The basic age equation of thermoluminescence dating contains two types of quantities, namely accumulated dose and dose-rates which, on closer inspection, are dependent on the size of grains used in the dating experiment. This is caused by the attenuation of radiation within the grains and can be made more explicit by introducing functions into the age equation, which quantitatively describe the effect of attenuation. The age then becomes a function of grain size and concentration of radioactive elements. As the specific functions for alpha-, beta-and gamma-radiation contribute to very different degrees to the total annual dose, a potential age determination is offered. In a first approximation it is based only on the grain size attenuation of beta-radiation to which the object was exposed. Such kind of dating requires several grain sizes to be investigated, preferably ranging from 100 to 1000/zm in order to make differences in the archaeodose more easily measurable. The linear relation between archaeodose and attenuation factor of beta-radiation permits the evaluation of the age from the gradient and the envionmental dose-rate from the intercept of an appropriate plot. The technique has been tested with quartz grains extracted from well-dated 700-800-years-old bricks. Results obtained agree fairly well with known historical dates and also indicated that this dating procedure avoids several disadvantages of the former subtraction dating technique. As the environmental dose-rate is eliminated, it seems a suitable way to date cores of hollow cast objects.