  Potential theory on the complement of a subset of the real axis attracts a
lot of attention both in function theory and applied sciences. The paper
discusses one aspect of the theory - the logarithmic capacity of closed subsets
of the real line. We give simple but precise upper and lower bounds for the
logarithmic capacity of multiple intervals and a lower bound valid also for
closed sets comprising an infinite number of intervals. Using some known
methods to compute the exact values of capacity we demonstrate graphically how
our estimates compare with them. The main machinery behind our results are
separating transformation and dissymmetrization developed by V.N. Dubinin and a
version of the latter by K. Haliste as well as some classical symmetrization
and projection result for logarithmic capacity. The results of the paper
improve some previous achievements by A.Yu. Solynin and K. Shiefermayr.
