Dipole interaction correction to effective conductivity ($a^{\ast }\approx a_{0}I+p\beta I-{\beta }^2{\sum }_i{\Lambda }_i$)

If the first exciting-field correction at inclusion $i$ is $-\beta {\Lambda }_{i}E/p_i$, its revised polarization is $\beta {\chi }_i(E-\beta {\Lambda }_{i}E/p_i)$. Averaging weights it by $p_i$ and gives the displayed second-reflection approximation. Further dipole reflections and finite-size multipoles are neglected.