A theoretical discussion is given of the experimental results described in part I. Contributions to the low-temperature specific heat from dipole-dipole and exchange interaction are shown to depend linearly on the dilution factor when dilution has occurred in a purely random manner. From a comparison of the results for the diluted and undiluted salts it is shown that a part of the specific heat is independent of the degree of dilution. This part is identified with the nuclear specific heat expected from nuclear-electronic interaction within the atom. The interaction constants are evaluated and are of the order of 0$\cdot $01 degrees K. These results are in agreement with observations of the hyperfine structure in dilute copper salts made from paramagnetic resonance experiments. The effect of exchange interaction is also discussed.