  Electric quadrupolar state in a frustrated quantum magnet $\rm Tb_{2+\it
\delta}Ti_{2-\it \delta}O_7$ has been studied by means of ultrasonic and
magnetostriction measurements. A single crystal showed elastic anomaly at about
0.4 K, manifesting a long-range quadrupole ordering. By investigating
anisotropy of the magnetoelastic responses, we found a crossover temperature
for the strongly correlated quadrupole state, below which the experimental data
of elastic constant and magnetostriction become qualitatively different from
their calculations based on a single-ion model. We suppose that relatively high
onset temperature of the quadrupole correlation compared with the transition
temperature is ascribed to the geometrical frustration effect, and this
correlated state seems to be responsible for the unusual properties in the
paramagentic state of $\rm Tb_2Ti_2O_7$.
