This dissertation describes some new methods for discrimina'ting between the light element characteristic wavelengths in an x-ray scanning microanalyser. For long wavelength microanalysis purposes, the classica1 methods of x-ray spectrometr.v are impracticable. The proportional counter, the best of several possibilities, has there~ore been employed as a dispersive detector, the output pulses subsequently being fu"'1.alysed electronically to yield the necessar.v line intensity information. Proportional counter operation with low energy x-rays is analysed and discussed, and the construction of a suitable counter is described � .Measurements of the quantum yields from carbon and aluminium, . made with this counter, are reported; these measurements, apart from their :fundamental significance., provide an estimate of the performance to be expected from a light element microanalyser. � Several methods of pulse height distribution analysis (deconvolution) are described practically a'tld analysed theoretically. One of the methods, in which the outputs from several pulse anal.yser channels are treated as a set of linear equations which can be solved simultaneously in an electrica1 network, is chosen for development and incorporation into a scanning microanalyser. The design., constrv.ction1 Elld operation of this instrument are described; i ts use is demonstrated 1n several practical examples. The results are presented ElS pictures. with r3solution of 4-5 mi.crons1 showing the surface concentrations of elements as light as beryllium {Z = 4). \