  We study the spin gap of the S=1/2 Heisenberg model on the distorted diamond
chain, which is recently proposed to represent magnetic properties of Cu_3 Cl_6
(H_2 O)_2 2H_8 C_4 SO_2. This model is composed of stacked trimers and has
three kinds of exchange interactions J_1, J_2 and J_3. Using the numerical
diagonalization, we obtain a contour map of the spin gap in the J_2/J_1-J_3/J_1
plane. We argue possible values of the exchange constants based on the contour
map and the observed value of the spin gap.
