  The logarithmic capacity (also called Chebyshev constant or transfinite
diameter) of two real intervals $[-1,\alpha]\cup[\beta,1]$ has been given
explicitly with the help of Jacobi's elliptic and theta functions already by
Achieser in 1930. By proving several inequalities for these elliptic and theta
functions, an upper bound for the logarithmic capacity in terms of elementary
functions of $\alpha$ and $\beta$ is derived.
