The pressure dependence of the Gr¿neisen parameter can be determined by the measurement of temperature changes associated with adiabatic compression using the thermodynamic relationship &ggr;=Bs/T (∂T/∂P)s. Bs, the adiabatic bulk modulus, is known from ultrasonic measurements. The measurement of (∂T/∂P)s is carried out in an end-loaded piston cylinder apparatus at pressures up to 35 kbar using a fluid cell. Results are presented for a series of fluids, metals, salts, and minerals. For fluids an increase in &ggr; with pressure is observed. For all solids investigated, &ggr; decreases with pressure. A drastic increase in &ggr; is observed when a substance undergoes a phase transition. We find a systematic behavior of (∂T/∂P)s versus volume except for minerals. The average value of q=-(∂Piln&ggr;/PmLPilnV)T is 1.3. The value of &ggr; for iron at a compression equivalent to the core mantle boundary is discussed, but the uncertainties are too large to permit us to predict with confidence &ggr; for iron at the temperatures and pressures of the core.