See — Temperature of the Sun and Ages of Stars and Nebulae. 35 



k=i 



Hence T= jK « , and as 2ro,C, = (7, 



« ,i ^ feo 



our final equation takes the form 



In this expression /?,- is the only secular variable, and hence 

 the fundamental law of temperature retains its original form. 

 If, however, the gases diffused according to a new law when 

 the mass shrunk, it would require us to take account of this 

 slowly modifying cause. For considerable intervals it might 

 be neglected, but for very great periods an error would at 

 length develop and necessitate a new integration. The form 



would then be T = ' ^ ', where t is the time and ft a small 



R 



secular coefficient. It thus appears that the law T = ^ holds 



for every layer of the Sun's mass, and consequently for the 

 mean temperature of that globe. It is not probable that un- 

 known conditions arising in gaseous stars and nebulae are 

 likely to render this law appreciably inexact, and hence we 

 are, I think, justified in regarding it as one of the most fund- 

 amental as it is the most simple of all the laws of Nature. 



The question will doubtless be asked how far this law is ap- 

 plicable to the evolutionary history of the Solar System. We 

 may observe that as the Sun is still gaseous, it now has a 

 mean density a little greater than one thousand times that of 

 atmospheric air. As the molecules in a vacuum produced by 

 the air pump still roughly follow the laws of gases when the 

 density is reduced to about one-millionth of the ordinary den- 

 sity, we see that gases may undergo a change of density of a 

 billionfold without wholly invalidating their known physical 

 laws. It thus appears that our Sun would probably behave 

 sensiblv as a gas when its radius was one thousand times 

 larger than at present ; or that the Solar Nebula has been 

 gaseous since it came within the orbit of Jupiter. Even if 

 the above law of temperature hold only within the thousand- 



