Evaluation of Functions Related to Tait's Mean Free Path

A new and extended table of values is given for the functions, Ψ(x)=xexp(-x²)+(2x²+1)∫0ˣexp(-y²)dy,and x⁵Ψ(x),which occur frequently in kinetic theory. The integrals Θₙ=∫0^∞4xⁿexp(-x²)Ψ(x)dxn=3, 4, 5$ are evaluated by numerical quadrature. The new values disagree with the values found by Tait, but agree with the values fond by Boltzmann. The value of ${{Θ}}₄$, which determines Tait's mean free path for a single system, is 0.6774560. A table is given for the function ${Φ}({α})={{α}}²{∫}{0}^{{∞}}{{x}⁵exp({-}{α}{x}²)}{{Ψ}(x)}dx,$which is useful in scattering experiments. ${Φ}({α})$ is evaluated by numerical quadrature for 27 selected values of ${α}$.