A theory is presented which describes the simultaneous radiogenic ingrowth and loss of a radiogenic isotope by volume diffusion in crystals cooling slowly above their closure temperatures. When the diffusion parameters of a given radiogenic isotope in the host mineral are known, the age deficit resulting from the open system behavior can be simply related to the cooling rate. An application to the apparent 147Sm-143Nd ages of pyrope garnets in Archean eclogite xenoliths attests to the slow cooling rate of the subcontinental lithosphere.