ASTRONOMY 529 



diffusion of molecules from its outer boundary. The rate 

 of loss is greater the higher the temperature and the weaker 

 the gravitational field, as more molecules then acquire a 

 sufhciently large velocity to have a chance of escaping. From 

 this point of view, it is at first sight difficult to understand the 

 existence of large giant stars. Such stars have an extremely 

 low densit}^ a fairly high temperature, and are so large that 

 the value of the gravitational attraction at their outer boundary 

 is very small. It might be thought, therefore, that the atmo- 

 spheres of such stars would be rapidly dissipated and that, 

 since these stars are gaseous, they would gradually be com- 

 pletely dissipated. In a paper read before the British Asso- 

 ciation at its last meeting by A. A. Milne, it was shown that 

 this argument is fallacious. He shows that the critical velocity 

 of escape depends not on the acceleration due to gravity at 

 the boundary, but on the gravitational potential there. Even 

 for a giant star, the potential at the boundar\'^ is large compared 

 with that at the boundary of the Moon, so that the dissipation 

 should be far slower for a giant star than for the Moon. Milne's 

 investigation, in fact, shows that it will be quite inappreciable 

 for all stars. He finds that there is a fairly narrow layer in 

 the atmosphere of the star in which most of the dissipation 

 occurs. At this height, the density is such as to correspond 

 to a mean free path / given by 



llr = Alq, 



where q = mVjRT,r is the radius of the star and ^ is a numerical 

 constant whose value ma}/ be taken to be about 3. From 

 this formula it is deduced that the mean free path for helium 

 at the escape level in the earth's atmosphere is about 130 kms. 

 corresponding to a height of about 600 kms. For hydrogen in 

 the Sun's atmosphere, / = 400 kms., and for a giant star of 

 the same mass as the Sun at a temperature of 3,000°, / = 1-5 X 

 lo* kms. 



It is apparent that the loss by escape will be highest for 

 stars with a low value of q. For giant stars, q is much smaller 

 than for dwarfs, and for giants of given mass it decreases with 

 the temperature. It is shown that it has an absolute minimum 

 when the radiation pressure is one-fifth of the total pressure. 

 Assuming a mean molecular mass of 4, this occurs when the 

 mass is 0-85 of the Sun's mass. It is a striking fact that this 

 is approximately the average mass of a star. The conclusion 

 is that the most favourably placed of all stars for loss by 

 diffusion to be appreciable is a giant star of about the mass 

 of the Sun. 



It is further pointed out that the surface gravitational 



