In magnetism literature, usually the applied or external field H-0 is taken to present the results of an investigation. But for certain purposes, it is advantageous to work with the internal magnetic field H that occurs inside a magnetic body. It is well-known that the susceptibility of the material and the demagnetization effect, given by the geometry of a body, link the two usually different fields under consideration. If a probe is a long needle with the external magnetic field and the magnetization in the probe parallel to the axis of the slender body, the two fields are identical. But when building thermomagnetic machines, other demands may require also other shapes (porous materials, particle beds, wavy structures, etc.) of the magnetized material and then a correct distinction of these fields becomes important and in some cases also laborious if one of them must be theoretically determined from the other. This article shows how-from a theoretical point of view-the most important physical properties of thermomagnetism/magnetocalorics, namely, the adiabatic entropy change, the effective specific heat capacity, and the adiabatic temperature change must be transformed. Furthermore, this theory reveals the invariants of magnetocalorics, which are combinations of these three most important properties. (c) 2015 AIP Publishing LLC.