The terminal solid solubility (TSS) of hydrogen or deuterium is an important parameter in Zr alloys that are used in the nuclear industry. If this solubility es exceeded, it can make the alloys susceptible to delayed hydride cracking. Accurate expressions for the TSS are necessary for modelling delayed hydride cracking as well as deuterium ingress into pressure tubes and blister formation in pressure tubes in contact with their calandria tubes. Measurements of the changes in the dynamic elastic modulus have been used to establish expressions for the TSS as a function of temperature and to study the hysteresis between hydride dissolution and precipitation. It is shown that the hysteresis is particularly sensitive to the thermal history of the sample (such as the prior maximum temperature, hold time at maximum temperature and cooling rate). As a result, the precipitation TSS (TSSP) has a range of values bounded by the solubility equations designated TSSP1 and TSSP2. These are obtained, respectively, by cooling from an upper- and lower-bound maximum temperature. The TSSD equation obtained in this study is very close to previously determined expressions, but the TSSP equations differ significantly from earlier results.