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We describe long distance QCD by a dual theory in which the fundamentalvariables are dual potentials coupled to monopole fields and use this dualtheory to determine the effective Lagrangian for constituent quarks. We findthe color field distribution surrounding a quark anti-quark pair to first orderin their velocities. Using these distributions we eliminate the dual potentialsand 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-quarkcoordinates and velocities, valid to second order in their velocities. Wepropose $ L_I $ as the Lagrangian describing the long distance interaction ofconstituent quarks

The Dual Description of Long Distance QCD and the Effective Lagrangian for Constituent Quarks