160 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1944 
even an apparent divergence of 30 percent from uniformity of den- 
sity is not evidence weighty or certain enough to overthrow the 
Lemaitre theory of an expanding universe. 
IV 
Important advances have been made recently by Gamow and 
Bethe in our understanding of the sources of energy within stars 
which permit them to radiate energy as they do. Bethe has given 
an exposition of a cyclical sequence of atomic changes and interac- 
tions whose net result leaves a star with fewer hydrogen atoms, but 
with more helium and the liberation of excess nuclear energy in the 
form of gammarays. This is now generally referred to as the carbon 
cycle and it is too beautiful not to be recorded here, for though 
published a few months before the war, it has been during the war 
years that it has become a part of astronomical thinking. Of the 
six stages, four result from collisions with hydrogen atoms in the 
deep, hot interiors of main sequence stars, and two are spontaneous 
disintegrations of unstable nuclei. 
1.C%+H! = N®+y 
2,.N8— C8 + _ positron 
3.C8+H = N¥+y 
4.N¥4+H! = OB+y 
5. 0% > N® + positron 
6, N2.-) Ht, ==. 1 OC let 
The two positrons rapidly interact with electrons to give rise to 
gamma radiation. Thus is produced the penetrating radiation, most 
of which in the course of its progress toward the boundary of the 
star becomes transformed into the heat, light, and ultraviolet radiation 
that pour out from the photosphere. The central temperatures of 
the cool giant stars are insufficient to maintain this active cycle, but 
theory can explain their radiant energy in terms of atomic collisions 
and transmutations which are, however, noncyclical. Hydrogen, 
deuterium, lithium, beryllium, boron are slowly transformed into 
helium. 
If the central regions of the hottest stars are not the crucibles of 
nature wherein the elements are built up, where and under what 
conditions were they formed? A highly speculative answer is to be 
found in an intensely interesting piece of theoretical research carried 
out during the early years of this war by Chandrasekhar and Heinrich. 
They have been inquiring under what conditions of nature the basic 
units of matter—electrons, protons, neutrons, positrons—could be ex- 
pected to come together to form, in their various proportions, the 
atoms of all the isotopes of the elements familiar to the chemist. As 
