Capacitance coefficients

Charges (q₁, ..., q_n) of a system of conductors can be expressed in terms of coefficients of electric induction (C_ij) by the following equations:
q₁ = C_1∞V₁ + C₁₂(V₁-V₂ ) + ... + C_1n(V₁ - V_n)
q₂ = C₂₁(V₂ - V₁) + C_2∞V₂ + ... + C_2n(V₂ - V_n)
q_n = C_n1(V_n - V₁) + C_n2(V_n - V₂) + ... + C_n∞V_n
where
C_km = C_km(m ≠ k)
and
C_m∞ = C_m1 + C_m2 + ... + C_m(n-1) + C_mn
They are the fundamental relations for partial capacitances of a number of conductors, e.g., electrodes in valves, conductors in cables, variable air-capacitors.