  We have studied the hidden long-range order (LRO) of the frustrated
pyrochlore magnet Tb$_2$Ti$_2$O$_7$ by means of specific-heat experiments and
Monte-Carlo (MC) simulations, which has been discussed as the LRO of quadrupole
moments inherent to the non-Kramers ion of Tb$^{3+}$. We have found that the
sharp specific-heat peak is collapsed into a broad hump by magnetic fields
above 0.3 T for $H//[001]$. This result, qualitatively reproduced by MC
simulations, suggests that a field-induced magnetic state overcomes the
quadrupolar LRO state, as a similar case of a classical spin ice. The present
results support the interpretation that Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ is a
unique material in the boundary between the quadrupolar ($x \geq x_c =
-0.0025$) and spin-liquid ($x \leq x_c$) states, where the magnetic field along
the [001] axis is a tuning parameter which induces the magnetic ordered state.
