For the scattering lengths of the S-wave pion-nucleon scattering, Chew, Goldberger, Low and Nambu have shown that the result of their dispersion relation without subtraction exhibits an excellent agreement with the observations, as long as the integrations are carried out over the 3-3 resonance alone. Correspondence of their result to the Hamiltonian formalism is examined by replacing the 3-3 resonant state by an isobaric particle of spin 3/2, which is described by the Rarita-Schwinger theory. The scattering amplitudes are calculated by means of the lowest order perturbation theory. By requiring further that hte amplitudes should decrease to zero in the high energy limit, it is found necessary to introduce the interaction terms other than the conventional one. These terms are left undetermined from the location and the width of the 3-3 resonance. By the appropriate choice of the parameters involved in these terms, CGLN's result can be reproduced in the narrow width approximation.