THERMAL EXPANSION OF LIQUID HELIUM II.

The thermal-expansion coefficient of liquid helium II under its saturated vapor pressure has been measured from 0.85 K to within 0.4 mK of the $\ensuremath{\lambda}$ transition. The capacitive technique employed was well suited for these measurements. With the aid of the Clausius-Mossotti equation, we could resolve a relative change in density of 1 part in ${10}^{6}$ in a manner free from sources of systematic error. The data below 1.60 K were analyzed to obtain information about the density derivatives of the Landau parameters $\ensuremath{\Delta}$, ${p}_{0}$, and $\ensuremath{\mu}$ with the following results: $\frac{\ensuremath{\rho}}{\ensuremath{\Delta}}\frac{\ensuremath{\partial}\ensuremath{\Delta}}{\ensuremath{\partial}\ensuremath{\rho}}=\ensuremath{-}0.763\ifmmode\pm\else\textpm\fi{}0.012 \mathrm{and} \frac{1}{2}\frac{\ensuremath{\rho}}{\ensuremath{\mu}}\frac{\ensuremath{\partial}\ensuremath{\mu}}{\ensuremath{\partial}\ensuremath{\rho}}+2\frac{\ensuremath{\rho}}{{p}_{0}}\frac{\ensuremath{\partial}{p}_{0}}{\ensuremath{\partial}\ensuremath{\rho}}+\frac{\ensuremath{\rho}}{\ensuremath{\Delta}}\frac{\ensuremath{\partial}\ensuremath{\Delta}}{\ensuremath{\partial}\ensuremath{\rho}}=\ensuremath{-}1.638\ifmmode\pm\else\textpm\fi{}0.077.$ The results of a reanalysis of the data obtained by other workers in this temperature interval are presented in order to provide a valid comparison with the present results. The techniques employed also allowed measurements to be taken to within 0.4 mK of the $\ensuremath{\lambda}$ transition. At this temperature, the uncertainty in an individual measurement (one standard deviation) had reached about \ifmmode\pm\else\textpm\fi{} 10%. This represents a considerable improvement over previous measurements and allows a detailed examination of the validity of the Pippard-Buckingham-Fairbank relations. It was found that the agreement between theory and experiment is good if the temperature dependence of all the terms in these relations is taken into account. The capacitance bridge was also employed to measure absolute values of the dielectric constant of liquid helium at temperatures of approximately 1.0 K and a frequency of 5 kHz. Analysis of these measurements yielded a value for the molar polarizability of 0.123 296 \ifmmode\pm\else\textpm\fi{} 0.000 030 ${\mathrm{cm}}^{3}$ ${\mathrm{mole}}^{\ensuremath{-}1}$.