152 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1923 



this increases — and is also proportional to the ratio which the radia- 

 tion pressure bears to the total pressure at any part inside the star. 

 This ratio increases rapidly with the star's mass, and the brightness 

 should do the same. 



These conclusions form a theory of giant stars. To extend it to 

 dwarf stars Eddington repeated his calculations, taking into ac- 

 count the manner in which the compressibility of a gas decreases 

 with increasing density, and obtained a theoretical table which rep- 

 resents the way in which the absolute magnitude and temperature 

 of a star should depend upon its mass and density throughout the 

 whole range of these quantities. This table reproduces the actual 

 characteristics of the dwarf stars and those of maximum tempera- 

 ture, as well as the giants, with a fidelity which is almost uncanny, 

 and far more than justifies its author's modest claim that the theory 

 upon which it is based " gives a fair approximation to the facts." 



But Eddington's theory goes beyond this. It actually shows us 

 why the masses of the stars are so much alike, and why they are of 

 their actual order of magnitude. If (3 is the fraction of the whole 

 pressure within the star which is balanced by the gas pressure, leav- 

 ing the fraction 1— (3 for the radiation pressure, he derives by reason- 

 ing of a very general character, the equation 



1 ^ = 4.6X10- 88 J1/ 2 

 P 



where M is the mass of the star in grams. The extraordinarily small 

 numerical coefficient depends only upon a few very fundamental 

 natural constants — the gravitational constant, the quantum, and the 

 average mass of one of the "molecules" in the star (including in 

 this term atoms, nuclei, and free electrons). The numerical value 

 here given depends on the assumption that the last quantity is 2.8 

 times the mass of a hydrogen atom, an estimate which must be nearly 

 correct if the atoms are dissociated into nuclei and electrons to the 

 degree which has been described. 



Now, following Eddington's argument, we may imagine a set of 

 spheres -of gas, each isolated in space and in equilibrium under its 

 own gravitation and radiation, the first mass of 10 grams, the next 

 100 grams, the third 1,000 grams, and so on. Then, by means of his 

 equation, we find that the proportion which the radiation pressure 

 bears to the whole will be quite negligible in all the spheres up to 

 No. 32, will increase rapidly for Nos. 33 and 34; while for sphere 

 35 and all those beyond it the radiation pressure will be the dom- 

 inant partner, leaving little for the gas pressure to do. 



Upon this long line of spheres, therefore, we find a small region 

 in which a certain natural factor changes from an insignificant to a 

 controlling role. On general physical principles, therefore, as Ed- 



