  The Isochronous Mass Spectrometry (IMS) is a powerful technique developed in
heavy-ion storage rings for measuring masses of very short-lived exotic nuclei.
The IMS is based on the isochronous setting of the ring. One of the main
parameters of this setting is the transition energy $\gamma_{t}$. %The
transition energy $\gamma_{t}$ plays an important role in the isochronous mass
spectrometry (IMS). It has been a challenge to determine the $\gamma_{t}$ and
especially to monitor the variation of $\gamma_{t}$ during experiments. In this
paper we introduce a method to measure the $\gamma_{t}$ online during IMS
experiments by using the acquired experimental data. Furthermore, since the
storage ring has (in our context) a relatively large momentum acceptance, the
variation of the $\gamma_{t}$ across the ring acceptance is a source of
systematic uncertainty of measured masses. With the installation of two
time-of-flight (TOF) detectors, the velocity of each stored ion and its
revolution time are simultaneously available for the analysis. These quantities
enabled us to determine the $\gamma_{t}$ as a function of orbital length in the
ring. The presented method is especially important for future IMS experiments
planned at the new-generation storage ring facilities FAIR in Germany and HIAF
in China.
