Good point Grapes although the sound barrier was broken quite a while before my time (October 14, 1947). Interestingly enough I still remember my Calculus teacher almost cursing the engineers of that age for not following the airflow equations out to large enough values where they would have noticed a discontinuity in the function. He was quite upset at the number of test pilots who died because of this mathematical oversight. It certainly made me double check my Calculus answers.