  The conductance G of a pair of single-channel point contacts in series, one
of which is a spin filter, increases from 1/2 to 2/3 x e^2/h with more and more
spin-flip scattering. This excess conductance was observed in a quantum dot by
Zumbuhl et al., and proposed as a measure for the spin relaxation time T_1.
Here we present a quantum mechanical theory for the effect in a chaotic quantum
dot (mean level spacing Delta, dephasing time tau_phi, charging energy e^2/C),
in order to answer the question whether T_1 can be determined independently of
tau_phi and C. We find that this is possible in a
time-reversal-symmetry-breaking magnetic field, when the average conductance
follows closely the formula <G>=(2e^2/h)(T_1+h/Delta)/(4T_1+3h/Delta).
