The Life and Works of John Napier

The story of the invention of logarithms by John Napier has been told and retold so many times that it has become a legend. As often is the case with legends, however, many of the fine historical details have been rubbed off and footnotes left by the wayside. It is therefore most welcome that we have a fresh telling drawn directly from the original source material. The Life and Works of John Napier by Brian Rice, Enrique González-Velasco, and Alexander Corrigan, produced in tandem with the quadricentennial celebration of Napier’s invention, restores the details as well as the footnotes. At 13.5 pounds and 994 pages with twenty-nine illustrations, nineteen in full-color, the production by Springer deserves special mention. All of Napier’s books are included (translated from the Latin when necessary), so the reader can work with the expository essays in tandem with the source material.

Life and Times

Rice, both in the introductory chapter and in the appendices, provides the full sweep of the life and times of Napier: ancestry, family, religion, civil war, alchemy and invention, calculating tools, town and country life, publishing, and, of course, logarithms. There are multiple views of Merchiston Tower, where Napier lived, including floor plans, two color maps and a color portrait of Napier and another of his first wife. A revelatory bit of source material appears in the appendix: a color facsimile and transcription of Napier’s “Secrett Inventionis proffitabill and necessary in theis dayes for defence of this Iland, and withstanding of strangers, enemies of Godes truth and Religion.”

Plaine Discovery of the Whole Revelation of Saint John

Napier’s first book, published in 1593, is an interpretation of the book of Revelation. Fortuitously, Alexander Corrigan was working on his Ph.D. at the University of Edinburgh on the Plaine Discovery when Napier project was launched. I confess I didn’t attempt to read the Plaine Discovery, but Corrigan’s clear, concise, and eminently readable exegesis enables the reader to understand what Napier was about and, more importantly, how Plaine Discovery is of a piece with Napier’s mathematical works.

The version of Plaine Discovery reproduced in the book is the revised edition of 1611 with the wide margins that contained Napier’s notes. These have been faithfully typeset as marginalia in this book.

Napier’s Mathematics

Napier’s description of the table of logarithms and its use, Mirifici Logarithmorum Canonis Descriptio, was published in 1614. His explanation of its construction, Mirifici Logarithmorum Canonis Constructio, was only published after his death, in 1619. Two other works focused on practical calculation: Rabdology, or Calculating with Rods, and De Arte Logistica. All are included here together with an introduction describing their contents.

The introduction is divided into two parts. Part I, “Logarithms” covers Napier’s construction of his table of logarithms of sines, Briggs’s base ten logarithms of natural numbers, and a short section on Burgii’s table. Part II, “Mechanical Devices” covers Napier’s bones, the high-speed Promptuary and the chessboard abacus. Of particular note is a full-color plate of the only known Promptuary thought to have been built in the early 17th century and currently held in the Museo Arqueológico Nacional in Madrid. Of course, if this isn’t up-close enough for you, just skip ahead a couple pages and you can read how Napier himself put it.

González-Velasco’s description of how Napier went about creating logarithms is one of the best I’ve ever read. Rather than translating Napier into a twenty-first-century mindset, González-Velasco stays close to the Constructio text and strives to shed light on what Napier might have been thinking as he computed his table.

In the section titled “The Table of Logarithms” there is a fine example of a recovered detail mentioned in the introduction. The logarithm legend says that Napier worked on his table for over twenty years before it was finally sent to press in 1614, but is silent on the source of this knowledge. González-Velasco recovers it in the form of a letter from Kepler to Petrus Crugerus. After the tables in Descriptio is Brigg’s “The Use of the Triangular Table for the finding of the part Proportionall” and at the end of Constructio are Briggs’s “Notes.”

The section on the Rabdology, or Calculating with Rods explains the construction the rods (often called “Napier’s bones”) and their use, including applications to geometry and mechanics. Then come discussions of the construction and use of the Promptuary (a computational device described in De Arte Logistica) and what Napier calls “location arithmetic” which is arithmetic on a 25x25 chess board. William Hawkins, the translator of De Arte Logistica in this volume, considered the Promptuary to be the first true calculating machine ever built. (See Annals of the History of Computing, 10(1988) 35–67 for more on Hawkins’s translation and the backstory on Erwin Tomash’s discovery of the Spanish Promptuary.)

Rather than going into full detail on De Arte Logistica, the introduction refers the reader to Hawkins’s three-volume, 1114-page. 1982 PhD thesis. Some interpretive footnotes have been added to the text by González-Velasco and by Garry J. Tee, Hawkins’s thesis supervisor. On first thought this might seem a bit unfortunate, but it does provide the reader with the opportunity to do some of their own primary source reading. González-Velasco observes “… the present typesetting has been formatted to be as close as possible to the style of the original Latin publication, which Hawkins could not achieve in 1982 using a typewriter.” Not only would the layout of De Arte Logistica have been typographic challenge, Napier uses many special characters which weren’t available as Typits.

There are nine appendices which contain additional information about the Napier name and Merchiston Tower, Napier’s note about manuring of field land, and his Secrett Inventionis as well as some correspondence.

Conclusion

The Life and Works of John Napier is much more than just a compilation of primary material. It is a legendary story retold tightly bound to the legend’s sources. From the authors’ point of view it must have been a daunting project; from the publisher’s point of view it was certainly a risky one. But it works and it’s a joy. Both the authors and the publisher are to be commended for their vision, their persistence and most importantly for their dogged dedication to quality. One can only hope that the book serve as an aspirational example for others of the same genre.

Scott Guthery is the founder and editor of Docent Press and co-founder of Life-Notes.