"points, lines, and planes" which usually precede them. In Machine Drawing and Design, again, the deficiency was still greater, there being no choice between sheets of Diagrams and Text-Books which, although they produce admirable copyists, are utterly devoid of any utility as regards education in design. The well-known treatise by Prof. Unwin is, of course, most excellent as an aid to design, but it does not profess to teach drawing, and is certainly not intended for elementary students.

Under these conditions, I found myself obliged to arrange questions so graduated in regard to sequence and difficulty as to be really helpful in "teaching" the subject, by bringing out important principles, by making clear mathematical relations, and by requiring the application of real thought and the knowledge gained in other classes and subjects. The setting of the questions was always preceded by a lesson in which, for geometrical drawing, typical problems were worked upon the blackboard and explained; and for machine drawing, the parts concerned were drawn separately or together, or illustrated by models, and the relations of, and reasons for, the shape and size of the different parts made clear. The book, then, has grown out of my own felt wants, and the effort to supply them by the questions and lecture-notes mentioned.

In Part I., I have included chapters on those parts of Practical Geometry already referred to as usually taken later, because I believe them to be essential to a good elementary course of Practical Geometry, and admirably suited for the ordinary engineering or technical student commencing without previous knowledge, and desiring

to go on to an intelligent study of Machine Drawing and Design. I have also included some special cases of intersection, such as occur in metal plate work and in the drawing of some engine parts, in order that students may have no excuse for putting in the necessary curves by "guess work." Thus, in preparing Part I., I have steadily kept in view the work of Part II., from the conviction that Plane and Solid Geometry should always precede Machine Drawing, just as Arithmetic precedes Algebra.

In Part II., I have avoided dimensioning the illustrations except in rare cases, and have endeavoured to build up the subjects so that all primary and common parts are first explained and understood, such explanations not being repeated when the parts occur in connection with larger or complete designs. Such a method will, I am sure, commend itself to all true teachers. A student ought not to be told the sizes of bolts and nuts, or the diameter of flanges, or the details of stuffing boxes in drawing an engine cylinder, any more than we should expect to have to prove to him the truth of the triangle of forces, at each step in the graphical determination of the stresses in a roof-truss. But such an arrangement obviously requires that the examples be worked through in the order given, and especially is this so in the Sections on Engine Design, the examples in which have been intentionally arranged to show the interdependence of the different parts. I have throughout endeavoured to give the reasons for all features of the designs; when these are purely empirical or for workshop convenience, this is stated. My object will have been attained if I have made it impossible for a student to

draw any part without having an intelligent reason for all he does.

It has certainly been my desire to make the book suitable for beginners, believing that the sizes and arrangements of simple common parts cannot be acquired too early, and I have therefore endeavoured to teach the principle of drawing" as well as of "design." I have found some difficulty in deciding what terms and definitions to employ in order to make the book acceptable to the ordinary student and teacher, and yet free from unscientific and ambiguous expressions. Workshop terms are not fully satisfactory, for they vary with different localities, while scientific terms are often misused. I have restricted the word "compression" to represent a strain or change of form, and in other ways have adhered to the following notation :—

My thanks are especially due to Mr. F. W. Sanderson, M.A., Head-Master of Oundle Grammar Schools, who, during my association with him at Dulwich College, gave me much assistance in preparing the Examples, and who has been good enough to read the proof-sheets and to make many valuable suggestions, and to Professor Goodman, M. I. Mech. E., Assoc. M. Inst. C. E. of the Yorkshire College, Leeds, for much helpful counsel as to the arrangement of Part. II. I am indebted also to Mr. J. H. Wicksteed, M.I.C.E., M.I.Mech.E., for useful suggestions and drawings, and to Messrs. Allan & Co., Lambeth; Messrs.

Marshall & Sons, Gainsborough; Mr. W. Allchin, Globe Works, Northampton; The Kirkstall Forge Co.; The Globe Engineering Co.; Messrs. Schaffer & Budenberg of Manchester; and the Atkinson Gas Engine Co., for kindly supplying drawings for insertion in the text. Finally, I have to acknowledge the assistance received from the works of Professors Unwin and Ripper, and Mr. Henry Angel.

I shall be grateful to teachers and others who may use the book for information as to any errors which may have been overlooked.

BATTERSEA POLYTECHNIC INSTITUTE, S. W.

September, 1893.

SIDNEY H. WELLS.