  We study the distribution of Mahler's measures of reciprocal polynomials with
complex coefficients and bounded even degree. We discover that the distribution
function associated to Mahler's measure restricted to monic reciprocal
polynomials is a reciprocal (or anti-reciprocal) Laurent polynomial on
[1,\infty) and identically zero on [0,1). Moreover, the coefficients of this
Laurent polynomial are rational numbers times a power of \pi. We are led to
this discovery by the computation of the Mellin transform of the distribution
function. This Mellin transform is an even (or odd) rational function with
poles at small integers and residues that are rational numbers times a power of
\pi. We also use this Mellin transform to show that the volume of the set of
reciprocal polynomials with complex coefficients, bounded degree and Mahler's
measure less than or equal to one is a rational number times a power of \pi.
