"Version: 202112"--Title page verso.

Includes bibliographical references.

Dr. Jeffrey Huw Williams (1956-2021)--an appreciation xiii -- Introduction : the language that is science xvii -- 1. The origin of units -- 1.1. The syst�eme internationale des unit�es (the SI)

2. A brief history of dimensional analysis : a holistic approach to physics -- 2.1. Homogeneity of units -- 2.2. Geometry of motion -- 2.3. Derived units -- 2.4. Fourier and the nature of physical quantities -- 2.5. Dimensional arguments

3. Introduction to dimensions -- 3.1. Dimensional formulae -- 3.2. Conversion from one system of units to another system of units -- 3.3. Dimensional homogeneity -- 3.4. Approaching dimensional analysis

4. Why, and how we play with variables -- 4.1. The de-dimensionalization of equations -- 4.2. Some of the more widely-used nondimensional groups -- 4.3. Some examples of straightforward dimensional analyses

5. The Buckingham [Pi]-theorem and its application -- 5.1. The Buckingham [Pi]-technique -- 5.2. Some examples of dimensional analysis involving the [Pi]-theorem

6. Scaling and similitude -- 6.1. Astronomy and the music of the spheres -- 6.2. Dimensional analysis of the pendulum : the first precision measuring device -- 6.3. Harmonic oscillations

7. Rules of thumb, intuitive planning and physical insight -- 7.1. Dimensional variables -- 7.2. Nondimensional variables -- 7.3. Eliminating a variable you suspect could be negligible : the design of golf-balls -- 7.4. The Rayleigh-Riabouchinsky Paradox

8. Continuum forces -- 8.1. The basic concepts of fluid mechanics -- 8.2. Drag forces -- 8.3. Bubbles in fizzy drinks -- 8.4. Magnetic-braking : the terminal velocity of a magnet falling in a tube of a non-magnetic metal

9. Why is the sky blue? -- 9.1. Quantifying light intensity : subjectively and in absolute terms -- 9.2. Polarizability -- 9.3. Rayleigh scattering -- 9.4. Collision-induced light scattering

10. The equilibrium between matter and energy -- 10.1. Black-body radiation and dimensional analysis -- 10.2. The displacement law of Wilhelm Wien -- 10.3. The cosmic microwave background

11. Dimensions involving molecules and fields -- 11.1. Polarization and magnetization -- 11.2. Electromagnetic fields -- 11.3. Dimensional homogeneity in electrostatics -- 11.4. Molecules and fields -- 11.5. Interacting magnetic dipoles, and the origin of radiation at 21 cm -- 11.6. Units and the SI -- 11.7. Final point : electro- and magneto-optics

12. The dynamics of atoms and molecules -- 12.1. Rutherford's model of the hydrogen atom -- 12.2. The earliest quantum view of the atom -- 12.3. Electric dipole transitions -- 12.4. Melting in organic solids

13. Modelling phenomena -- 13.1. Prototypes -- 13.2. Experimental design and interpretation -- 13.3. Dimensional analysis of a water sport

14. The great principle of similitude in biology and sport -- 14.1. Scaling of flight -- 14.2. Walking and running with dinosaurs -- 14.3. Constructing the best First-VIII -- 14.4. How much can you lift?

15. A miscellany of analyses by dimension -- 15.1. Dimensional analysis of cooking -- 15.2. Black holes -- 15.3. The Aeolian harp -- 15.4. The final frontier of dimensional analysis : the Drake equation.

Dimensional analysis is a powerful method to analyse complex physical phenomena, including those for which we cannot pose, much less solve governing equations. Its use in science and engineering is ubiquitous and has been central to the work of greats such as Lord Rayleigh, Bohr and Einstein. It offers a method for reducing complex physical problems to their simplest forms and provides a powerful tool for checking whether or not equations are dimensionally consistent and suggests plausible equations when we know which quantities are involved.

Students in physical and life sciences, as well as engineering disciplines and mathematics.

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The author was born in Swansea, UK, in 1956. He attended the University College of Wales, Aberystwyth, and Cambridge University; being awarded a PhD in chemical physics from the University of Cambridge in 1981. Subsequently, his career as a research scientist was in the physical sciences. First, as a research scientist in the universities of Cambridge, Oxford, Harvard and Illinois, and subsequently as an experimental physicist at the Institute Laue-Langevin, Grenoble, which remains one of the world's leading centres for research involving neutrons.

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