86.

For the total radiation density in space of the black radiation in the vacuum we find $u={\int }_0^{\infty }𝗎d\nu =\frac{1}{c^3}{\int }_0^{\infty }{\nu }^{3}F\left(\frac{T}{\nu }\right)d\nu ,\mathrm{\backslash Label}[eqn](102)\text{upshape (102)}$ or, on introducing ${\displaystyle \frac{T}{\nu }}=x$ as the variable of integration instead of $\nu$, $u=\frac{T^4}{c^3}{\int }_0^{\infty }\frac{F(x)}{x^5}dx.\mathrm{\backslash Label}[eqn](103)\text{upshape (103)}$ If we let the absolute constant $\frac{1}{c^3}{\int }_0^{\infty }\frac{F(x)}{x^5}dx=a\mathrm{\backslash Label}[eqn](104)\text{upshape (104)}$ the equation reduces to the form of the Stefan-Boltzmann law of radiation expressed in equation [eqn:(75)] (75).