MONATOMIC GAS: DIFFUSION, VISCOSITY, AND THERMAL CONDUCTION. 12.3 
(d) Some Convenient Limitations of the Problem. 
Our immediate aim is to determine functions f (Ui, Vi, Wi), f 2 (U 2 , V 2 , W 2 ) which 
define the distribution of the peculiar velocities of the molecules, i.e., which are such 
that the number of molecules of the group considered (the appropriate suffix 1 or 2 
being added throughout), the components of whose velocities lie between (U, V, W) 
and (U + dll, V + c£v, W + cZW) respectively, is 
(119) v/(U. V, W)dU dVdW 
per unit volume. Besides the independent variables U, V, W, these functions 
/( U, V, W) will also involve such quantities as v, X, P, c, h and their derivatives, all 
of which are functions of (x, y, z, t ). The distribution of the peculiar velocities is, 
however, clearly unaffected by the absolute magnitude of the mean velocity c 0 
(though the same is not true of the derivatives of c 0 ). We may, therefore, legiti¬ 
mately make the simplifying convention that c 0 = 0 at the particular point and time 
under consideration. This merely amounts to a particular choice of uniformly moving 
axes of reference, a choice which the laws of dynamics leave quite unrestricted. 
Our concern being with problems of molecular rather than mass motion, we shall 
suppose that the acceleration of the gas as a whole is of the first order only, which 
requires that the resultant force on unit mass of the gas, viz., P 0 /m 0 , shall be small. 
We shall also suppose throughout that the velocity c\ of interdiffusion, and the 
derivatives, with respect to space and time, of v, X, c, h, are all of the first order, at 
most*; consequently, since in this paper we shall neglect second order quantities, 
products and derivatives of any of the small quantities just mentioned will he omitted 
from our analysis. 
§ 2. The Equation of Transfer of Molecular Properties. 
(a) The Equation of Continuity. 
The general equation of transfer for a function Q x of the velocity components 
{u) i, (v)i, (tv )i of a molecule of the first kind ist 
(2'01) AQ, = f- (nQ.) + 2 £ 
Ct x,y, z \_CX If ?/]_ I C \^/1 J — 
where AQi denotes the rate of change of at (x, y , 2 , t ) produced by the encounter 
of the molecules of the first kind with others of the same or the other kind. 
* [And likewise p o, T' 0 , when we are considering unsteady states in which T x ^ T a .—June 2, 
1916] 
t Cf. Chapter IX. of Jeans’ ‘Treatise’ (2nd ed.), and also, for the details of the reduction of (2 - 01)- 
(2’02) and (2• 09), ‘Phil. Trans.,’ A, vol. 216, p. 285. 
VOL. CCXVII.—A. 
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