An apparatus and techniques are described which have been found adequate for making nominally 1% accurate specific heat measurements on relatively low thermal conductivity alloys in the range of temperature from 0.5 to 10 K and in magnetic fields of 0 to 1.5 T (15 kG). Emphasis is given to thermometry and to experimental methods of establishing the accuracy of the measurements. Several competing effects which must be quite delicatelybalanced in the design of the calorimeter are discussed and the necessary experimental compromises are described in detail. Some consideration is given to techniques for extending the useful range of temperature and magnetic field.