IT has recently been discovered by S. Chandrasekhar,1 B. Swirles,2 and R. C. Majumdar,3 independently, that the opacity of a degenerate gas is very small compared with what would be computed for a classical gas at the same density and temperature, the ratio being an inverse power of Sommerfeld's degeneracy-criterion parameter. This discovery seriously affects estimates of the internal temperatures in white dwarf stars. It has previously been held that interiors of the white dwarf stars are amongst the hottest of stellar interiors; for example, Russell and Atkinson4 remark that their internal temperatures must be of the order of 50 times those of a main sequence star built on the ‘diffuse’ model. Again, Jeans5 says “it appears that the central temperatures of the white dwarfs must be enormously high, while those of giant stars of large radius must be comparatively low”. This has given rise to the paradox that the coolest stellar interiors appeared to be the best generators of stellar energy, the hottest the worst. To quote Jeans6 again, “... many of the hottest and densest stars are entirely put to shame in the matter of radiation by very cool stars of low density, such as Antares and Betelgeuse”.