In the first part, the stability of two-dimensional parallel flow is discussed. A more restrictively general stability criterion for inviscid parallel flow is obtained analytically. First, a sufficient criterion for stability is found as either −μ1 < U ′′ U−Us < 0 or 0 < U ′′ U−Us in the flow, where Us is the velocity at the inflection point, and μ1 is the eigenvalue of Poincaré’s problem. Seco...