02-14.33MEN 2-10-1753 PREFACE. THE inability of artizan students to profit by much of the technical instruction given in polytechnics and similar institutes is largely due to insufficient preliminary training in Mathematics, for without a fair knowledge of this subject little or no real progress can be made in any branch of Physical Science. Notwithstanding this, classes in pure Mathematics are neither popular nor well attended by students of the industrial class. Even the enthusiastic apprentice seems to find it difficult to connect the instruction usually given in arithmetic, algebra, and geometry with the work of the shop or factory. A number of attempts have been made to remedy this state of affairs. Classes in Technical and Workshop Arithmetic, Machine Calculations, Mensuration, and similar subjects have been started in many centres. The latest attempt to interest and benefit the "practical man" is the syllabus of Practical Mathematics issued by the Department of Science and Art. Judging from the Examination paper of May last, and the lectures delivered by Prof. Perry, F.R.S., to working men and to science teachers, the object of the course is to show the student how to prove and verify truths by experiment instead of arriving at elementary results through the ordinary processes of Euclid and other academic authorities. Abstract reasoning is to be relegated to the background, and concrete facts are to form the basis of the student's work. The syllabus of Practical Mathematics, to which reference has been made, is so extensive in its scope that it is difficult to deal satisfactorily with all the points in it in a text-book such as the present. The course of study outlined in the following pages will consequently be found more than can be undertaken by backward students in one session. In such cases the plan of completing the course in two years may reasonably be adopted. Readers familiar with the published works of Prof. Perry, and those who have attended his lectures, will at once perceive how much of the plan of the book is due to his inspiration. But while claiming little originality, the writer has certainly endeavoured to give teachers of the subject the results of a long experience in instructing practical men how to apply the methods of the Mathematician to their everyday work. The exercises, which number close upon 1400, are either original or have been selected after careful consideration from public examination papers. The writer is glad to take this opportunity of thanking Mr. F. W. Arnold, A.R.C.S., A.M.I.C.E., for reading through the proof sheets, and to express his indebtedness to Prof. R. A. Gregory and Mr. A. T. Simmons, A.R.C.S., B.Sc., for very valuable criticisms and help. F. CASTLE. LONDON, August, 1899. CONTENTS. Contracted Multiplication and Division. Italian Method of Division. Involution and Evolution. Simple Application of Arithmetical |