In an attempt to discover a reasonable explanation of the origin and duration of the solar radiation, all possible sources of energy are examined. The following hypotheses are reviewed and discarded, the arguments against their validity being too well known to necessitate a review at this place; (1) Original Heat; (2) Chemical; (3) Gravitational, (a) Meteoric, (b) Contraction; (4) Radioactive. In view of the failure of the above hypotheses, serious consideration is given to the possible transmutation of matter into energy. Eddington's massluminosity relation appears to demand such a process as the general source of stellar radiation. It is shown that any theory which makes the production of energy a function of temperature and pressure is subject to severe criticisms--(a) the observed rate of energy transformation is greater in the giant than in the hotter and denser dwarf stars; (b) the adiabatic nature of a star would be insufficient to regulate the generation of heat. Jeans assumes that we have, in the center of stars, a quantity of atoms of atomic weight higher than uranium, whose super-radioactive powers lead to decomposition into energy. The success of the theory in accounting for the following observed facts is enough to demand its serious consideration. 1--Life of stars of order of 1013 years 2--Better value of the stellar absorption coefficient 3--Giant and dwarf stars 4--White dwarfs 5--Early spectral type of spectroscopic binaries 6--Relations between visual double stars 7--Sufficiently long time for evolution of orbits of visual binaries 8--Cepheid and Long Period Variables (?) The main objection of Eddington to the theory appears to be invalid.