The Virial expansion is a systematic correction to the ideal gas law which takes the form of an expansion around the number density, $\rho$, of the gas in question. It looks like this: $$\frac{p}{k_bT}=\rho+B_2(T)\rho^2+B_3(T)\rho^3+\cdots$$ The form of this equation is not surprising. An ideal gas is simply one for which the coefficients $B_2$, $B_3$, etc. are equal to zero. These are called the second and third Virial coefficients.
According to Wikipedia (and I have heard this elsewhere), the Virial coefficients systematically correct the ideal gas law by considering specific interactions. To quote the Wikipedia article,
The second virial coefficient $B_{2}$ depends only on the pair interaction between the particles, the third ($B_{3}$) depends on 2- and non-additive 3-body interactions, and so on.
This quote gives me quite a good idea of how I would determine these coefficients theoretically using $\textit{ab initio}$ calculations, but I can't imagine how I could calculate only the 2-body interactions experimentally...
Indeed, this paper seems to present one way to determine them by the so-called Burnett method, but I don't have a way of accessing this paper and have never heard of this method.
So, if anyone could give me a summary of how to determine these coefficients, I would appreciate that and am quite interested to hear the answers.