  We have observed the Be/X-ray pulsar binary system X Per/4U 0352+30 on 61
occasions spanning an interval of 600 days with the PCA instrument on RXTE.
Pulse timing analyses of the 837-s pulsations yield strong evidence for the
presence of orbital Doppler delays. We confirm the Doppler delays by using
measurements made with the RXTE All-Sky Monitor. We obtain an orbital period of
250 days, a projected semimajor axis of the neutron star of 454 lt-s, a mass
function of 1.61 solar masses, and a modest eccentricity of 0.11. We discuss
the formation of the system in the context of the standard evolutionary
scenario for Be/X-ray binaries with consideration of the possibility that the
birth of the neutron star was accompanied by a kick of the type often inferred
from the velocity distribution of isolated radio pulsars. The orbital
eccentricity just after the supernova explosion was almost certainly virtually
the same as at present, because the Be star is much smaller than the orbital
separation. We find that the system most likely formed from a pair of massive
progenitor stars, and probably involved a quasi-stable and nearly conservative
transfer of mass from the primary to the secondary. We find that the He star
remnant of the primary most likely had a mass less than 6 solar masses after
mass transfer. Finally, we speculate that there may be a substantial population
of neutron stars formed with little or no kick.
