At an atmospheric pressure of \(1.00 \mathrm{~atm}\), the height of the liquid in the tube of a mercury barometer is \(760 \mathrm{~mm}\) only if you ignore capillary rise in the tube. Obtain an expression that shows how \(h\), the number of millimeters the mercury height differs from \(760 \mathrm{~mm}\), depends on the diameter \(d\) of the tube, and then calculate the value of \(h\) for \(d=7.0 \mathrm{~mm}\). The contact angle for mercury on this glass tube is \(137^{\circ}\), and its mass density is \(13.5 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\).