IN 'an experience of more than ten years in teaching machine-shop work to evening classes of men and boys actually engaged in the trade, the author has observed a decided lack of mathematical knowledge among ordinary mechanics. Many leave school from the grammar grades. Any mathematical training that they once may have received is, therefore, so far behind them by the time they are well started in their trade that it has practically been forgotten. About all that has been retained is a fair under standing of addition, subtraction, multiplication and divi~ sion. For such, the natural starting point for a further knowledge of mathematics is the study of fractions. Beginning with fractions, this book aims to give, in elementary form, an explanation of the calculations most frequently occurring in machine-shop work. The treat ment has been made as simple as possible, in some places almost too simple, perhaps, with the desire to put the ex planation in such a form as to be easily understood.