Water rises in a capillary tube due to surface tension and the adhesive force between water and the glass wall. The height $h$ is given by Jurin's law: $h=\frac{2\gamma \cos \theta }{\rho gr}$, where $\gamma$ is surface tension, $\theta$ is the contact angle, $\rho$ is density, $g$ is gravity, and $r$ is the tube radius. To increase $h$, we must decrease the effective gravity. Placing the apparatus in a downward-accelerating elevator reduces the net downward acceleration, thus increasing the height.

Final answer: Place the whole apparatus in an elevator accelerating downwards.