According to Sir Graham Sutton, "The task of the applied mathematician is exactly that of using the tools provided by pure mathematics to clarify and extend the observations of the physicist." Phenomena must be measured and reduced to number in order to become part of the body of scientific knowledge. It is the purpose of this book to show that process in action. Unlike many texts in this area, this straightforward account is written for the layman, and is accessible to high school students and undergraduates - anyone with a grasp of rudimentary calculus. Moreover, its generalized view of the topic makes the book of special interest to young mathematicians, physicists and engineers. In illuminating the nature of applied mathematics and its influence on modern ideas concerning the physical nature of the universe, the author illustrates his points with examples from ballistics, automatic calculating machines, radio waves, atoms and electrons, theory of flight, statistics and meterology. The book is divided into seven chapters: I. The Mathematician and his Task - II. Tools of the trade - III. Ballistics, or Newtonian dynamics in war - IV. An essay on waves - V. Mathematics of flight -- VI. Statistics, or the weighing of evidence - VII. Mathematics and the weather. In the first two chapters, Sir Graham gives a lucid account of the role of the mathematician in applied sicence and the nature of his tools, covering such topics as theories of physics, mathematical techniques, complex numbers, new geometries and atomistic and field theories of physics. The remaining five chapters are devoted to specific applications in ballistics (gunnery as an exact science, calculation of trajectories, etc), waves (waves in the natural world, Fourier series, waves and particles, etc.) mathematics of flight (fundamentals of fluid motion theory, Joukowski's solution of the two dimension aerofoil problem, etc.), as well as applications in statistics and meteorology. -- from back cover.