The translation of an early (1957), Russian article on the development of x-ray computed tomography is provided. The article demonstrates a principle possibility of determining the local attenuation coefficient in every element of a three-dimensional object using penetrating radiation... The task is expressed as an integral equation and the experimental conditions are chosen such that this equation has a unique solution. The possibility of obtaining volumetric x-ray images and radiographs of thin layers is shown as well as the use of conditional color contrasting. The considered method is of promising interest for x-ray and gamma-based defect detection as well as for medical diagnostics. (read more)