  We investigate the large phase shifts of the bi-color spatial soliton pair in
a cylindrical lead glass rod. The theoretical study suggests a synchronous
propagation of a strong pump beam and a weak signal beam under the required
initial condition. We experimentally obtain a $\pi$ phase shift of the signal
beam by changing the power of the pump beam by about 14 mW around the soliton
critical power, which agrees qualitatively with our theoretical result. The
ratio of the phase shift rate of the signal soliton to that of the pump soliton
shows a close match to the theoretical estimation.
