Chapman. — On Temporary Stars. 141 



that the volume diminishes is in itself a cause of the generation 

 of heat. Each particle in moving to the centre obviously falls ; 

 in falling it gives out energy ; that energy appears as heat. 



To change the mode of statement : Each particle approach- 

 ing the centre constitutes a compression of the whole mass, 

 but the temperatme of a gas rises when it is compressed : the 

 temperature of the sun therefore rises. The extent to which 

 it rises is governed by the circumstance that an equilibrium is 

 again sought. But our particle, having fallen, is now nearer 

 than it was to the centre ; its gravitation is therefore increased ; 

 its tendency to continue to fall requires now a greater force to 

 balance it : in other words, to preserve equilibrium the tempera- 

 ture must be higher than before. The additional temperature 

 is derived, as pointed out, from the compression of the mass. 

 Hence we have what may appear to some a paradoxical result — 

 i.e., that by abstracting heat from the sun (by radiation) the 

 temperature is caused to rise and not to fall — contrary to our 

 experience of cooling bodies. In reality there is no paradox. 

 Part of the heat is due to the contraction. 



There are two kinds of energy in the sun, one heat, the other 

 energy of position or potential. If we take away some of the 

 former we, so to speak, call for contribution from the latter, 

 and that contribution is on a scale a little more liberal than 

 necessary to merely compensate what is taken away. The 

 abstraction of heat causes shrinkage, and the shrinkage causes 

 the development of more heat than that abstracted. This is 

 capable of exact calculation, it being known that a shrinkage 

 of about one-eleventh of a mile will account for the radiation 

 of the sun for a year, and (if the sun is gaseous throughout) still 

 leave the sun a trace hotter at the end of the year than it was 

 at the beginning. 



The apparent (not real) paradox is exactly analogous to that 

 arising in the case of a secondary body moving about its primary. 

 Supposing a secondary were moving in a resisting medium, 

 which at first sight might be supposed to diminish its velocity, 

 the real observable effect would be that its velocity would be 

 increased through its fall towards the primary. The evidence 

 of a resisting medium, supposed to be furnished by Encke's 

 Comet, is not that its velocity diminishes, but that it increases. 



Now, I took the case of heat being abstracted because it is 

 what is going on in the case of the sun, but the whole process 

 above indicated is reversible. 



Supposing, again, the star in momentary equilibrium kept so, 

 as before, by gravitation tending to draw each particle to the 

 centre, and the expansive force created by heat balancing gravi- 

 tation. Now let heat be added : in the first case the subtraction 



