0322 
21-88 
•no 
•0303 
22-88 
•0288 
22-82 
•105 
•0269 
23-95 
•0257 
2383 
•100 
•0238 
25*10 
•0227 
24-94 
§ 38. From this table we see that it is possible to have the same mass of 
an ideal Boylean gas (e 2 m/KBor = 219) distributed in two different equi- 
librium conditions within a given sphere (o-/r = ’ 115). We see also that in 
all smaller spheres the mass has increased, and in greater spheres it has 
decreased through the alteration of density at the centre from 1 to 121 . 
Indeed, when we trace the changes in the condition of any stated mass of a 
Boylean gas as its central density ideally increases from very small to very 
great values, we find that its radius diminishes till a certain central density 
has been reached, after which it increases till it becomes infinite. 
§ 39. By taking any two values of C in equation (26) above, and 
comparing the two solutions thus obtained as in § 37, it may be verified 
that results similar to those found in the case of a finite mass of an ideal 
Boylean gas, are found also in the case of a finite mass of any gas for 
which /c>3, or Tc< 1J ; while for any finite mass of a gas for which /c<3, an 
increase in the density at the centre is always accompanied by a decrease 
in the radius of the shell enclosing the mass in equilibrium. These 
differences in the behaviour of the Boylean gas from that of gases for 
which k< 3, and the resemblances of the Boylean gas and of gases for 
which k> 3 (of which it may be regarded as the limiting case, k = oo), 
