The book has been brought up to date to cover the latest advances in research. The new edition also shows how much one of our greatest teachers has developed his teaching technique since the work first appeared. The experience gained, not only in the lecture-hall and laboratory but in the colossal teaching experiments Science for the Citizen and Mathematics for the Million, is applied in this new edition. The book is for the upper forms of schools and for universities, polytechnics, and private students. A textbook by an outstanding research worker who is also a brilliant teacher is rare.