Meter a lapse of about five years the experimental attack on the secrets of the otomio nucleus hau begun again. The num her of ocientistr3 now engaged in this work and the number of particle decelerators which exact or are under coaztruction are very much greater than at any other p rcviouo time. 1ý Since the gar there have emerged several new promising methods of accelerating particles to very high enargiea. In every case the size, expense and time of eonmtruction of the o, pnratu3 are very 1nrge. The machine which is most suitable for accelerating particles to the highest energies is the proton synchrotron. Until recently this development wes confined to the BirminChe. n University, whore a machine designed to' accelerate protons to 109 eV (and possibly deuterons and of -particles to "6x 109 aV and 109 eV reapoctinely) in v2cll under construction. It id with the theory and construction of such an accelerator that this thesis is mainly concerned (Chapters III, IV and V). While building ouch a complicated picco of apparatus it in bf course essential to appreciate its likely uses. Since the proton synchrotron will be capable of deliýrering pcrtiolea over a very viide ranee of energies (protons from 2 ý- 1,000 MoV) the possible experim©nta are likely to include nearly all thoac cihich can be performed with arty accelerator. Naturally attention will be confined largely to the very high energy region.