RADIATION AND TEMPERATURE. 257 



the fall of temperature outwards from the centre being such that a mass 

 moving outwards arid expanding as it moves will cool, owing to dimin- 

 ished pressure through expansion, at such a rate that it is in equilibrium 

 with its surroundings. 



If the temperature falls as we go outwards less rapidly than this, a 

 mass raised up from the inside will be colder than its surroundings, and 

 therefore denser, and will tend to sink, or the equilibrium is stable. 

 But if the temperature falls more rapidly, a mass raised up from the 

 inside will be warmer than its surroundings, and will be less dense, and 

 will, therefore, continue to rise, or if equilibrium exists it will be un- 

 stable. Hence, as the cooling goes on from the outside, there is a limit 

 to the slope of temperature according to this convection law. As soon 

 as the slope is greater than this limit, the arrangement is unstable, and 

 circulation takes place, cooler material from the outside sinking down 

 and being replaced by hotter material from the inside, until the slope is 

 equal to or less than that of convective equilibrium. We probably see 

 such disturbances taking place in sunspots, which appear to be due to 

 the increased absorption of the colder layers thickened by the disturbance. 



Source Of Solar Energy. The enormous rate of loss of energy by 

 the sun a radiation of probably 10,000 to 15,000 h.p. per square foot 

 requires some explanation. We cannot suppose that the supply of energy 

 is merely yielded by the cooling of the body of the sun, for at such a 

 rate the sun would have cooled very appreciably within historic times, 

 and of this there is no evidence. There must be, therefore, some other 

 form of energy continually being converted into heat to keep the tem- 

 perature up. This cannot be chemical energy, for not only is the sun 

 above the temperature at which we believe chemical combination to be 

 possible, but even had it been composed originally of separate elements 

 giving out the greatest known amount of energy by chemical com- 

 bination, the energy would last but a few thousand years. One very 

 probable source was pointed out by Helmholtz, who suggested that the 

 sun's heat is the equivalent of the potential energy of the matter of the 

 sun gradually converted into kinetic energy, and then into heat, as the 

 body of the sun contracts. 



As the sun cools slightly, the matter comes nearer together. The 

 potential energy thus disappearing is converted into heat, which not 

 only keeps the temperature up nearly to its original value, but yields an 

 enormous surplus which is radiated out. 



If the sun were of uniform density throughout, and if as it con- 

 tracted every part were of the same density, a contraction of the radius 

 of the order of 200 feet or 6000 cm. per annum would yield potential 

 energy mechanically equivalent to that radiated out. This would not 

 amount to more than one second of arc in 6000 years, so that we can 

 hardly expect as yet to obtain direct evidence for the contraction. 



It appears possible, too, that the solar energy is in part maintained 

 by the disintegration of radio-active bodies present in the sun. This was 

 suggested by Rutherford and Soddy,* and Rutherford states that 2'5 

 parts of radium per million by weight in the sun would account for its 

 present rate of emission of energy. 



* Rutherford, Radio-activity, chap. x. 



