The investigation of electrons of all possible initial phases and phase velocities at transition between betatron and synchrotron phases of an electron synchrotron has been undertaken with a view toward determining the effect of different ways of applying the r‐f. It has been found that for an average accelerator there is an advantage in a moderately slow increase of the voltage from zero to its final value, while for the extreme case where particles enter the transition region with large phase velocity, an asymptotic final radial oscillation amplitude is reached which is independent of the manner in which the voltage is applied, provided only that it is applied adiabatically.