Foreword; 1. Summary; 2. Introductory example; 3. The choice of cooordinate differences; 4. The fundamental equations; 5. Finding the vertical velocity; 6. Special treatment for the stratosphere; 7. The arrangement of points and instants; 8. Review of operations in sequence; 9. An example worked on computing forms; 10. Smoothing the initial data; 11. Some remaining problems; 12. Units and notation; Index of persons; Index of subsidiary subjects.