The original purpose of this thesis was to determine the offset of injection over a period of time which is large compared to the interval over which electrons can be accepted. This has been done for the case of constant-momentum injection; Eq. (b5) shows the dependence of this acceptance period upon the momentum of injection, the radius of injection, and a complicated function of the field configuration. A relationship similar to Eq. (65) has been used to approximate acceptance periods for the ISC synchrotron these results being given in Fig. 6;An approximation for the case of pulsed injection has also been made. These results in general are not too satisfactory due to the extreme nature of the assumed waveform. However the results are sufficient to show some of the possibilities of momentum-matching;There is considerable work yet to do with respect to the experimental measurement of acceptance time. The method described here has several weaknesses, one of which could be overcome by the use of a better-shaped current pulse;In order to establish more firmly the operating characteristics of the ISC synchrotron, considerably more data should be obtained. In particular an attempt should be made to clarify the situation existing when capture is attempted on the leading or the trailing edge of the injection pulse. Further experiments should also include injection at different values of magnet current and with a selection of injection devices.