Werrett frames his argument as a before and after. In the beginning was “oeconomy,” an early modern spelling of our modern word “economy” which was derived from Latin, middle French, and middle English. Economy has had many meanings over time; Werrett uses oeconomy to denote the sense of stewardship, prudence, and “well-functioning” associated with the management of a household.  By the middle, at least, of the 19C the most common senses of “economy” were technical and financial; the older sense of household management became known as home or domestic economy, and national financial affairs became political economy. Closely related to oeconomy are the practices, the ethos, that are consistent with it; thrifty practices are those that promote stewardship, prudence, and so forth. “Thrifty science” then is the kind of knowledge-seeking one gets in thrifty oeconomical world. This is Werrett’s, sometimes jarring, but mostly effective, way of reminding his readers that the early modern experimentalist may have had different values and objectives. Werrett’s first task is to orient his readers to the experience of his early modern subjects. As he develops his frame, Werrett also uses a modern concept from anthropology/sociology, the concept of “incomplete” or “unfinished” objects, i.e., objects without specific purposes, or “open-ended” objects. With these simple definitional frames established, Werrett uses them deftly to illustrate the world of thrifty science.

Beginning with the site of much early modern experimental philosophy, the house, Werrett argues that the new style houses with multiple rooms and hearths that were gradually replacing the older center-hall single-hearth houses of the Middle Ages were themselves open-ended objects. Rooms in these new houses did not yet have designated functions; for instance, with multiple hearths, multiple rooms could be used to prepare meals. Similarly, household utensils of the early modern period could be used for multiple purposes, including use in experimental investigations for testing recipes or chymical reactions. Werrett uses the notions of unfinished objects and the oeconomical ethos to illustrate the practice of early modern thrifty science. These elite practitioners “made use of” what was at hand. They “made do” with and “shifted” the uses of unfinished objects. Collectively, they practiced “thrifty science.”

Objects wear, break, and are no longer needed. Werrett describes the quotidian stewardship of objects – how they are maintained, repaired, and recycled. In the oeconomic ethos durability, maintainability, repairability were desirable qualities. It was good to have a well-made thing that could be used for multiple purposes, but only if it could be maintained and repaired. Much maintenance and repair were done in the household, but some repairs required skilled outsiders, e.g., compass pointers needed to have their tips remagnetized. Werrett shows by example how the worlds of elites and artisans intertwine. And by following the arc of an object’s life, he is able to show how thrifty science intersects with the world of scavengers, dustmen, and nightsoil collectors.

Some objects may be loaned, given, traded, or sold. Werrett describes a social economy of gift-giving and exchange for scientific objects that is like that for recipes and often involves the same households. Instrument makers and dealers commonly repaired and sold both new and second-hand objects; “second-hand” was not thought to mean inferior in the world of thrifty science. The number of second-hand markets and dealers for books and objects increased in the 18C. Scientific collections and equipment were included in estates and sold at auction. Werrett uses probate and auction records to trace this growing activity and to show how maintenance, repair and reuse practices were incorporated into the collective activity he calls thrifty science.

By the end of the 18C, the markets for scientific apparatus, books, material, collections, and related expertise had grown. The intense debates during the last part of the 18C between researchers arguing phlogiston and oxygen theories led to what has come to be called the “chemical revolution,” a productive way to explore the properties of matter that led to modern chemistry. Chemistry laboratories required increasingly specialized equipment and storage facilities. Other scientific equipment became more specialized, and sometimes became larger, e.g., larger lenses on telescopes. Ambiguities in experimental results led to searches for more precise measurements. Universities built special purpose facilities. The home, too, became specialized as rooms acquired designated purposes: kitchen, parlor, sitting room, storeroom, etc. As the scope and scale of experimental investigations increased and homes became less suitable, scientific activity moved out of the home, and, Werrett argues, the scientific enterprise became increasingly dominated by men. Werrett outlines the development of larger scale scientific investigation throughout the 19C and leading up World War I and notes that the increasing specialization of equipment gave “unfinished” objects a specific purpose. Such single-purpose objects were no longer part of the oeconomical ethos, but rather were part of “economic science.”

By the end of the 16C maritime references were common. In Twelfth Night, a comedy first performed in 1602, Shakespeare refers, obliquely, to the “new” Mercator maps with their rhumb lines, and assumes his audience will understand. In 1590, after returning from Walter Ralegh’s ill-fated Roanoke colony, Thomas Harriot sought to understand the mathematics of the helical secant lines that Mercator used. (Arianrhod, pp 92-94) How could such an abstruse topic as long distance ocean navigation become a topic that could be used for popular humor as well as mathematical research?

Margaret Schotte’s 2019 book, Sailing School, provides an explanation. Although educated at Harvard and Princeton, Schotte is from Canada. She is a York (Toronto) history professor with an interest in the history of science. Her interest in the history of navigation is personal as well as professional; she has ancestors from the Netherlands and learned to sail on visits to her grandparents home in Halifax. Her book is based on her dissertation thesis, and both the thesis and book received prizes.

One reason navigation became so important is that the only way to profit from the supposed riches of the lands discovered by European explorers in the 15^th and 16^th centuries was by ship, and those ships had to be able to go and return across oceans. All sea-facing states in the 16C knew how to build ships, but pilot-navigators were scarce. Schotte uses four case studies to show how navigators’ educations evolved between 1550 and 1800. She begins with a brief discussion of the first “sailing school” which was established in Seville in the mid-16C. Her case studies focus on Netherlands (two chapters), France, and England. Another chapter discusses a case involving a British naval ship that hit an iceberg in the South Indian Ocean. Naval training, including navigational training, skill, and luck enabled the captain to bring the ship to port over a two-month journey. An epilogue surveys the arc of navigational education over her time period. Her conclusion is that navigators were made, not born.

In the 16C there was still a debate about how to get more navigators. Some thought the skill was innate, so navigators had to be found; debates focused on the essential qualities, often focused on family status. Others thought navigation was teachable, but there was no agreement on how that was to be accomplished. Schotte’s case studies show how the “navigation is teachable” intuition translated into specific pedagogical and institutional arrangements and how those arrangements changed over time. The major military powers—Spain, France, and England—established state-run schools. Sailing schools in the Netherlands were independent. Unsurprisingly, each country had its own maritime tradition and its own geographical circumstances. For instance, the mercantile interests of the Netherlands had created an extensive trade network throughout the Baltics; knowledge of specific ports, tides, currents, hazards, and coastal landmarks, what was known as “small navigation,” was essential for Dutch navigator-pilots who captained relatively small ships. Navigators on large ships on long ocean voyages needed additional navigational skills; locating a ship in the featureless ocean required specialized instruments and astronomical and mathematical knowledge, i.e., celestial navigation. This developing skill-set, or “large navigation,” was taught at all the sailing schools of the period.

During the roughly 250-year period that is the focus of Schotte’s book, the main problems faced by “large navigation” practitioners were measuring a ship’s speed and its longitude. Latitude could be measured with a crossbar or astrolabe (or an octant or sextant by the late 18C). Direction could be measured with a compass. These tools were well-understood, and their use had long been incorporated into common maritime practice. What was beginning to change was the quality of the instruments, the measurement protocols, and the use of more accurate and easier to use tables to adjust raw observations for the earth’s position in its orbit. Although elements of plane trigonometry had been known since antiquity, practical application to celestial navigation on a sphere, took place primarily in the 17C and required what were considered at the time to be difficult and time-consuming calculations. Logarithms and devices based on them greatly simplified calculation by transforming multiplication and division operations into simpler addition and subtraction, or physical manipulation. By increasing the quality of the tools, procedures, and mathematical techniques, navigators could improve the accuracy of their estimates of latitude. But few tools or techniques were available for estimating speed and longitude; experience, careful observation, and the techniques of dead reckoning remained the primary method used to complete the determination of ship’s position for most of the period.

Over time the curriculum of the sailing schools changed. Initially, the schools’ students were mostly experienced sailors who had multiple years of practical experience; they only needed to be instructed in state-of-the-art navigation techniques and examined for competency. Few early students were literate or numerate, so instruction typically consisted of recitation, demonstration, and discussion. Gradually students became more literate and numerate, and this allowed the schools to incorporate textbooks into their curriculum. This was especially true in the Netherlands (and, to some degree, England) where there was a widespread network of commercial mathematics instructors for students interested in commercial mathematics (basic arithmetic, accounting, weights and measures). Amsterdam was also a major printing location, so navigational textbooks flourished there. As basic literacy and numeracy spread more students of the sailing schools came prepared for more advanced topics and the schools’ instructors obliged. The royal schools in France and England were more centralized, and this led to documentation of the debate over curriculum which Schotte has used to good effect to show change in curricular emphasis over time.

By the end of the 18C, knowledge of celestial navigation had become an essential skill for sailors who wished to be navigators or captains. The baseline level of knowledge and mathematical knowledge was much higher than it had been even in 1700. The instruments were easier to use and more accurate. Speed calculations had been made easier. Marine chronometers were beginning to be used so longitude could be calculated with good accuracy. Navigational expertise was no longer scarce; the sailing schools now had to emphasize judgment and basic maritime skills that had been common among 16C students.

By 1800 thousands of men from many parts of Europe were involved in the maritime effort as sailors, stevedores, and merchants. Schotte estimates that for some large cities one in six men were involved in marine activities. Knowledge of marine activities appears to have been commonplace. Celestial navigation posed interesting and novel problems that drew the attention of mathematicians, physicists, and other natural philosophers. Both playgoers and mathematicians became more familiar with abstract symbols, such as those used in maps (e.g., the rhumb lines that Shakespeare compared to the lines on Malvolio’s face), numbers, and letters. All of this knowledge indicates a growing use of the tools needed for thinking about the natural world in the new “mechanical” way.

Much is known about Ralegh, but Harriot is almost unknown. He did original research in mathematics, physics, astronomy, and linguistics. He was, arguably, the first European diplomat and linguist to a North American tribe. He left thousands of pages of manuscripts, but very little has been published. The only biography of Harriot was published more than 70 years ago. Recently his papers have been digitized and scholarly interest is increasing with recent monographs on Harriot’s work.

In 2019 the Oxford Press published Thomas Harriot: A Life in Science. The author, Robyn Arianrhod, has written what she describes as a popular treatment of Harriot’s life and work. Much of the book is, indeed, written for a popular audience, but Arianrhod is a mathematician and her treatment of the problems Harriot studied assumes her readers will have a working knowledge of high school algebra, geometry, trigonometry, and combinatorial mathematics. Extensive exhibits and graphs are provided. Arianrhod provides some background on Elizabethan and Jacobean England, so her book would be of interest to students of early modern England and England’s early colonial activities. The main audience, though, will be geographers and historians of science, mathematics, and navigation.

Harriot’s contributions are presented chronologically, so we begin with his work on navigation: refining navigational charts, improving instruments, and teaching Ralegh’s captains and navigators. He taught basic astronomy and how to use instruments and charts. A constant theme of Harriot’s life is his constant drive to improve accuracy and simplify. In the navigational context this means teaching consistent measurement practices, introducing easier to use and more accurate instruments, and ensuring that navigational tables are accurate. Arianrhod describes the navigational problems of the late 16C and shows how Harriot’s efforts over time improved accuracy.

Next, Arianrhod relates the expedition to establish a colony on Roanoke Island and Harriot’s activities in America.  Harriot is the main interpreter. He learns the Algonquin language and teaches the Americans English. He records the culture of the tribe. Upon his return to England he writes up his observations and publishes them. The remainder of the book describes Harriot’s work to improve navigation and his own research into problems of mathematics and physics. As Harriot’s contributions accumulate and he is assured of continuing financial support more of his time is spent on more theoretical work. But he is always involved in helping his patrons with their practical problems, whether they involved navigation or plumbing.

One of the practical problems that Harriot worked on led to a theoretical problem that occupied him for years. The maps made by Mercator were a great boon to early navigators. They represented the earth’s spherical shape on a plane in such a way that it simplified practical navigation. But Mercator didn’t reveal how he made his maps. When Harriot finally understood the problem he was able to make his own maps faster and more accurately and to refine his navigational tables. Eventually Harriot’s improvements allowed a trained navigator to estimate their latitude to within a mile, a significant improvement in accuracy. He also worked on a construction project for his patron that required him to estimate water forces, flow rates and pressures, and specify pipe sizes. He was a general purpose analyst.

Harriot’s technique in solving problems was consistent: he tried to abstract away as many extraneous details as possible, collect data, and then try to develop a simple formulation of a more general problem. To collect data he would sometimes calculate hundreds of numbers in an effort to see patterns that he could use to imagine or infer a general solution.

As Harriot became more established he hired an assistant and spent more time on his own studies. Arianrhod describes these studies within the larger context of Jacobean political and religious intrigue. Under Elizabeth Harriot’s patrons were favored; under James they were persecuted. Harriot’s patronage and research continued throughout James’s reign, but with considerably more drama. Against this more stressful backdrop, Harriot does significant original work in optics (index of refraction, rainbows), spherical geometry, symbolic algebra, combinatorial mathematics, binomial theorem and applications, sums of infinite series, gravitation and motion, and much more. None of it was published in his lifetime and little of it was known to any except a few close friends. Arianrhod describes the nature of each problem that Harriot works on, provides a brief summary of the history of work on the problem, describes Harriot’s attempts to solve the problem, translates his results into contemporary concepts and notation, and describes subsequent developments. It’s an effective way to understand Harriot’s contributions.

Arianrhod devotes roughly equal attention to Harriot’s work and the social and political environment of England from roughly 1580 to 1620. Since little of Harriot’s research was known to his contemporaries it seems probable that he had little, if any, influence on the course of scientific development. His improvements to navigational practice were also unpublished, but copies of his more accurate charts and instruments, together with his trained navigators, probably helped improve navigational practices generally. His work shows that many of the problems he worked on were susceptible to existing or improved conceptual and analytical tools at least a generation before his more famous successors began publishing their results. Arianrhod shows how Harriot worked and gives examples from his notes. For those interested in how the process of scientific and technological discovery works, her examples will be instructive, and the social & historical context may provide useful context. For those interested in the social and cultural history of early modern England the contextual material will allow them to place this intellectual activity in its broader context.