Meyer's hardness law and its relation to other measures of ball hardness tests

The force dependence of the ball indentation hardness can be described in many cases by MEYER's hardness law. The characteristic material parameters are the MEYER constant K and the MEYER exponent n. But often other simple measures of hardness are used for technical applications. Examples are the difference of hardness for two different loads, which gives a good view of the hardening capability of the material, and the BRINELL hardness. It is shown that empirical found relations between the mentioned measures of hardness and the MEYER parameters are strong consequences of the validity of MEYER'S law. In special ranges of the values of the material parameters these empirical relations are linear ones. As a result of the theoretical considerations one must recommend to use the theoretical relations to fit the experimental values, because only in this case all physical conditions are fulfiled automatically.