The thermal expansivity of a single crystal of EuO was determined in the temperature range 25 to 250°K by a differential-strain-gauge method. The temperature of the peak in the λ curve of expansivity is 69.2°K, in agreement with the specific-heat measurements. After correcting for the normal lattice expansivity using the Grüneisen theory, we observe that the resulting magnetoelastic component of expansivity αme obeys a magnetic Grüneisen law, being proportional to the magnetic specific heat Cm over wide ranges of temperature both above and below the λ transition. Europium oxide can therefore be characterized by a temperature-independent "magnetic" Grüneisen constant, lnUmlnV=-5.3, given by -3αmeCm-1BT, where the isothermal bulk modulus BT=1.07×10+12 dyn/cm2. The lattice Grüneisen constant, lnUllnV=1.9, was similarly derived from the data at temperatures well above the λ anomaly. For Um, the internal magnetic energy, we also derive the variation with temperature Um(T)Um(0), the variation with pressure lnUmP=4.9×10-12 dyn-1 cm2, and the value Um(0)=-4.9×108 erg/cm3 at 0°K. Comparison with results of other experiments and with theories based on the Heisenberg Hamiltonian is also presented. The model of D. C. Mattis and T. D. Schultz and of E. Pytte is consistent with the observed proportionality between Cm and αme. A more general model proposed by E. R. Callen and H. B. Callen includes magnetoelastic coupling of unequal strengths to first- and second-nearest neighbors. When the second-neighbor interaction is weaker than the first, this model is also consistent with a single effective magnetic Grüneisen constant not only because the model then differs only slightly from a special case of that of Mattis and Schultz and of Pytte, but also because the spin correlation functions S•S′1stneighbor and ãS•S′2ndneighbor appear to be nearly proportional to each other over a wide temperature range. © 1967 The American Physical Society.