Intermediate Asymptotics

When I entered my third year of university study, I was introduced to the topic of Fluid Mechanics $-$ the mathematical analysis of the flow of liquids and gases. I found that the concept of a fluid that is analyzed in that context is not exactly that which applies to real fluids.  The "fluids" discussed in the lectures had local properties, such as density, pressure and velocity, described by continuous functions for which it was possible to assign values at points situated in the fluid.  However, we all know that real fluids are composed of atoms and/or molecules and so do not correspond to such a description.  This discrepancy is addressed in the opening chapter of one of the textbooks we were set: D. E. Rutherford's2 Fluid Dynamics (Edinburgh: Oliver & Boyd, 1959).  Rutherford's careful discussion bears quoting in full.