Spectrometer measurements were made of the x‐ray diffraction peaks for cold‐worked filings of thoriated tungsten: 99.25 tungsten, 0.75 thoria. A Fourier analysis was made of the peak shapes, and the instrumental broadening corrected by using the peaks of annealed material. When the particle size and the distortion effects were separated, it was found that the particle size broadening corresponded to a sizeL¯=200A. This value is to be interpreted as the size of the coherently diffracting domains, and is a measure of the distance between layers of slip planes or layers of dislocations. The coherent distortion broadening indicated that strains in this material vary appreciably over distances of 25A or less. Strain distribution curves were obtained from a Fourier transform of the experimental coefficients. There is an indication that strains are smaller in the larger coherent regions. The measured root mean square strain corresponds to an elastic energy of 0.18 cal/g. Within experimental accuracy the integrated intensities are the same for the cold‐worked or the annealed samples.