FOUNDATIONS OF THE KINETIC THEORY OE GASES. 261 



Maxwell was led by his experimental measures of Viscosity, which seemed 

 to show""' that it increases nearly in proportion to the first power of the absolute 

 temperature, to discard the notion of hard spheres, and to introduce the 

 hypothesis of particles repelling one another with force inversely as the fifth 

 power of the distance. I have already stated that there are very grave ob- 

 jections to the introduction of repulsion into this subject, except of course in 

 the form of elastic restitution. That the particles of a gas have this property 

 is plain from their capability of vibrating, so that they must lose energy of 

 translation by impact ; and I intend, in the next instalment of this investigation, 

 so far to modify the fundamental assumption hitherto made as to deduce the 

 effects corresponding to a coefficient of restitution less than unity; and also to 

 take account of molecular attraction, specially limited in its range to distances 

 not much greater than the diameter of a sphere. 



XIII. Thermal Conductivity. 



38. We must content ourselves with the comparatively simple case of the 

 steady flow of heat in one direction ; say parallel to the axis of x. This will be 

 assumed to be vertical, the temperature in the gas increasing upwards, so as to 

 prevent convection currents. No attention need, otherwise, be paid to the 

 effects of gravity. 



Hence the following conditions must be satisfied : — 



(a) Each horizontal layer of the gas is in the special state, compounded 



with a definite translation vertically. 



(b) The pressure is constant throughout the gas. 



(c) There is, on the whole, no passage of gas across any horizontal plane. 



(d) Equal amounts of energy are, on the whole, transferred (in the same 



direction) across unit area of all such planes. 



39. Let n be the number of particles per unit volume in the layer between 

 x and x + dx; v the fraction of them whose speed, relatively to the neighbours 

 as a whole, lies between v and v + dv ; a the speed of translation of the layer. 



The number of particles which pass, per unit area per second, from x positive 

 through the plane x = 0, is the sum of those escaping, after collision, from all the 

 layers for positive, x, and not arrested on their way : — viz., 



\ f P /£«•—•/•""■ sin 6d6 vcos0 -^dx . 



?/o Jo Jo vcos6 



Here a, though in any ordinary case it need not be more than a very small 

 fraction of an inch, is a quantity large compared with the mean free path of a 



* Cf., however, Stokes, Phil. Trans., 1886, vol. clxxvii. p. 786. 



