Very High-Resolution Heat-Capacity Measurements near the Lambda Point of Helium

New measurements of the heat capacity of a sample of helium 3 mm high are reported which extend to within 5×${10}^{-8\mathrm{}}$ deg of the lambda transition at the vapor pressure. From an analysis of the results allowing for the effect of gravity, the values -0.0127± 0.0026 ($2\sigma$) for the exponent $\alpha (={\alpha }^{\prime })$ and 1.058±0.004 for the leading singularity ratio $\frac{A}{A^{\prime }}$ are obtained. These values are in closer agreement with the theoretical predictions than those reported previously.