A method is presented for measuring M, the ratio of the Gaussian (saddle splay) elastic modulus to the bending elastic modulus of a lipid monolayer. The ratio M is determined from measurements of the equilibrium bicontinuous inverted cubic (Q(II)) phase unit cell size in excess water as a function of temperature. The analysis includes the effect of a curvature elastic term that is second-order in the Gaussian curvature, K. Preliminary results using data on DOPE-Me validate the method. The fitted value of M is within 8% of the value estimated in an earlier treatment. The method can be used to measure changes in M due to addition of exogenous lipids and peptides to a host lipid system. The Gaussian elastic modulus has a substantial effect on the stability of fusion intermediates (stalks, hemifusion diaphragms, and fusion pores). Studying the effects of peptides and different lipids on M via this method may yield insights into how fusion protein moieties stabilize intermediates in membrane fusion in vivo. The contribution of the K2 curvature elastic term to the free energy of Q(II) phase and fusion pores explains some features of fusion pore stability and dynamics, and some peculiar observations concerning the mechanism of L(alpha)/Q(II) phase transitions.