310 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1958 
in nuclear reactions which lead to the transmutation of hydrogen into 
helium. The sun and the stars derive their energy from this 
transmutation. 
THE ISOTOPIC COMPOSITION OF THE ELEMENTS 
The nuclei of the atoms are composed of neutrons and protons. 
Nuclei containing the same number of protons are called isotopes; 
they belong to the same chemical element and in general cannot be 
separated from one another by natural chemical processes. Most 
elements are composed of more than one isotope. The isotopic com- 
position of all the elements is known with great accuracy. 
For most elements, this composition is absolutely constant. It is 
the same in all terrestrial material and in meteorites. Small varia- 
tions have only been observed for light elements as a consequence of 
minute differences in the chemical properties due to the difference in 
mass. Variations also occur if one or more isotopes of an element 
are produced by radioactive decay as in the case of lead. Otherwise 
we have reason to assume that the isotopic composition of the ele- 
ments is basically a universal quantity valid for our solar system and 
for many stars. 
If one plots the logarithm of the percentage of each isotope in a 
given element against the mass number (the number of neutrons plus 
protons) of the isotope, very peculiar figures are obtained, as shown 
in figure 1, taking several elements as examples. It was impossible 
for a long time to interpret these figures and to explain them in a 
quantitative way. Many scientists have been fascinated by their 
mysterious appearance in the same way that men have been fascinated 
by the mysterious features of the constellations in the night sky for 
the past thousands of years. 
Certain rules have been recognized governing the isotopic com- 
position of the elements, as for example the rule of Harkins which 
states that isotopes with an odd mass number are on the average less 
abundant than their even-mass-numbered neighbors. Another re- 
markable observation can be expressed in the following way: the 
geometry of the figures obtained by plotting the logarithms of the 
isotope abundances of a given element against their mass number, as 
shown in figure 2, is similar for neighboring elements with even 
atomic number. The character of the figures changes in general only 
gradually with atomic number. 
However, in regions where the nuclei contain certain numbers 
of neutrons, an abrupt change occurs. These numbers of neutrons, 
the so-called magic numbers, signify nuclear shell closures. ‘The 
prominent magic numbers are: 8, 20, 28, 50, 82, and 126. The irregu- 
larities that occur beyond barium may be interpreted on this basis, 
since we are dealing with isotopes of a “magic number” of 82. 
