20 PHYSICS. 
the crown was of pure gold. He is reported to have been so overjoyed at_ 
the discovery, that he forgot to dress himself, and rushed through the 
streets, crying: ‘I have found it! I have found it!’ To test the crown, 
he first found the absolute weight of a piece of pure gold, and then its 
weight when immersed in water. He treated the crown in like manner, 
and found that it displaced more water in proportion to its weight than 
the piece of pure gold, which proved that the metal had been mixed with - 
something lighter. 
5. A floating body displaces its own weight of the liquid. We have seen 
that, when a body is immersed in water, a pressure equal to the weight of 
the water displaced acts upon it, pushing it upward, while its own weight 
tends to make it sink. If, then, these two pressures are equal, the body 
will rest in any part of the liquid; if the weight of the body is 
greater than the weight of an equal volume of water, the body will sink 
to the bottom ; while, if the weight of a quantity of water, equal in 
volume to the body, is greater than the weight of the body, it will 
be forced upward to the surface. When this last takes place, the body is 
said to float. And, of course, part of it must rise above the surface, 
because, if it were to rest with its surface exactly level with the surface of 
the liquid, it might have rested at any part of the liquid; but it is 
supposed to have been forced upward to the surface. 
The question, then, comes to be, How much of the 
body will rise above the surface? or, which is the 
same thing, How much of. it will be in the water? 
We have seen that a body, immersed in a liquid, 
remains at rest when the weight of a quantity of the 
liquid equal in volume to itself,»is equal to its own 
weight ; and from this it is clear that a floating body 
. (as AB) will be at rest, when the weight of the water displaced by the 
submerged part B is exactly equal to the weight of the body. Thus 
the heaviest bodies can be made to float on a liquid, if only they can 
be so arranged as to displace a quantity of the liquid of weight greater 
than their own. A piece of iron sinks in water, but ships can be made of 
iron, because they are hollow, and displace a quantity of water of greater 
weight than their own. 















