  PSR J1518+4904 is one of only 9 known double neutron star systems. These
systems are highly valuable for measuring the masses of neutron stars,
measuring the effects of gravity, and testing gravitational theories. We
determine an improved timing solution for a mildly relativistic double neutron
star system, combining data from multiple telescopes. We set better constraints
on relativistic parameters and the separate masses of the system, and discuss
the evolution of PSR J1518+4904 in the context of other double neutron star
systems. PSR J1518+4904 has been regularly observed for more than 10 years by
the European Pulsar Timing Array (EPTA) network using the Westerbork, Jodrell
Bank, Effelsberg and Nancay radio telescopes. The data were analysed using the
updated timing software Tempo2. We have improved the timing solution for this
double neutron star system. The periastron advance has been refined and a
significant detection of proper motion is presented. It is not likely that more
post-Keplerian parameters, with which the individual neutron star masses and
the inclination angle of the system can be determined separately, can be
measured in the near future. Using a combination of the high-quality data sets
present in the EPTA collaboration, extended with the original GBT data, we have
constrained the masses in the system to m_p<1.17 msun and m_c>1.55 msun (95.4%
confidence), and the inclination angle of the orbit to be less than 47 degrees
(99%). From this we derive that the pulsar in this system possibly has one of
the lowest neutron star masses measured to date. From evolutionary
considerations it seems likely that the companion star, despite its high mass,
was formed in an electron-capture supernova.
