This book is the result of 12 years experience as supervisor of apprentices, designing, shop foreman and instructor in evening classes in technical schools. The author has made every effort to simplify and analyze, step by step, the various phases of industrial mathematics. The problems, examples and illustrations have been carefully selected and chosen to make them as practical and interesting as possible so that they will stimulate and encourage the student to think clearly, reason and analyze for himself. The first few pages are intended to be used for review or reference work at the discretion Of the student, or for those who have only an elementary knowledge Of mathematics. Standard formulas and data, such as are usually found in mechanics' hand books, trade journals and technical litera ture, are frequently used and sufficient material in the way of explanations, illustrations and examples are given along with each subject so that the student will become familiar with them. It is hoped that such information will make this book of permanent value for reference and as a hand book.