a Spherical Gaseous Nebula. 697 
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 kilo- 
metres thick — a conclusion which may possibly be tested, 
demonstrated, or contradicted, by sufficiently searching 
spectroscopic analysis. The character of the test would be 
to find the thickness of the outermost layer from which the 
bright spectrum lines proceed. If it were 'V as seen from 
the earth, it would be 73 kilometres thick. 
& 20. Considering the great force of gravity at the sun's 
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 atmo- 
sphere 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 kilo- 
metres 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 thickness of his bright-line- 
emitting outermost layer very much greater than one hundred 
kilometres. Groing 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 realization 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 "1 ; on the assumption that we know the 
specific volume (S) and the ratio of specific heats (k) 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 
