200 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1950 



56/(26 + 1) or 2.1. The mean molecular weight of completely ionized 

 oxygen will be 16/(8 + 1) or 1.8. However, the molecular weights 

 of completely ionized hydrogen and helium will be only 0.5 and 1.3 

 respectively. Consequently, while the equilibrium within a star will 

 not be very sensitive to the relative proportions of the heavier 

 elements present, it will be very sensitive to the amounts of hydrogen 

 and helium. 



Thus, if we know the mass, the radius, and the luminosity of a 

 star, we can determine its mean molecular weight and, as a result, 

 the approximate hydrogen content of the star. In order to determine 

 the hydrogen and helium contents more precisely, particularly rela- 

 tive to the next most abundant elements (carbon, nitrogen, and 

 oxygen) , use can be made of our knowledge concerning the mechanism 

 of energy production in the main-sequence stars. In 1939, Bethe 

 demonstrated that the mechanism of energy production in the sun, 

 and probably in all main-sequence stars, is a cycle of nuclear reactions 

 involving carbon, nitrogen, and oxygen as intermediates, and resulting 

 in the net conversion of hydrogen into helium. The mathematical 

 relationships involved in the carbon cycle can be coupled with the 

 general relationships which describe the equilibria within stellar in- 

 teriors, and a unique solution for the relative proportions of hydrogen 

 and helium present in a given star may be obtained. 



Recently Greenstein recomputed the abundances of hydrogen and 

 helium relative to other elements (primarily carbon, nitrogen, and 

 oxygen) . His results indicate that for every atom of heavier elements 

 present in the sun, there are approximately 100 atoms of helium and 

 1,000 atoms of hydrogen. Thus it appears that in our region of 

 space, hydrogen and helium together account for more than 99.8 

 percent of the matter present! Relative to these elements, the ele- 

 ments that we encounter in such high abundance on the surface of 

 the earth exist in stars in amounts that are quite insignificant. 



How does this reasoning concerning the hydrogen and helium con- 

 tent of stars, and their abundances relative to other elements, apply 

 to individual stars? Do stars differ appreciably one from the other 

 in composition? We know that stars differ considerably one from 

 the other in their energy release per unit weight of the star, so they 

 must be consuming hydrogen and producing helium at rates which 

 differ widely. As a result one would expect that the hydrogen and 

 helium contents of stars would vary considerably. Indeed, we find 

 collapsed stars known as white dwarfs where the hydrogen contents 

 appear to have been virtually exhausted. Similarly, one would expect 

 to find variations within main-sequence stars of the abundances of 

 carbon, nitrogen, and oxygen. The ratios of these elements will be 



