Prof. W. Thomson on the Secular Cooling of the Earth. 11 



not assume the depth of this lava ocean to have been more than 

 50 or 100 miles ; although we need not exclude the supposition 

 of any greater depth, or of an entire globe of liquid. 



21. In the process of refrigeration, the fluid must (as I have 

 remarked regarding the sun, in a recent article in ' Macmilian's 

 Magazine '*, and regarding the earth's atmosphere, in a com- 

 munication to the Literary and Philosophical Society of Man- 

 chesterf) be brought by convection to fulfil a definite law of dis- 

 tribution of temperature which I have called " convective equi- 

 librium of temperature.-" That is to say, the temperatures at 

 different parts in the interior must differ according to the dif- 

 ferent pressures by the difference of temperatures which any 

 one portion of the liquid would present, if given at the tem- 

 perature and pressure of any part, and then subjected to varia- 

 tion of pressure, but prevented from losing or gaining heat. 

 The reason for this is the extreme slowness of true thermal 

 conduction, and the consequently preponderating influence of 

 great currents throughout a continuous fluid mass in determin- 

 ing the distribution of temperature through the whole. 



22. The thermo-dynamic law connecting temperature and 

 pressure in a fluid mass, not allowed to lose or gain heat, inves- 

 tigated theoretically, and experimentally verified in the cases of 

 air and water by Dr. Joule and myself J, shows, therefore, that 

 the temperature in the liquid will increase from the surface 

 downwards, if, as is most probably the case, the liquid contracts 

 in cooling. On the other hand, if the liquid, like water near its 

 freezing-point, expanded in cooling, the temperature, according 

 to the convective and thermo-dynamic laws just stated (§§ 21, 

 22), would actually be lower at great depths than near the sur- 

 face, even although the liquid is cooling from the surface ; but 

 there would be a very thin superficial layer of lighter and cooler 

 liquid, losing heat by true conduction, until solidification at the 

 surface would commence. 



23. Again, according to the thermo-dynamic law of freezing, 



* March 1862. 



t Proceedings, Jan. 1862, "On the Convective Equilibrium of Tem- 

 perature in the Atmosphere." 



X Joule, " On the Changes of Temperature produced by the Rarefaction 

 and Condensation of Air," Phil. Mag. S. 3. vol. xxv. p. 369. Thomson, 

 " On a Method for determining Experimentally the Heat evolved by the 

 Compression of Air ; Dynamical Theory of Heat, part 4," Trans. Roy. 

 Soc. Edinb., Session 1850-51 ; and reprinted, Phil. Mag. S. 4. vol. iv. 

 p. 424. Joule and Thomson, "On the Thermal Effects of Fluids in 

 Motion," Trans. Roy. Soc. Lond., June 1853 and June 1854. Joule and 

 Thomson, " On the Alterations of Temperature accompanying Changes of 

 Pressure in Fluids," Phil. Mag. S. iv. vol. xv. p. 538. 



