A new method of high-precision isotherm thermometry has been developed in which the density of helium gas is determined from dielectric constant measurements using the virial expansion of the Clausius-Mossotti equation. The technique is shown to be accurate at the level of -0.3 mK for the range 4.2-27.1 K, with potential for both increased accuracy and increased range. The results confirm that the gas thermometer scale NPL-75 is internally consistent to better than 1 mK, and that Berry's recent values for the second virial coefficient of helium are correct at the levelf 0.05 cm3 mol-'.The results also give a value for the third virial coefficient, C(T) = (5420 f 225)/T cm6 mol-2, and a value of 517.257 f 0.025 x cm3 mol-' for the polarizability of He.

The area, A, and the duration of contact, T, have been measured as a function of impact speed, U, for balls striking a flat surface. The balls lost about 40% of their kinetic energy over the range of speeds studied, but, surprisingly, the results for A(U) and T(U) appear to be consistent with Hertz’s elastic theory of impact. Possible reasons are discussed for this unexpected behavior.

The second and third dielectric virial coefficients of 4He have been measured by the symmetrical gasexpansion technique of Buckingham, Cole and Sutter for six isotherms between 3,OO K and 17,68 K. The effects of helium adsorption are important, and are considered in detail. No temperature dependence of the second coefficient is seen at a level of 6b= &0,008 cm3mol-', and average values of the second and third coefficients are b = 0,006 (10) cm3 mol-and c = -5 (4) cm6 mol-', respectively. The uncertainty for b is relatively large because it has a systematic dependence on c: reanalysis of all the existing data shows that a more probable value of the third coefficient is c= -2 (1) cm6mol-', which when combined with our data gives b ( 3 K -18 K)= -0,001 (4) cm-,mol-'. The very small value suggests that theoretical calculations of the excess polarizability of the helium diatom need to be reconsidered. The small value and the small uncertainty of b indicate that future work to improve experimental values of the second density virial coefficient of 4He for this temperature range may without ambiguity make use of the methods of dielectric constant gas thermometry.

The highly accurate conventional isotherms of Berry and dielectric constant isotherms of Gugan and Michel have been analysed in a mutually consistent way between 2.6 K and 27 K by the method of surface-fitting. Semi-empirical expressions are presented for the variation of the virial Coefficients C ( T ) and D(T). A variety of expressions which conform to the expected theoretical constraints have been examined for B(T): the best of these agrees closely down to about 9 K with values recently calculated by Feltgen et al. using a potential derived from scattering experiments. The second dielectric virial coefficient b(T) shows a temperature dependence reasonably close to that calculated from the pair-polarizability given by Dacre, and the internal consistency of these results suggests that the values obtained for B ( T ) have an uncertainty of about f 0.05 cm3 mol-' down to 6 K, rising to perhaps f 0.2 cm3 mol-' below this. The temperature scale NPL-75 is assessed against several recent experiments: while there are indications of minor discrepancies the evidence is not conclusive and NPL-75 appears to be accurate at very close to the level originally claimed.

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