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Horace Lamb
Dover Publications
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
William J. Satzer
, on

This classic work on the motion of fluids is 139 years old. In its earliest edition it was called A Treatise on the Mathematical Theory of the Motion of Fluids. From the second edition on to the current sixth edition it has had its current title, and over time it has grown from 258 to 768 pages. The version we have now from Dover is an unabridged and unaltered version of the sixth edition that was first published in 1945.

Natural questions arise: why is this still in print and why would anyone aside from historians be interested in it? A simple answer is that it continues to be a complete and elegant introduction to the subject written with an admirable level of clarity.

Besides growing in length, the book has evolved considerably from edition to edition. The first edition focused on the mathematical theory of an ideal fluid. Subsequent editions engage more with the underlying natural phenomena and experimental results. Numerical computations appear. Turbulent flow — a subject still not well understood — is described in the partial and incomplete form it had at the time of each publication. By the third edition the basic character of the book was in place; it is the classical theory of the motion of an ideal inviscid incompressible fluid and the theory of waves.

On the book’s one hundred year anniversary the applied mathematician Leslie Howarth reviewed it and remembered that he received Lamb’s book as a college prize and found it “rather frightening”. He concluded that it had a remarkable staying power because it incorporated “so much information relevant to modern applications of classical hydrodynamics.” On the face of it, the book is intimidating; it is huge and dense. But, given a chance, it pulls the reader in bit by bit with charm, directness and clarity. Lamb never skimps on detail, but he never overdoes it either.

The scope is enormous, and it is impossible to do it justice in a short review. Lamb’s work is very strong on the fundamentals and he choses applications carefully. The chapters on tides and surface waves are among the best in the book. The consideration of rotating masses of liquids at the very end of the book was motivated by questions about the formation and shape of the earth and other planets. Lamb’s treatment is elegant.

Hydrodynamics in Lamb’s time was largely synonymous with fluid dynamics, but the latter now incorporates aerodynamics as well. More modern standard texts on the subject include Batchelor’s An Introduction to Fluid Dynamics and Lighthill’s Waves in Fluids, although no single book available now has the scope of Lamb’s. 

Bill Satzer ( was a senior intellectual property scientist at 3M Company. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.

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