# Letter: Sinking feeling

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Sir: I am surprised there is so much confusion over Archimedes' principle. (Technoquest, 23 September; letters, 26, 27 September).

A body immersed in water displaces its own volume. If you put an object into a bath filled to the brim, and collect the water that flows over the edge and pour it into a measuring cylinder, you have the volume of the object. (According to legend, when Archimedes made his discovery he had been asked by the king to determine whether his new crown was solid gold. He knew the mass or weight of the crown - as far as he was concerned, the two terms were equivalent and can be treated as such in this case. He also knew what volume that weight of gold should have. He now needed to measure the volume of the crown without destroying it, and the bath gave him the method.)

The displaced water has to be raised against the force of gravity, and the weight of this water leads to the buoyant force resisting the immersion of the object. For a material denser than water, such as lead or gold, this force is less than the weight of the object and it sinks. For a body made of a substance less dense than water, such as wood, or that is hollow, such as a ship, the weight of water displaced is greater than the weight of the body, and the object floats, reaching an equilibrium at the level where the weight of the volume of water displaced equals the weight of the object.

PAUL DORMER

Guildford,

Surrey

Sir: It is common for mass and weight to be confused, but Joy Bampton (letter, 27 September) has managed to confuse mass and weight and volume, all at the same time. Volume and mass are not the same thing.

Whether or not an object floats depends on its density, which is its mass divided by its volume. If its density is less than that of water, gravity will pull an equal volume of water down harder than it pulls the object, so the object will rise and the water sink. If the object's density is greater, it will sink and the water will rise.

ALAN ROBINSON

York

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