  We are concerned with conservation laws and integral relations associated
with rational solutions of the Boussinesq equation, a soliton equation solvable
by inverse scattering which was first introduced by Boussinesq in 1871. The
rational solutions are logarithmic derivatives of a polynomial, are
algebraically decaying and have a similar appearance to rogue-wave solutions of
the focusing nonlinear Schr\"{o}dinger equation. For these rational solutions
the constants of motion associated with the conserved quantities are zero and
they have some interesting integral relations which depend on the total degree
of the associated polynomial.
