A clean glass capillary tube of inner radius $0.40\ \text{mm}$, open at both ends and with a very thin wall, is held vertical. Water is run into it from the top, and the extra water is allowed to drip out of the lower end until the dripping stops. The surface tension of water is $0.072\ \text{N/m}$, its contact angle with clean glass is zero, its density is $1000\ \text{kg/m}^3$, and $g = 10\ \text{m/s}^2$. At its lower end the water can bulge out of the tube, at most into a half sphere of the tube's inner radius. What is the longest column of water that the tube can hold in this way?