A method used by Tsien to derive similarity rules for hypersonic flows is utilized to derive Von Karman's similarity rules for transonic flows. At the lower limit of the transonic region of flow the theory yields a formula for the critical stream Mach numbers of a given family of symmetrical profiles. It is further shown that this formula can also be obtained by means of the Prandtl-Glauert small-perturbation method. Investigation of the behavior of the similarity parameter in the region where the thickness coefficient approaches zero and the critical stream Mach number approaches unity shows that it possesses a limiting value characteristic of the prescribed family of shapes.