This little book is written in the first place for students in technical colleges taking the National Certificate Courses in Applied Physics; it is hoped it will appeal also to students of physics, and pernaps chemistry, in the sixth forms of grammar schools and in the universltIes. For wherever experimental work in physics, or in science generally, is undertakcn the degree of accuracy of the measurements, and of the res,!lts of the experiments, must be of the first importance. Every teacher of experimental physics knows how "results" given to three or four decimal plaees are often in error in the first place; students suffer from "delusions of accuracy. " At a higher level too, more experieneed workers sometimes claim a degree of accuracy which cannot be justified. Perhaps a considera tion of the topics discussed in this monograph will stimulate in students an attitude to experimental results at onee more modest and more profound. The mathematical treatment throughout has been kept as simple as possible. It has seemed advisable, however, to explain the statistical concepts at the basis of the main considerations, and it is hoped that Chapter 2 contains as elementary an account of the leading statistical ideas involved as is possible in such small compass. It is a necessary link between the simple introduction to the nature and estimation of errors given in Chapter 1, and the theory of errors discussed in Chapter 3.