The Heirs of Archimedes: Science and the Art of War through the Age of Enlightenment.

Brett D. Steele and Tamera Dorland, eds. The Heirs of Archimedes: Science and the Art of War through the Age of Enlightenment.

Cambridge, MA, and London: The MIT Press, 2005. vii + 397 pp. index. illus. tbls. $55. ISBN: 0-262-19516-X.

The heirs of Archimedes of the title are those who applied science and mathematics to practical matters, in particular to Western and Northern European and Ottoman warfare in the sixteenth through the eighteenth centuries. The specific influence of Archimedes himself in this period is rather metaphorical, as little is known of the real details of his practical contributions in his own time; the virtuosity of his new results, methods, and theories is only matched by the strange sterility of his mathematical legacy, to be explained as much by the ultimate limitations of his methods as by the incapacity of his followers. As for his technologies, these were reported, without much detail, as almost magical.

Despite this, one can perhaps see a basis of inspiration in the idea of relating theory and practice, brought out in many of the fourteen contributions to this volume, including a lengthy and informative editorial introduction. These are centered around the development and use of gunpowder (mainly in Sweden, France, and England), military engineering and gunnery, and the nautical sciences of shipbuilding and navigation.

Much of this, even late in the period, was a matter of experimentation, of trial and error. Ballistics as a science begins in the eighteenth century with the work of Robins, Daniel Bernoulli, and Euler. As Lohne has shown, the earlier work of Harriot and James Gregorie was too little known to have had any effect. Modern scholars tend to mention Galileo's work (1638), but gunners, being practical men, found this of little use--the devil was in the details, which he did not give. This was not for want of serious efforts: Newton (1687) in his controversial Book 2, Proposition 10, of the Principia (corrected in 1713), related the density of a path to the velocity-dependent resistance; he also suggested alterations to ships' bow shapes to reduce resistance.

During the later sixteenth-century, the English had been successful with most questions of mathematical navigation--longitude excepted--including amplitude corrections of magnetic variation. It was early realized that a decent clock would do the trick, but the necessary practical precision was not attained until the eighteenth century, and Tobias Mayer's distinct method of lunar distances was a useful prior contribution, which continued in use long after the commercial development of Harrison's chronometers. The true sea-chart (Mercator's projection), probably foreseen early in the sixteenth century, was solved by John Dee who, the late E. G. R. Taylor thought in 1959, understood the so-called nautical triangle before 1560--that is, before the birth of Harriot, who later (1594 onwards) produced a complete mathematical solution, involving original work in conformality, the first known plain and twisted rectifications, inverse exponentials, interpolation, and so on. This escapes mention in the second section of this book, an opportunity missed. However, Edward Wright's elegant work (1599 and later editions) does receive attention; this, as with Dee's solution, and Harriot's first (1584) solution, involves the addition of secants, adequate at lower latitudes, but leading to errors hard to quantify nearer the poles.

It is strange, if partly true, to see Harriot and Wright described as geographers and mathematical practitioners. Both were able mathematicians, the former (with Vieta [1540-1603]) the greatest of the period and a notable scientist, who inter alia first solved the refraction problem long before Snell or Descartes, a necessity for the best astronomical and navigational tables. Alexander's chapter is the more reliable on this matter. Incidentally, Harriot was not really unfortunate in his patronage (186), despite a few close shaves, a feature of those dangerous times. Percy paid him a good pension from 1597 and built him a house in 1608. He was a scientific adviser, rather than a tutor, to Raleigh. It is hard to see how he could have done better.

For the rest, Alexzandra Hildred describes the armaments of the Mary Rose (sunk 1545)--a rare survival--and something of its construction, for which we have the later work of both Matthew Baker and Harriot--a necessarily conservative activity little-altered before the advent of iron ships, which became a necessity because of the loss of woodland caused by shipbuilding. In an interesting final chapter, one of the editors (Steele) describes various eighteenth-century military schools, which were about the only places where a new "Newtonian" technical education (including calculus) was available. His useful footnote (10) touches on questions of technological determinism, an increasing disease of our own period.

JON V. PEPPER

University College London