If the scales are in equilibrium the weights in one pan will equal the combined weights of the glass tube and the column of mercury in the tube which is above the level of the mercury in the vessel beneath.
In fact the closed upper end of the tube is subject to atmospheric pressure, i.e, to the force exerted by the column of air above, the weight of which equals in practice the weight of the column of mercury in the tube. The thickness of the glass sides need not be taken into account, since atmospheric pressure also acts on them from below. But atmospheric pressure does not act on the tube from below. (Atmospheric pressure causes a rise of the mercury in the tube, but since the mercury does not reach the top end of the tube, this pressure is not transmitted to the top end.)
In this we are neglecting the loss of weight of the end of the barometer tube which is immersed in the vessel.
143. The Torricellian experiment will not work in this case. Although, in a vertical position, there will be a position of equilibrium obtaining for the two liquids, this will be unstable equilibrium, since the common centre of gravity of the liquids does not occupy its lowest position. Therefore the mercury will flow out of the tube and the water will flow in.
THE MECHANICS OF LIQUIDS AND GASES 175