  We describe long distance QCD by a dual theory in which the fundamental
variables are dual potentials coupled to monopole fields and use this dual
theory to determine the effective Lagrangian for constituent quarks. We find
the color field distribution surrounding a quark anti-quark pair to first order
in their velocities. Using these distributions we eliminate the dual potentials
and obtain an effective interaction Lagrangian $L_I ( \vec x_1 \, , \vec x_2 \,
; \vec v_1 \, , \vec v_2 )$ depending only upon the quark and anti-quark
coordinates and velocities, valid to second order in their velocities. We
propose $ L_I $ as the Lagrangian describing the long distance interaction of
constituent quarks.
