FOUNDATIONS OF THE KINETIC THEOEY OF GASES. 253 



fleeting occupants, the minority being (relatively) as it were permanent lodgers, 

 These are those whose speed perpendicular to the planes is very nearly that of 

 the planes themselves. The individuals of each class are perpetually changing, 

 those of the majority with extraordinary rapidity compared with those of the 

 minority; but each elms, as such, forms a definite "group of the community." 

 The method of averages obviously applies to each of these classes separately ; 

 and it shows that the minority will behave, so far as y and z motions are 

 concerned, as if they alone had been enclosed between two material planes, 

 and as if their lines of centres at impact were always parallel to these. The 

 instant that this ceases to be true of any one of them, that one ceases to belong 

 to the group ; — and another takes its place. Their behaviour under these 

 circumstances (though not their number) must obviously be independent of the 

 speed of the planes. Hence the law of distribution of components in the 

 velocity space-diagram must be of the form 



and symmetry at once gives the result above. 



[[Inserted March 5th, 1887.) Another objection, but of a diametrically 

 opposite character, raised by Mr Burbury " ;: " and supported by Professor 

 Boltzmann, t is to the effect that in my first paper I have unduly multiplied 

 the number of preliminary assumptions necessary for the proof of Maxwell's 

 Theorem concerning the distribution of energy in a mixture of two gases. 

 In form, perhaps, I may inadvertently have done so, but certainly not in 

 substance. 



The assumptions which (in addition to that made at the commencement of 

 the paper (§ 5) for provision against simultaneous impacts of three or more 

 particles, which was introduced expressly for the purpose of making the results 

 applicable to real gases, not merely to imaginary hard spheres,) I found it 

 necessary to make, are (§ 18) as follows ; briefly stated. 



(A) That the particles of the two systems are thoroughly mixed. 



* The Foundations of the Kinetic Theory of Gases. Phil. Mag. 1886, I, p. 481. 



f Uber die zum theoretischen Beweise des Avogadro'-schen Gesetzes erforderlichen Voraussetzungen. 

 Sitzb. derkais. Akad. XCIV, 1886, Oct. 7. In this article Prof. Boltzmann states that I have nowhere 

 expressly pointed out that my results are applicable only to the case of hard spheres. I might plead 

 that the article he refers to is a brief Abstract only of my paper ; but it contains the following state- 

 ments, which are surely explicit enough as to the object I had in view : — 



" This is specially the case with his [Maxwell's] investigation of the law of ultimate partition of 

 energy in a mixture of smooth spherical particles of two different kinds." 



" It has since been extended by Boltzmann and others to cases in which the particles are no longer 

 supposed to be hard smooth spheres." 



"Hence it is desirable that Maxwell's proof of his fundamental Theorem should be critically 

 examined." Then I proceed to examine it, not Professor Boltzmann's extension of it. In my paper 

 itself this limitation is most expressly insisted on. 



