Daniel’s phonological diagram has been the foundation of linguistic vowel phone research for more than 100 years.The primary defect of the diagram is that phone research,based on it,couldn’t be quantitative.On the basis of the discovery and the definition of the O-phoneme this paper attempts to create a Cartesian Coordinate System to construct mathematical models for quantitative and dynamic study for phonemes.As an example,a power function curve is developed for the characteristic analysis on English vowels.