  Among known strongly lensed quasar systems, ~25% have gravitational
potentials sufficiently flat (and sources sufficiently well aligned) to produce
four images rather than two. The projected flattening of the lensing galaxy and
tides from neighboring galaxies both contribute to the potential's quadrupole.
Witt's hyperbola and Wynne's ellipse permit determination of the overall
quadrupole from the positions of the quasar images. The position of the lensing
galaxy resolves the distinct contributions of intrinsic ellipticity and tidal
shear to that quadrupole. Among 31 quadruply lensed quasars systems with
statistically significant decompositions, 15 are either reliably ($2\sigma$) or
provisionally ($1\sigma$) shear-dominated and 11 are either reliably or
provisionally ellipticity-dominated. For the remaining 8, the two effects make
roughly equal contributions to the combined cross section (newly derived here)
for quadruple lensing. This observational result is strongly at variance with
the ellipticity-dominated forecast of Oguri & Marshall (2010).
