114 Physical Properties [CH. vi 



It appears from this that the values of the mean velocities can be obtained 



~~ 



by multiplying the last column in the above table by AK or '921. 



V O7T 



At this stage, we obtain our first insight, as regards quantitative 

 measurements, into the internal mechanism of a gas. The order of 

 magnitude of the molecular-velocities could, however, have been predicted 

 without actual detailed calculation. 



For instance, if gas is allowed to stream out into a vacuum through 

 a small hole in the containing vessel, the velocity of efflux is nothing else 

 than the velocities of the individual molecules, which would have been 

 simply molecular-velocities inside the vessel, had the hole not been present. 

 Thus the mean molecular-velocity must be comparable with the velocity of 

 efflux of the main stream of gas, and this velocity is known to be of the 

 order of magnitude of the velocities tabulated in the last column of the 

 table on the preceding page. 



Or again, a disturbance at any point in a gas will produce an effect on 

 the molecules in its immediate neighbourhood. - When these molecules 

 collide with those in the next layer of gas, the effect of this disturbance is 

 carried on into that layer, and so on indefinitely. Thus the molecules act as 

 carriers of the effect of any disturbance, so that the disturbance is propa- 

 gated, on the whole, with a velocity comparable with the mean velocity of 

 motion of the molecules, just as, for instance, news which is carried by relays 

 of messengers, spreads with a velocity comparable with the mean rate of 

 travelling of the messengers. The propagation of a disturbance in the gas 

 is, however, nothing but the passage of a wave of sound, and the velocity of 

 sound is known to be comparable with the values of G given in the table. 



MOLECULES OF FINITE SIZE. 

 Calculation of Pressure. 



132. When the size of the molecules may not be regarded as infinitesimal, 

 the calculation of the pressure which has been given, in which the size of the 

 molecules was neglected, requires correction. 



A correction of this type was first given by Van der Waals, in his great 

 essay On the Continuity of the Liquid and Gaseous States*. We shall first 

 give an explanation of the corrections given by Van der Waals, which, it will 

 be found, lead to an equation which expresses the deviations from Boyle's 

 Law to a first approximation only, and we shall afterwards give a more 

 general calculation of the pressure, which will not be restricted to small 

 deviations from Boyle's Law. 



* The original edition (1873) is in Dutch, published by Sigthoff, Leyden. There is a German 

 translation by Roth (1881, Earth, Leipzig) and this has been translated into English by Threlfall 

 and Adair (1890, Physical Memoirs published under the direction of the Physical Society, Taylor 

 and Francis, London). The references in the present book are to the English Translation. 



