Note on Grüneisen's Constant for the Incompressible Metals

Gr\"uneisen's constant can be determined in terms of the thermal expansion, compressibility, and specific heat, as originally shown by Gr\"uneisen. It can also be found from the compressibility and change of compressibility with pressure. Theoretically the two methods should give approximately the same result. This has proved to be the case experimentally, except for the more incompressible metals, where the discrepancies have been very great. Bridgman has now redetermined the change of compressibility of iron with pressure, obtaining a much smaller value than before, and as iron was used as a standard, this brings about a revision of other changes of compressibility with pressure, largest in proportion for the incompressible metals, whose volume change is about the same as for iron. It is shown that this revision is just enough to bring the two methods of finding into agreement, for practically all the metals.