  We characterize the changes in the longitudinal photospheric magnetic field
during 38 X-class and 39 M-class flares within $65^{\circ}$ of disk-center
using 1-minute GONG magnetograms. In all 77 cases we identify at least one site
in the flaring active region where clear, permanent, stepwise field changes
occurred. The median duration of the field changes was about 15 minutes and was
approximately equal for X-class and for M-class flares. The absolute values of
the field changes ranged from the detection limit of $\sim\!\!10$~G to as high
as $\sim\!\!450$~G in two exceptional cases. The median value was 69~G. Field
changes were significantly stronger for X-class than for M-class flares and for
limb flares than for disk-center flares. Longitudinal field changes less than
100~G tended to decrease longitudinal field strengths, both close to
disk-center and close to the limb, while field changes greater than 100~G
showed no such pattern. Likewise, longitudinal flux strengths tended to
decrease during flares. Flux changes, particularly net flux changes near
disk-center, correlated better than local field changes with GOES peak X-ray
flux. The strongest longitudinal field and flux changes occurred in flares
observed close to the limb. We estimate the change of Lorentz force associated
with each flare and find that this is large enough in some cases to power
seismic waves. We find that longitudinal field decreases would likely outnumber
increases at all parts of the solar disk within $65^{\circ}$ of disk-center, as
in our observations, if photospheric field tilts increase during flares as
predicted by Hudson et al.
