  We present a general description of low temperature transport through a
quantum dot with any number of electrons at filling factor $1<\nu <2$. We
provide a general description of a novel Kondo effect which is turned on by
application of an appropriate magnetic field. The spin-flip scattering of
carriers by the quantum dot only involves two states of the scatterer which may
have a large spin. This process is described by spin-flip Hubbard operators,
which change the angular momentum, leading to a Kondo Hamiltonian. We obtain
antiferromagnetic exchange couplings depending on tunneling amplitudes and
correlation effects. Since Kondo temperature has an exponential dependence on
exchange couplings, quantitative variations of the parameters in different
regimes have important experimental consequences. In particular, we discuss the
{\it chess board} aspect of the experimental conductance when represented in a
grey scale as a function of both the magnetic field and the gate potential
affecting the quantum dot.
