  Gravitational wave emissions (GWEs) of pulsars could not only make them
promising targets for continuous gravitational wave searches but also leave
imprints in their timing data. We interpret the measured braking index of PSR
J1640-4631 with a model involving both the GWE and dipole magnetic field decay.
Combining the timing data of PSR J1640-4631 and the theory of magnetic field
decay, we propose a new approach of constraining the number of precession
cycles, $\xi$, which is highly uncertain currently but can be tightly related
to the interior physics of a neutron star and its GWE. We suggest that future
observation of the tilt angle $\chi$ of PSR J1640-4631 would not merely help to
constrain $\xi$ but also possibly provide information about the internal
magnetic field configuration of this pulsar. We find that $\xi$ would be larger
than previous estimates unless a tiny angle $\chi\lesssim5^\circ$ is observed.
Furthermore, a measured angle $\chi\gtrsim12^\circ$ would indicate $\xi\gtrsim
10^6$, which is at least ten times larger than that suggested previously.
