Tmatrix for electromagnetic scattering from an arbitrary number of scatterers with continuously varying electromagnetic properties

We consider monochromatic electromagnetic scattering from a fixed configuration of an arbitrary number of separate scatteres which are immersed in a medium with constant electric and magnetic properties. Within the scatterers the electric and magnetic properties are assumed to vary smoothly. By considering the integral equations for the scattering we show that the total $T$ matrix for the configuration of the scatterers can be expressed in terms of the $T$ matrices for the individual scatterers in the same way as was previously found for a similar configuration of scatterers, each having a discontinuity in the electric and magnetic properties at the surface and constant electric and magnetic properties in its interior.