■iS6 On certain supposed Irreversible Processes. 



contains products of the velocities, namely 



Q = l(u 2 + v 2 + ic*) +tlb{uu' + vc' + ww). 

 Here every b is negative, and is a function of /• the distance 

 between the two spheres whose velocities are u &c. and u' 

 &c., which function is very small unless r he very small. 

 This I claim to have proved in my Chapter V. The calcula- 

 tions are indeed laborious. I hope that some one, with or 

 without reading my chapter, will show us a more excellent 

 way. 



28. To show how the finite diameters of the spheres modi- 

 lies f 2 &c. let us suppose at a certain instant in a certain 



d£ 



region -~- is positive, and take the plane of the paper for that 



of x, z. Under these circumstances a sphere of finite 

 diameter having velocity from left to right is more likely to 

 experience a collision on its lower side, where f is less, than 

 on its upper, and is therefore on average deflected upwards. 

 A sphere moving from right to left is on average deflected 



downwards. The effect in either case is to increase -r~. If 



dz 



our molecules instead of being elastic spheres were centres of 



repulsive force of finite radius of action, the sphere moving 



to the right would experience on average a greater pressure 



on its under side. A sphere moving to the left a greater 



pressure on its upper side. The effect on -j- is the same as 





before 



(dP\ 2 

 . It follows that in the system of finite spheres I -7- J ? 



and therefore also p, has greater value than when the spheres 

 are infinitely small. 



29. It may be said that in criticising Boltzinann's process 

 I have set up a process of my own, namely the increase of f 2 

 &c.j and it maybe asked what is the directing condition in 

 this process, and is the process irreversible or not? The 

 answer is as follows : 



The finite dimensions of the molecules establish a limit 

 beyond which the condition of independence cannot exist. 

 Assuming that it can exist for molecules at considerable dis- 

 tance from each other, it cannot exist for molecules very near 

 each other. The argument is that if we assume the inde- 

 pendence absolutely, as I have done in my Chapter V., we 

 obtain a result inconsistent with that absolute independence. 

 For the form of distribution e _AQ is inconsistent with it. The 

 assumption of absolute independence is then inadmissible. 



