MOLECULAR MOTIONS AND TEMPERATURE 157 



side there will be the same number of impacts per 

 second as before, the number on each unit of area and 

 hence the pressure on the sides, also, will be. doubled. 

 We notice, then, that as the volume is halved the 

 pressure is doubled; in other words, the pressure 

 exerted by the moving gnats and the volume of their 

 container will vary inversely, exactly as Boyle found 

 was true for a definite volume of air. 



Suppose that we keep the volume constant but 

 introduce an additional number of gnats. If there 

 were originally N gnats, or rather let us say molecules, 

 and this number is increased to N' then the number 

 of impacts occurring each second should be N'/N times 

 as many as originally. The pressure will be propor- 

 tionately increased. Thus, if it was initially P it will 

 be P', where P'/P = N'/N. Let V be the volume. 

 It has not changed while more molecules were added. 

 If we now increase the volume until the pressure is 

 restored to its original value of P we shall find the new 

 volume, V, to be greater than V in the same pro- 

 portion as P' bore to P. Hence we have V'/V = N'/N. 

 Therefore, equal volumes at equal pressures will con- 

 tain equal numbers of molecules. Or, in general, if the 

 volumes are equal, the pressures will be directly as the 

 number of molecules. Similarly, if the pressures are 

 equal, the volumes will be directly as the number of 

 molecules. 



Consider again the original illustration of a swarm of 

 gnats. A person with poor eyesight who failed to see 

 the swarm might, nevertheless, feel the pressure of their 

 impacts. Suppose that some light object, larger than 

 a gnat, as for example a small bit of very thin tissue 



