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Proceedings of the Royal Society of Edinburgh. [Sess. 
temperature corresponding to its level, that is to say, its distance from the 
centre of the globe. The condition thus reached, when heat is continually 
being radiated away from the spherical boundary, is not perfect equilibrium. 
It is only an approximation to equilibrium, in which the temperature and 
density are each approximately uniform at any one distance from the 
centre, and vary slowly with time, the variable irregular convective 
currents being insufficient to cause any considerable deviation of the 
surfaces of equal density and temperature from sphericity. 
§ 2. The problem of the convective equilibrium of temperature, pressure 
and density, in a wholly gaseous, spherical fluid mass, kept together by 
mutual gravitation of its parts, was first dealt with by the late Mr Homer 
Lane, who, as we are told by Mr T. J. J. See, was for many years connected 
with the U.S. Coast and Geodetic Survey at Washington. His work was 
published in the American Journal of Science, July 1870, under the title 
“ On the theoretical Temperature of the Sun.” * 
In a letter to Joule, which was read before the Literary and Philosophical 
Society of Manchester, January 21, 1862, and published in the Memoirs 
of the Society under the title, “ On the Convective Equilibrium of Tempera- 
ture in the Atmosphere,” f it was shown that natural up and down stirring 
of the earth’s atmosphere, due to upward currents of somewhat warmer 
air, and return downward flow of somewhat cooler air, in different localities, 
causes the average temperature of the air to diminish from the earth’s 
surface upwards to a definite limiting height, beyond which there is no air. 
It was also shown that, were it not for radiation of heat across the air, 
outwards from the earth’s surface, and inwards from the sun, the tem- 
perature of the highly rarefied air close to the bounding surface would be 
* The real subject of this paper is that stated in the text above. The application of 
the theory of gaseous convective equilibrium to sun heat and light is very largely vitiated 
by the greatness of the sun’s mean density (T4 times the standard density of Water). 
'Common air, oxygen, and carbonic acid gas show resistance to compression considerably in 
excess of the amount calculated according to Boyle’s Law, when compressed to densities 
exceeding four, or five, or six, tenths of the standard density of water. There seems strong 
reason to believe that every fluid whose density exceeds a quarter of the standard density 
of water resists compression much more than according to Boyle’s Law, whatever be the 
temperature of the fluid, however high, or however low. We may consider it indeed as 
quite certain that a large proportion of the sun’s interior, if not indeed the whole of the 
sun’s mass within the visible boundary, resists compression much more than according to 
Boyle’s Law. It seems indeed most probable that the boundary, which we see when looking 
at the sun through an ordinary telescope, is in reality a surface of separation between a 
liquid and its vapour ; and that all the fluid within this boundary resists compression so 
much more than according to Boyle’s Law that it does not even approximately satisfy the 
conditions of Homer Lane’s problem ; and that in reality its density increases inwards to 
the centre vastly less than according to Homer Lane’s solution (see § 56 below). 
t Republished in Sir William Thomson’s Math, and Phys. Papers , vol. iii. p. 255. 
