Period changes in both modes of RRd stars in M 15

A new approach of the phase or O - C diagram is presented. The Fourier phase diagram method combines the advantages of both the phase diagram and Fourier technique. The method is applied for 13 RRd stars in the metal poor Oo II type globular cluster, M 15. Previously published periods are corrected up to 6 digits. The precise periods allowed us to get period changes with higher accuracy. Period changes were obtained not only for the first overtone but at the first time for the lower amplitude fundamental mode, too. The period change rate of the fundamental mode is significantly larger for each star than that of the first overtone. The P1/P0 ratio is increasing for most of the stars. Each period change rate is negative for the fundamental mode (except v51). For the first overtone both positive (5) and negative (6) period change rates were obtained. The most striking result is the period change behaviour of different sign for the fundamental and first overtone modes. The most remarkable case is v53 with β = - 0.31±0.06 day/Myr for the fundamental mode and β= + 0.14±0.01 day/Myr for the first overtone. This result suggests that caution is needed in connecting the sign of the period change rate and the direction of the stars's evolution in the HR diagram. Observational comparison is given for RRab and RRc stars and the fundamental and first overtone modes of RRd in M 15.