The question is whether B(3) adds a third state of polarization, and whether it is an oscillator. The B(3) field adds a classical energy density:
(E / V) (B(3)) = B(3) dot B(3)* / mu0
so adds an intensity:
I = (c / muo) B(3) dot B(3)*
to the usual intensity:
I = epso (E(1) dot E(1)* + E(2) dot E(2)*) + (B(1) dot B(1)* + B(2) dot B(2)*) / muo
so B(3) also changes the proportionality constant in the Stefan Boltzmann law if it is incorporated in this way. However B(3) does not have a phase so is not an oscillator as defined by Rayleigh. The only contribution of Jeans was to adjust a proportionality constant.