16 MOLECULAR MOTION AND ITS ENEEGY 8 



possible causes of these variations. If Bernoulli's theory 

 gives, as its necessary consequence, a law that is only approxi- 

 mately exact, the hypothesis underlying the theory cannot be 

 quite true in every respect, but must be defective, even if only 

 slightly. 



In the assumptions with which we started there are two 

 different points which cannot be directly proved, and are there- 

 fore open to doubt. The first is the assumption that gases 

 are made up of molecules of very small dimensions, and the 

 second is the assumption that in gases there is no cohesion. 

 Neither of these is exactly true, and therefore neither can 

 be admitted except as an approximation to the truth ; and in 

 their inexactness lies ample ground for the departures from 

 Boyle's law. 



In the first place, if the dimensions of the molecules are 

 ^ not indefinitely small, the calculation which led to the law 

 is not exact. For it is only if the space actually occupied 

 by the molecules is absolutely negligible in respect of the 

 volume which contains them that we may justifiably conclude 

 that the frequency of collision is increased in the ratio s : 1 

 by a diminution of the volume in the ratio 1 : s 3 . If this con- 

 dition is not fulfilled there is less actual distance between 

 the molecules, which, therefore, collide the oftener with each 

 other and in the same ratio impinge the oftener against the 

 walls of the vessel in other words, the pressure is greater 

 than according to the former calculation ; and as this in- 

 crement in the pressure is the more considerable the less 

 the volume, the pressure must increase at a greater rate 

 than the volume diminishes. The denominator PV of the 

 ratio considered in 7, wherein P denotes the higher pres- 

 sure, is on this account greater than the numerator pv, 

 so that the ratio pvjPV has, as actually happens with 

 hydrogen, a value less than 1. 



A deviation in the reverse direction occurs when the 

 second hypothesis is sensibly in fault and the gas has 

 marked cohesion. For such a property will tend to lessen 

 the volume, which will, therefore, on this ground diminish 

 more rapidly than the pressure increases; PV will thus be 

 smaller than pv and the ratio pv/PV greater than 1, as is 



