286 
Proceedings of the Koyal Society of Edinburgh. [Sess. 
The radius of the outer boundary of the nebula is given by 
where 
R = 
- - 1 ) 
xC = q . 
• (73), 
( 74 ). 
We have therefore R = a-q X C x) , which, by means of equations (53) and 
(55), may be written in the form 
5 = 2-6527 
®'«(ff) 
-i/M 
E 
(75). 
For argon we have k — If, or /c = l'5; and S = 5 , 76 l 7 kilometres; and for 
nitrogen we have k — 1*4, or k = 2 5; and 8 = 8*256 kilometres. With these 
values of S and k, inserted in the above formulas, we obtain the results 
shown in the following table : — 
Matter 
in nebula. 
Total mass, 
that of 
Central 
density. 
Central tempera- 
ture in Centigrade 
degrees above 
absolute zero. 
Central pressure 
in metric tons 
per sq. kilometre. 
Radius of 
boundary in 
kilometres. 
Adiabatic Con- 
stant in kilo- 
metres. 
Argon 
Sun 
•1 
1-105 XlO 8 
2-33 x 10 14 
3-04 xlO 6 
1-08 xlO 7 
99 
Earth 
•1 
2-342 x 10 4 
4-95 x 10 10 
4-42 x 10 4 
2*30 x 10 4 
99 
Moon 
•1 
1-243 xlO 3 
2-63 xlO 9 
1-02 xlO 4 
1-22 xlO 2 
Nitrogen 
Sun 
•1 
6-383 xlO 7 
1-92 xlO 14 
4-79 x 1C 6 
4-82 x 10 6 
99 
Earth 
•1 
1-353 x 10 4 
4-07 x 10 10 
6-97 x 10 4 
1*02 x 10 3 
99 
Moon 
•1 
7-185 xlO 2 
2-16 xlO 9 
1-61 xlO 4 
54-3 
§ 58. The curves of figures 3 and 4 represent temperature and density 
at different distances from the centres of nebulas for which k has the 
values, 1*5, 2*5, 3, 4. The temperature curves are drawn from the numbers 
given in the third columns of Tables I IY. of the Appendix : the density 
curves, from the numbers given in the fourth columns. With properly 
chosen scales of ordinates and abscissas, the curves shown may represent 
the condition of any gaseous mass, corresponding to any of the solutions 
(26) above. Thus, with scales so chosen that 0R K = R = c 7 g _1 C _ ^ K ~ 1) , and 
OT = C, each curve, TR K , represents the temperature reckoned from 
absolute zero; and with OD K = (SC/A) K , each curve, D^R*, represents the 
density ; in a nebula composed of gas for which k has one of the values 
given above, when the central temperature is C. 
Each curve shown meets the axis of R at a finite angle ; this angle being 
so small for the density curves that they appear to meet OR tangentially. 
