a Spherical Gaseous Nebula. 68£ 
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 Temperature in the 
Atmosphere " *, 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 temperature of the highly 
rarefied air close to the bounding surface would be just over 
absolute zero ; that is to say, temperature and density would 
come to zero at the same height as we ideally rise through 
the air to the boundary of the atmosphere. Homer Lane's 
problem gives us a corresponding law of zero density and 
zero temperature, at an absolutely defined spherical bounding 
surface (see § 27 below). In fact it is clear that if in Lane's 
problem we first deal only with a region adjoining the 
spherical boundary, and having all its dimensions very small 
in comparison with the radius, we have the same problem of 
convective equilibrium as that which was dealt with in my 
letter to Joule. 
§ 3. According to the definition of " convective equi- 
librium " given in that letter, any fluid under the influence 
of gravity is said to be in convective equilibrium if density 
and temperature are so distributed throughout the whole 
fluid mass that the surfaces of equal temperature, and of 
excess of the amount calculated according to Boyle's Law, when com- 
pressed 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). 
* Republished in Sir "William Thomson's Math, and Phys. Papers,, 
vol. iii. p. 255. 
