173, 174] Equations of Mass Motion 153 



These forces may arise either from forces between pairs of molecules, or 

 from the action upon the molecules of an external field of force. If there is 

 an external field of force of amount H, H, Z per unit mass, the contribution 

 made to ^X will of course be 



Hmvdxdydz .............................. (361). 



This part of the system of forces need not be discussed further: we now 

 turn to the intermolecular forces. We are supposing those molecules to be 

 inside dxdydz of which the centres are inside dxdydz. To discuss the 

 intermolecular forces, then, consistently with the suppositions already made, 

 we must regard the molecules as point-centres of force, the position of the 

 centre of force coinciding with the centre of the molecule. This supposition 

 is, of course, perfectly general. For instance, if the molecules are elastic 

 spheres of diameter <r, we take the law of force between the supposed 

 point-centres to be some function of the distance which becomes infinite 

 when the distance is less than er, and zero when the distance is greater 



f(T\ n 



than a e.g. f-J where n is infinitely great. 



In general, it is not possible to represent the effect of a system of forces 

 acting upon a material medium by a system of suitably-chosen pressures 

 inside the medium. In the present case, however, this is possible, if we make 

 the assumption that the range of molecular action is small compared with 

 the linear scale of variation of density, etc., in the gas. For subject to this 

 assumption we shall be able to choose the element dxdydz of such a size 

 that the density, etc., may be regarded as constant throughout, while at the 

 same time the intermolecular forces experienced by the molecules inside it 

 are solely forces between pairs of molecules both of which are very near to 

 one and the same face of the element : the element can, in fact, be too 

 great for intermolecular action across it to be perceptible. 



Choosing the element of volume in this way, the forces exerted across any 

 one of the faces of the element may be regarded simply as a system of pressures 

 acting upon the surface of the element. The components of pressure will 

 obviously be continuous functions of position in space, so long as it is under- 

 stood that the edges of the faces of the element are large compared with 

 the distance between adjacent molecules. 



If we denote the components of pressure per unit area acting across a 

 small plane area perpendicular to the axis of x by vr xx , Ts xy , ^ xz , and adopt a 

 similar notation as regards pressures across planes perpendicular to the axes 

 of y and z, we see that the ^-component of all the molecular forces which act 

 on the element dxdydz can be put in the form 



+ 



dy d 



