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The purpose of this book is to provide the reader with a series of work- ed examples in X -ray spectrometry and X -ray diffractometry, in such a way that each example can be treated either as a posed question, i. e. one to which the reader must himself provide an answer, or as a guide to the method of treating a similar problem. The latter, of course, also pro- vides a check on the answer produced by the reader. Although much basic theory can be derived by study of this work the first intention of the book is not to provide a source of basic theoretical knowledge in X -ray analy- sis. It is hoped that the book will be utilized more as a guide line in the tackling of theoretical and practical problems and as a means of estab- lishing whether or not the reader is able to work out for himself a certain type of problem. For example, the series of examples on counting statis- tics has been chosen in such a way that after working through and under- standing these, the reader should be able to handle most of the calculations that he is likely to come up against in this area.