express intrinsic energy in an explicit form as a function of pressure and density. Instead he uses general thermodynamic formulas which include entropy.
On the processes of heat transfer within the discontinuity, he imposes a condition, , the physical significance of this condition is that in a shock wave there occurs only an exchange of heat between neighboring layers, so that the amount of heat removed from one layer is equal to the amount of heat received by the other one, which means that there are no exterior heat sources.
It takes Rankine some effort to derive a system of equations equivalent to that in Chapter 8 from the combination with the general thermodynamic formulas, and he then writes the equations for an ideal gas. Thus, Hugoniot's adiabatic equation in its customary form (Eq. (VIII-10)), could be derived from the formulas contained in Rankine's work by means of elementary algebraic transformations. Let us remind the reader, however, that Rankine preceded Hugoniot's work by some fifteen years.
Rayleigh summarized in 1910 the evolution of the history of shock waves [79]. He particularly emphasizes the unfairness involved in the term "Hugoniot's adiabatic curve".
Among the occasional papers it is interesting to note that as early as 1858 the English priest Earnshaw [49] came quite close to creating a theory of shock waves. Like Riemann he proceeded from the investigation of a compression wave of finite width in which (see Chapter 2) the wave crest overtakes the region of low pressure thus resulting in a discontinuity. However, the Reverend Earnshaw all of a sudden makes the surprising inference that nature does not suffer discontinuities or jumps. He makes some obscure statements on reflections, and implies that nature will somehow manage to prevent the formation of a shock wave or of a discontinuity. This is an educational example of the bad influence exerted by an erroneous philosophy on scientific research.
In a latter time, already after the discoveries of Riemann, Rankine and Hugoniot, the French scientist Pierre Duhem (one of the leaders of the "energetics" movement fashionable at the beginning of the twentieth century) denied the existence of shock waves on the assumption that in equations of gas dynamics involving viscosity and thermal conductivity there can be no
