The advantages to be derived from a successful application of the photographic method of detecting nuclear particles to the study of the scattering of the high-energy beams of particles provided by the cyclotron are discussed. The design of a 'camera' for this purpose is described. The most important feature of the method lies in the fact that a single plate, exposed to the scattered particles for a few minutes, contains the information required for a complete examination of the variation of the scattered intensity in the angular range from 10 to 170 degrees with the direction of the primary beam. A very great saving is thus effected in the time the cyclotron is occupied in making such experiments as compared with other methods of detection. The theory of the method is discussed in some detail, and tests of the performance of the instrument are described which demonstrate its reliability. It is shown that the angular resolving power of the method is of the order of $\pm $2 degrees, and that its ability to distinguish different groups of scattered and disintegration particles from range distribution curves is superior to that hitherto achieved with counter and other methods of detection.