The fluorescence quenching by oxygen of 9,10-dimethylanthracene (DMEA) in liquid ethane and propane at pressures up to 60 MPa and 25 degrees C was investigated. The apparent activation volumes for the quenching rate constant, k(q),DeltaV++(q) , were 5.0 +/- 3.4 and 7.4 +/- 1.0 cm(3)/mol, whereas those for the solvent viscosity, eta,DeltaV++(eta) , were 190 +/- 22 and 42 +/- 1 cm(3)/mol in ethane and propane at 6.0 MPa, respectively. These results were discussed together with those in n-alkanes (C(4)-C(7)) and methylcyclohexane (MCH) that were previously reported, and it was found that DeltaV++(q) increases monotonically but DeltaV++(eta) decreases rapidly with increasing the number of carbon atoms in n-alkanes. The plot of ln k(q) against ln eta showed a leveling-off with decreasing eta. These observations were analyzed satisfactorily by the pressure dependence of the solvent viscosity on k(q) coupled with that of the radial distribution function, g(sigma), at contact with a hard sphere assumption. The apparent bimolecular rate constant, k(bim,0), for the quenching in the solvent cage was evaluated by extrapolating to g(sigma)eta = 0 in the plot of g(sigma)/k(q) against g(sigma)eta, and it was found that k(bim,0) decreased with increasing the radius of the solvent molecule. From the solvent size dependence of k(bim,0), the solvent cage effect was discussed phenomenologically.