PRINCIPLE OF ARCHIMEDES 53 



balance below the bridge, and, with the sinker still in water, weigh. Now 

 tie the cork to the lead ; lower into the water, taking care to remove air 

 bubbles, and find weight. As the lead is in the water throughout the 

 weighings the result is not affected by it. Find the weight, volume, and 

 density of the cork. 



The volume of small solids of irregular shape. The volume of a 

 solid can be found by observing the amount of water which it displaces 

 in a graduated vessel. As the graduations on cylinders seldom read 

 by less than 1 c.c. it is evident that this method does not admit of a 

 degree of accuracy much beyond the whole number. The Principle 

 of Archimedes provides a means of finding the volume of a small solid, 

 correct to the second place of decimals. By weighing the body in air 

 and in water as described in Section iii. the loss of weight is found. 

 This gives the weight of a volume of water equal to the volume of 

 the body. And since one gram of water has a volume of one cubic 

 centimetre, the number of grams of water displaced gives the number 

 of cubic centimetres also, and hence the volume. 



Relative density of solids. The fact that when a body is immersed 

 in water it loses weight equal to the weight of the water displaced by 

 it, provides the means of determining the density of a solid compared 

 with water. 



All it is necessary to know is : 



1. The weight of the object ; this can be determined by weighing 



it in air. 



2. The weight of an equal volume of water. 



The Principle of Archimedes enables this to be done in the following 

 manner : 



The object is suspended by means of a fine thread, from one side of 

 the beam of a balance, in such a way that it is completely immersed 

 in water. Then by weighing it is found that the weight is less than 

 when hanging in air, on account of the loss of weight in the water. 

 The buoyancy of the water acting upwards overcomes part of the pull 

 of the earth downwards. The difference in the weight of the object 

 in air and its weight when immersed in water gives the weight of a 

 volume of water equal to the volume of the object. From these numbers 

 the density of the solid compared with water as a standard can be 

 calculated at once. 



weight of the object in air 



Relative density of the solid = weight of an equal vohime of water 



weight in air 



loss of weight in water 



