212 PHENOMENA DEPENDENT ON MOLECULAR PATHS 84 



84. Phenomena in very Rarefied Gases 



The molecular free path increases with increase of rare- 

 faction in the ratio of the increase of the volume ; so too, 

 therefore, does the coefficient of slip. But we cannot, 

 therefore, believe that the molecular paths in excessively 

 rarefied gases, as in the vacuum of a mercury air-pump, 

 attain a considerable length. If we assume, for instance, 

 that such a pump were to rarefy the air 100,000 times, or to 

 a pressure of less than y^ mm., the free path, which is 

 -00001 cm. under atmospheric pressure, would become 

 1 cm. ; it therefore always remains a remarkably small 

 path for a body projected with a speed of something like 

 450 metres per second. The number of encounters to which 

 a molecule is exposed remains still very great even in such 

 a condition of rarefaction ; it would amount to 46,500 per 

 second. 



This calculation certainly does not deserve unconditional 

 confidence, if only because Boyle's law does not hold at 

 such small pressures. But, under any circumstances, this 

 consideration is well suited to show that a gas, even if 

 exceedingly rarefied, is anything but a vacuum. A nomi- 

 nally vacuous space, obtained either by an air-pump or even 

 by Torricelli's method, is distinctly not vacuous, but is so 

 uniformly filled with a medium, of a density certainly very 

 small, that our observations will still give us the impression 

 of the space being continuously filled. 



The lengthening of the free path helps, indeed, to remove 

 more quickly and easily any inequalities that exist in the 

 distribution of pressure, temperature, &c. According to the 

 kinetic theory, the transference of any action is the result of 

 the transference of molecules from one layer to another. 

 The longer the paths of the molecules, the wider will therefore 

 be the ranges within which all inequalities will be removed. 



This remark remains of force, even when the inequality 



consists in the distribution of electrical tension. This is the 



reason why electrical discharges in regions of rarefied air, as, 



'for instance, in Geissler's tubes, take place at far greater 



distances than in denser air. 



