I have been fortunate in the help received during the preparation of this work. The manuscript was read with great thoroughness by Dr Sheila M. Edmonds, of Newnham College, Cambridge, whose criticisms and suggestions were of great value and kept me firmly in the paths of rigour. Dr J. W. S. Cassels, of Trinity College, Cambridge, read the proofs and drew attention to a number of slips. To both I would express my sincere thanks.

A number of pupils helped me in the preparation of the answers. Special mention must be made of Mr J. E. Wallington and Mr P. A. Wallington, who, acting almost as a committee, provided me with a complete set of checked answers; any slips that remain must be due to my own carelessness in transcription. I am deeply indebted to them for a very substantial piece of work.

As on former occasions, I have been greatly helped by the staff of the Cambridge University Press, and I should like to place on record how much I owe to their skilled interpretation of the manuscript.

The Examples come from many sources—the Oxford and Cambridge Schools Examination Board, Scholarship examinations in the University of Cambridge, and Degree Examinations in the Universities of Cambridge and London. I am grateful for permission to reproduce them.