Sol. 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 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 in 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.