His proof first argued that for wavelength λ and at temperature T, at thermal equilibrium, all perfectly black bodies of the same size and shape have the one and the same common value of emissive power E (λ, T, BB), with the dimensions of power. His proof noted that the dimensionless wavelength-specific absorptivity a (λ, T, BB) of a perfectly black body is by definition exactly 1. Then for a perfectly black body, the wavelength-specific ratio of emissive power to absorptivity E (λ, T, BB) / a (λ, T, BB) is again just E (λ, T, BB), with the dimensions of power. Kirchhoff considered, successively, thermal equilibrium with the arbitrary non-ideal body, and with a perfectly black body of the same size and shape, in place in his cavity in equilibrium at temperature T. He argued that the flows of heat radiation must be the same in each case. Thus he argued that at thermal equilibrium the ratio E (λ, T, i) / a (λ, T, i) was equal to E (λ, T, BB), which may now be denoted B λ (λ, T), a continuous function, dependent only on λ at fixed temperature T, and an increasing function of T at fixed wavelength λ, at low temperatures vanishing for visible but not for longer wavelengths, with positive values for visible wavelengths at higher temperatures, which does not depend on the nature i of the arbitrary non-ideal body. (Geometrical factors, taken into detailed account by Kirchhoff, have been ignored in the foregoing.)