A photon transmission technique was used to monitor the multiple phase transitions in a 4-butoxyphenyl4(')-declyoxybenzoate (BOPDOB) liquid crystal. Drastic decreases in the transmitted photon intensity (I) were attributed to the sequential phase transitions in BOPDOB upon cooling. In this paper, it is assumed that the order parameter rho is proportional to the transmitted photon intensity. The isotropic-nematic and nematic-smectic-A transitions were observed and found to be of first order. It was observed that the smectic-A-smectic-C and smectic-C-smectic-G transitions are second order. It was found that for the smectic-A-smectic-C transition, critical exponent crosses over from beta=0.513+/-0.006, which is consistent with mean-field theory, to beta=0.35+/-0.009, which is consistent with heliumlike behavior, as the Ginzburg criterion predicts. The critical exponent for the smectic-C-smectic-G transition was found to be beta=0.703+/-0.001. Transition temperatures were established at each phase transitions and found to be 84.92 degrees C, 74.85 degrees C, 52.96 degrees C, and 33.03 degrees C for isotropic-nematic, nematic-smectic-A, smectic-A-smectic-C and, smectic-C-smectic-G transitions, respectively.