The paper deals with the long standing problem of stylochronometry: periodization of texts with time of creation divided only by short period of time. Using exponential function we investigate the distribution of parts of speech in the first and last strong positions in verse (poetry) of a famous American romantic poet and abolitionist J.G. Whittier. The function fits the data with high precision, especially for the rhymed position, which points at the fact that the revealed tendency prevails over resistance of material. Comparison with similar data for H.W. Longfellow demonstrates universal character of the found tendency. The obtained coefficients of exponential functions make it possible to plot the texts in two-dimensional space of function coefficients, and to explicitly differentiate groups of texts which were written at different periods of time. Thus a tendency has been established, which was not mentioned before in stylometry or verse study. The investigated parameter is sensitive to weak alterations in style and possesses high relevancy for objective periodization of creative activity of an author.