vii PRINCIPLE OF ARCHIMEDES 95 



to the number of cubic centimetres above the initial level. 

 Take out the test-tube and weigh it ; the weight will be found 

 equal to the weight of water displaced. Repeat the experiment 

 with the test-tube floating at different depths. 



Applications of Ar chimedes's Principle. From the foregoing 

 experiments it is easy to understand many interesting facts. 

 For instance, a ship made of iron and containing all kinds of 

 heavy things is able to float in water although the material of 

 which they are made is heavier than water. Evidently the 

 reason is that the ship and all its contents only weighs the same 

 as the volume of water displaced by the immersed part of the 

 hull. Or, to put the fact another way, the ship as a whole 

 weighs less than a mass of water the same size as the ship would 

 weigh. We have seen (Expt. 79) that when an object weighs 

 the same as an equal volume of water, it will remain suspended 

 in the water ; when it weighs more than an equal volume of 

 water it sinks (Expt. 78) ; and when it weighs less than an equal 

 volume of water it floats (Expts. 81 and 82). This principle 

 applies to all fluids, that is, all liquids, and to all gases as well. 

 It explains that a balloon rises because the gas contained in it, 

 together with the bag and all the tackle, weighs less than the 

 weight of an equal volume of air. If the balloon were free to 

 ascend it would rise to a height where its weight would be equal 

 to the weight of an equal volume of the surrounding air. 



Density. We shall now apply the principle demonstrated by 

 the foregoing experiments to the determination of the densities 

 of solids and liquids. 



EXPT. 85. Procure equal volumes of different substances, 

 e.g., a cubic inch of wood, lead, cork, marble, and determine 

 their masses by means of a balance. Notice they are different. 



EXPT. 86. Compare the volume of a pint of water with that 

 of one and a quarter pounds of iron. Observe their masses, 

 as determined by a balance, are equal, but their volumes very 

 unequal. 



EXPT. 87. Fill two equal flasks with water and methylated 

 spirit respectively, and weigh. Show that the masses are 

 different, 



We thus see that equal volumes of different substances have 

 different masses, This truth is expressed by saying they have 

 different densities. 



If we keep to the unit of volume, the numbers representing 



