DIFFUSION. 627 



cannot point out one place in which the .lower fluid is ascending, and another 

 in which the upper fluid is descending. There are no currents visible to us, 

 and the motion of the material substances goes on as imperceptibly as the 

 conduction of heat or of electricity. Hence the motion which constitutes dif- 

 fusion must be distinguished from those motions of fluids which we can trace 

 by means of floating motes. It may be described as a motion of the fluids, 

 not in mass but by molecules. 



When we reason upon the hypothesis that a fluid is a continuous homo- 

 geneous substance, it is comparatively easy to define its density and velocity; 

 but when we admit that it may consist of molecules of different kinds, we 

 must revise our definitions. We therefore define these quantities by considering 

 that part of the medium which at a given instant is within a certain small 

 region surrounding a given point. This region must be so small that the 

 properties of the medium as a whole are sensibly the same throughout the 

 region, and yet it must be so large as to include a large number of mole- 

 cules. We then define the density of the medium at the given point as the 

 mass of the medium within this region divided by its volume, and the 

 velocity of the medium as the momentum of this portion of the medium 

 divided by its mass. 



If we consider the motion of the medium relative to an imaginary surface 

 supposed to exist within the region occupied by the medium, and if we define 

 the flow of the medium through the surface as the mass of the medium 

 which in unit of time passes through unit of area of the surface, then it 

 follows from the above definitions that the velocity of the medium resolved 

 in the direction of the normal to the surface is equal to the flow divided by 

 the density. If we suppose the surface itself to move with the same velo- 

 city as the fluid, and in the same direction, there will be no flow through it. 



Having thus defined the density, velocity, and flow of the medium as a 

 whole, or, as it is sometimes expressed, "in mass," we may now consider one 

 of the fluids which constitute the medium, and define its density, velocity, 

 and flow in the same way. The velocity of this fluid may be different from 

 that of the medium in mass, and its velocity relative to that of the medium 

 is the velocity of diffusion which we have to study. 



792 



