267 
1907-8.] The Problem of a Spherical Gaseous Nebula. 
if in purely convective equilibrium, and undisturbed by radiations and other 
complications, the temperature would increase at the rate of 280 degrees 
Centigrade per kilometre downwards, and, looking forward to § 27 below, 
we see that the increase of temperature would start from absolute zero at 
the boundary, where density, pressure, and temperature, are all zero. It 
would require very robust faith in the suggestion of convective equilibrium 
for the gaseous atmosphere of the sun to believe in +7° C., being the actual 
temperature of the sun’s atmosphere at one kilometre below the boundary. 
I am afraid I cannot quite profess that faith. It seems to me that the 
enormous radiation from below would, if the upward and downward 
currents were moderately tranquil, overheat the air in the uppermost 
kilometre of the sun’s atmosphere to far above the temperatures ranging 
from —273° Centigrade to +7° Centigrade, calculated as above from the 
adiabatic convective theory. 
§ 19. Keeping, however, for the present by way of example to the 
calculated results of this theory, with the data for S and k chosen in § 15, 
we find that at ten and at fifty kilometres below the boundary, the 
temperatures, reckoned in Centigrade degrees above absolute zero, would be 
respectively 2800 and 14000. Calling these temperatures t' and t, and the 
densities at the same places p and p, we find by (14) 
p _ /14000YJ 
p V 2800/ 
55*9 
(15). 
Suppose for example p to be '001 (1/1000 of the density of water), we 
should have p == *056. This last is nearly but not quite too great a density 
for approximate fulfilment of the gaseous laws for the same gaseous mixture 
as our air. Thus, if not too much disturbed by radiation of heat from 
below, the uppermost fifty kilometres of the sun’s atmosphere might be 
quite approximately in gaseous convective equilibrium ; with density and 
temperature augmenting from zero at the boundary, to density '056, and 
temperature 14000 Centigrade degrees above absolute zero, at the fifty 
kilometres depth. But, going down fifty kilometres deeper, we find that 
the temperature at one hundred kilometres depth would be 28000°, and the 
density would be ’316. This density is much too great to allow even an 
approximate fulfilment of the gaseous laws, by any substance known to 
us, even if its temperature were as high as 28000°. This single example 
is almost enough to demonstrate that the approximately gaseous outer shell 
of the sun cannot be as much as 100 kilometres thick, — a conclusion which 
may possibly be tested, demonstrated or contradicted, by sufficiently 
searching spectroscopic analysis. The character of ; the test would be to 
