140 Transactions 



unaltered, so far as we can tell, after thousands or millions of 

 vears of cooling. How long, then, ought a body take to cool 

 which can shine as a star of the first magnitude though so far 

 distant as to have no measurable parallax ? 



I have to consider this question, and show that the rapid 

 cooling of a " Nova " is a necessary consequence of the added 

 heat, from whatever cause due, and will take place though the 

 body be equal in mass to, or greater than, the sun. 



Consider a star of dimensions and mass comparable with those 

 of the sun, and assume, as is generally supposed, that the whole 

 is in a state which may be termed gaseous — that is, the tempera- 

 ture is so high that every part responds to increase and diminu- 

 tion of pressure in the same manner as a gas does. It is not 

 necessary to assume that the ratio of expansion to increment 

 of heat follows the law of gases. I make the assumption of the 

 gaseous nature of a "Nova" because, first, there can be but 

 little doubt that a " Nova " at least is in this state, and, secondly, 

 because my arguments have no application to a solid or non- 

 gaseous star. Assuming, then, the star to behave as a gas, 

 we may also assume that at any moment it has such dimen- 

 sions that an equilibrium exists between the tendency to ex- 

 pand and that to shrink. Each particle will at that moment 

 be solicited by two forces — one the attraction of the mass, which 

 tends to draw the particle towards the centre, the other the 

 expansive force due to the high temperature of the gaseous 

 mass. These opposing forces must exactly neutralise each other 

 to produce an equilibrium. If there is any disturbance of that 

 equilibrium the particle will move towards or away from the 

 centre according as the gravitation or the expansion due to heat 

 is in excess. In the case of the sun the equilibrium is being 

 disturbed from moment to moment by the continuous radiation 

 away of heat. 



Consider the effect on a particle : Heat is radiated away, 

 the amount of heat available to balance gravitation is diminished ; 

 but by the hypothesis the heat before radiation was exactly 

 sufficient to balance gravitation ; there is therefore after radia- 

 tion an unbalanced tendency towards the centre, and the 

 particle must take up a new position nearer the centre. This 

 must also be true of every other particle of the sun's mass : in 

 other words, the whole mass must shrink through loss of heat 

 radiated away. So far this accords with our experience : a 

 gaseous body — e.g., steam — contracts as it parts with its heat. 



Now, at first impression it might be suppossd that, heat 

 having been parted with, the sun's temperature would be lowered. 

 It would be so if the volume remained constant, but this is not 

 so ; as shown above, the volume diminishes, and the very fact 



