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Proceedings of the Royal Society of Edinburgh. [Sess. 
find the thickness of the outermost layer from which the bright spectrum 
lines proceed. If it were T" as seen from the earth, it would be 73 
kilometres thick. 
§ 20. Considering the great force of gravity at the suns surface (about 
28 times terrestrial gravity), it is scarcely possible to conceive that any 
fluid, composed of the chemical elements known to us, could be gaseous in 
the sun’s atmosphere at depths exceeding one hundred kilometres. I am 
forced to conclude that the uppermost luminous bright-line-emitting layer 
of our own sun’s atmosphere, and of the atmosphere of any other sun of 
equal mass, and of not greater radius, cannot probably be as much as one 
hundred kilometres thick. 
§ 21. There must have been a time, now very old, in the history of the 
sun, when the gravity at his boundary was much less than 28, and the thick- 
ness of his bright-line-emitting outermost layer very much greater than one 
hundred kilometres. Going far enough back through a sufficient number 
of million years, in all probability we find a time when the sun was wholly 
a gaseous spherical nebula from boundary to centre, and a splendid 
realisation of Homer Lane’s problem. The mathematical solution of Homer 
Lane’s problem will, for a spherical gaseous nebula of given mass, tell 
exactly what, under the condition of convective equilibrium, the density 
and temperature were at any point within the whole gaseous mass, when 
the central density was of any stated amount less than T ; on the assump- 
tion that we know the specific volume, (S), and the ratio of specific heats, 
(7c), for the actual mixture of gases constituting the nebula. It will also 
allow us to find, at the particular time when any stated quantity of heat 
has been radiated from the gaseous nebula into space, exactly what its 
radius was, what its central temperature and density were, and what were 
the temperature and density at any distance from the centre. Thus, on the 
assumption of S and k known, we have a complete history of the sun (or 
any other spherical star) for all the time before the central density had 
come to be as large as T. 
§ 22. To pass from the case of convective equilibrium in a gaseous 
atmosphere so thin that the force of gravity is practically constant through- 
out its thickness, to the problem of convective equilibrium through any 
depth, considerable in comparison with the radius, or through the whole 
depth down to the centre, provided the fluid is gaseous so far, we have only 
to use (13) and (14), with the proper value of g, varying according to 
distance from the centre. Remembering that we are taking g in terms of 
terrestrial gravity, and that the mean density of the earth is 5*6 in terms 
of the standard density of water, which we are taking as our unit density, 
