A U-tube has legs of unequal internal diameters d1 and d2, which are partly filled with immiscible liquids of densities, rho1 and rho2, respectively, and are open to the atmosphere at the top. If an additional small volume v2 of the second liquid is added to the right-hand leg, derive an expression-in terms of rho1, rho2, v2, d1 and d2-for sigma, the amount by which the level at B will fall. If rho1 is known, but rho2 is unknown, could the apparatus be used for determining the density of the second liquid?