FOUNDATIONS OF THE KINETIC THEORY OF GASES. 1039 



after Part I. was printed off, Prof. Burnside called my attention to the fact that the 

 equations of interchange of energy in § 23 are easily integrable without approximation. 

 But the approximate solution in the text suffices for the application made.] 



B. The Law of Distribution of Speed. 



In addition to what is said on this subject in the Introduction to Part II. , it may be 

 well to take the enclosed (from Proc. R. S. E., Jan. 30, 1888). 



" The behaviour parallel to y and z (though not the number) of particles whose 

 velocity-components are from x to x + dx, must obviously be independent of x, so that 

 the density of ' ends ' in the velocity space diagram is of the form 



fix) F(y,*). 



The word I have underlined may be very easily justified. No collisions count, except 

 those in which the line of centres is practically perpendicular to x (for the others each 

 dismiss a particle from the minority ; and its place is instantly supplied by another, 

 which behaves exactly as the first did), and therefore the component of the relative speed 

 involved in the collisions which we require to consider depends wholly on y and z motions. 

 Also, for the same reason, the frequency of collisions of various kinds (so far as x is con- 

 cerned) does not come into question. Thus the y and z speeds, not only in one x layer 

 but in all, are entirely independent of x ; though the number of particles in the layer- 

 depends on x alone." 



C. Viscosity. 



In my " Reply to Prof. Boltzmann " I promised to give a further approximation to the 

 value of the coefficient of Viscosity, by taking account of the alteration of permeability 

 of a gas which is caused by (slow) shearing disturbance. I then stated that a rough 

 calculation had shown me that the effect would be to change my first, avowedly approxi- 

 mate, result by 11 or 12 per cent. only. I now write again the equations of § 36, 

 modifying them in conformity with the altered point of view. 



The exponential expression in that section for the number of particles crossing the 

 plane of yz, must obviously now be written 



£ ° smOdO/z, 



where v is the velocity relative to the absorbing layer at £, and e also is no longer constant. 



But we have at once 



v = v + B£ sin 6 cos <£ , 

 so that the exponent above is 



SGC w 



' (ev + (ev)'Bi; sin 6 cos <f>)d^ . 



