A well-known theoretical treatment of the temperature dependence of magnetocrystalline anisotropy predicts the equality of the reduced first anisotropy constant and the nth power of the reduced spontaneous magnetization where n=10 at low temperatures. To allow for the effect of thermal expansion, the experimental values of this anisotropy constant should be corrected, according to Brenner (1957), by an amount dependent on b3, the third magnetoelastic coupling constant of Becker and Döring (1939). Measurements of the temperature dependence of magnetostriction constants and of elastic constants are used to calculate b3 as a function of temperature for nickel and it is then found that the experimental value of n is effectively reduced, from about 50 at low temperatures (Carr 1958), to much nearer the theoretical value of 10. A critical examination of possible errors is presented, particularly with reference to experiments in which the pressure dependence of anisotropy is measured.