William Gilbert’s Study of Magnetism and the Tension between Demonstration and Induction
Dr. Godfrey Guillaumin
Fifth Congress of the International Working Group in History of Philosophy
San Francisco, CA.
June 24-27, 2004
Nowadays, it is raising a variant among the historical studies of science and epistemology called historical epistemology. Roughly speaking, the expression “historical epistemology” refers to historical studies of epistemic ideas, its genesis, changes, development, and so on. Different perspectives have been developed to carry out this kind of historical study, which ranges from early twentieth century with French authors as Foucault, Canguilhem, and Bachelard, to latest scholars as Daston, Porter, Renn, in the Max Planck Institute in Berlin. Very recently, Ian Hacking (2000) has affirmed that the expression “historical epistemology” was originally coined to express a concern with very general concepts that have to do with knowledge, belief, opinion, objectivity, reason and so forth. According to him, recent works on historical epistemology, such as Daston (1991, 2000), Galison (1992), Porter (1995), etc., have indicated an important point, namely, that the epistemological concepts are not constants, freestanding ideas that are just there, timelessly (Hacking 2000, p.8).
In a recent work, I have articulated a notion of historical epistemology taking as its core the idea of evidence. I believe that it is possible to understand historically several epistemological issues as proof, confirmation, experiment, methodology, induction, and so on, by exploring the historicity of the idea of evidence. “Evidence”, however, is not a single notion, as Peter Achinstein (2001) clearly showed in his most recent and very interesting book about evidence. He claims that his book “is devoted to the [concept of evidence], and to the question of what it means to say that some fact is evidence that a certain hypothesis is true” (Achinstein 2001, p. 3). My perspective of the problem of evidence is different to Achinstein’s at least in two major points. At one hand, I am interesting in analyzing the historical way in which the concept of evidence has been changed through the development of specific practices of inquiry and, consequently, my formulation of the problem of evidence does not exclusively center the attention upon the support between data and hypothesis. On the other hand, I opt for a broader characterization of the problem of evidence in order to explore it through the history of science. In order to do that, my characterization of the idea of evidence is formed by the following question: What is the justification of inferences through which an observable thing points to the existence of another? Throughout the history of science we can analytically distinguish, even though they are intertwined, three epistemological difficulties associated with this characterization of evidence and these represent what I considered to be the problem of evidence. The first difficulty consists of establishing criteria to determine what is a reliable observation in specific fields of rational inquiry. For example, in the history of astronomy, medicine, botany, law, etc., it is very important to distinguish between trustworthy observations and unreliable observations. The second difficulty lies in establishing with what strength an observable thing points to another, that is, what is the degree of confidence in the inference to another thing. And finally, the third problem is to find criteria that establish the very existence of the thing inferred, i.e., criteria for empirical proofs, particularly when the thing inferred is not observable. We can call these, respectively, observational evidence, inductive evidence, and provable evidence. Thus, I understand the expression “historical epistemology” as a historical study that analyzes the way in which these three difficulties have been formulated and the way in which their mutual interrelation have been understood in specific contexts of inquiry.
The early seventeenth-century is a particularly interesting epoch from which to analyze the notion of evidence from a historical epistemological perspective due to the different, deeper, and generalized changes taking place in natural philosophy at that time. William Gilbert’s work on natural philosophy provides a clear case in which these three difficulties associated with my characterization of the problem of evidence generated interesting epistemological tensions. Gilbert’s work took place at the very beginning of a new conformation among these three aspects of the problem of evidence. Recent historians and philosophers of science call this new conformation, “the modern notion of evidence.” William Gilbert’s inquiries in natural philosophy were conducted at the very beginning of the historical process of the formation of the notion of modern evidence. What I want plan to analyze here is the manner in which these three difficulties of the problem of evidence were interrelated in Gilbert’s natural philosophy.
2. Discovery or demonstration: controversies about the nature of demonstrative knowledge at the end of the sixteenth-century
William Gilbert entered St. John’s College, Cambridge, in 1558 at the age of fourteen. He received his MD at Cambridge in 1569. He held the College’s junior position of mathematical examiner in 1565 and 1566, and was its bursar in 1570. The Cambridge of Gilbert’s era was very traditional as was university education in general at that time. Gaukroger has pointed out that there were certainly contentious issues in Cambridge by this time. The problem, roughly speaking, was one that had in fact determined the history of Aristotelianism, especially in its later stages. Gaukroger maintained that there were serious problems of later misinterpretations of Aristotle that generated a new separation between the acquisition of knowledge and its presentation. In earlier writings such as the Topics, Aristotle had elaborated procedures for the “discovery of knowledge.” These procedures were designing to guide one in finding the appropriate evidence and the most fruitful questions to ask. Also in his Physics, Aristotle says that, as with physical phenomena, so with the state and human society, the complex whole must first be analyzed into its elementary constituents, so that it can be reconstructed from those elements and so scientifically understood. (Physics, i. 1, 184a9-b1). However, in his later works such as the Analytics, there is a marked change of emphasis and Aristotle now pursues the question of the presentation of results, as his concerns shift to the validity of the reasoning used to establish conclusions on the bases of accepted premises. In other words, his concerns shifted from questions of discovery to questions of demonstration (Gaukroger, 2001, p. 41). Although this shift is not problematic itself, it becomes so in the development of subsequent thinking about the nature of discovery and demonstration and it was, according to Gaukroger, a twofold displacement of the original distinction.
First, Aristotle’s method of demonstration -syllogistic- came to be constructed as his method of discovery, and various procedures, most notably that of resolution and composition, were introduced to show how we can order our experience in such a way that it yields fundamental rational principles which reflect the way things are in nature. The problem of the discovery of knowledge becomes largely subsumed under the question of the organization of knowledge. Second, the original method of discovery, the topics, disappears from the scientific context altogether, although the topics do retain an importance in rhetoric. The final stage comes with the attempts of various sixteenth- and seventeenth-century thinkers to prize open the distinction between discovery and presentation, and to offer an independent account of discovery (Gaukroger 2001, p. 41)
Far from Cambridge, but in the same epoch, the University of Padua developed interesting controversies about the relation between demonstrative knowledge and discovery. Some scholars from this University such as Pietro Catena, Alessandro Piccolomini, and Benedictus Pereira disagreed about the difference between mathematical and syllogistic demonstrations. One common position that was considered to be controversial was that only mathematical demonstrations could serve in the discovery of new truths, whereas syllogistic demonstrations were effective in the orderly presentations of long-accepted truths (Feldhay, 1999, p. 88). Pereira sustained that the rigorous structure of mathematics secures its status as a discipline, but its objects and demonstrations exclude it from the realm of the sciences. Although Paduan controversies were about the status of demonstrative mathematical knowledge, it apparently created the same confusion mentioned by Gaukroger—that of considering a method of demonstration to be a method of discovery.
There was, in the sixteenth century, a proliferation of treatises on method, which brought into play an ever wider range of classical texts dealing with strategy for investigation, polemic, and teaching (Jardine 1986, p. 331). Among different intellectual streams, we find three major categories. First is the Aristotelian theory of scientific demonstration, based upon Posterior Analytics and his introduction to Physics, which was basically a method of proof. Second are the treatises on medical method, primarily based on the brief introduction to Galen’s Ars Parva which, according to Jardine, is often interpreted alongside the introduction to Aristotle’s Physics at a cost of great distortion to both texts. Third category corresponded to the development of the dialectic forged by the renaissance humanists as an educational alternative to Aristotelian logic.
Within an intellectual environment in which discussions about discovery were typically mixed with, or interpreted as, demonstrative knowledge, the methodological question according to Gilbert was, how is it possible to inquire into magnetic phenomena if Aristotelian framework does not explain them and it is not a mathematically analyzable phenomenon? It was not possible to develop mathematical demonstrations of this phenomenon, as Galileo criticized Gilbert for his inability to develop mathematical demonstrations for magnetic phenomena. However these demonstrations were not possible at that time nor was it possible to develop syllogistic demonstrations because the Aristotelian framework did not satisfactorily explain magnetic phenomena, mainly due to Aristotelian theory of matter. Gilbert’s interests in understanding and explaining magnetic phenomena outside of an Aristotelian framework faced him with a difficult methodological situation because either he needed to reformulate some of Aristotelian concepts of matter to explain magnetic phenomena, which means acceptance of the Aristotelian framework, or he needed to find a new method of inquiry and discovery in magnetic philosophy. As we all know, he chose the second option, but what has not been sufficiently explored is how exactly Gilbert found this new method of inquiry and what consequences his choice had for the idea of modern evidence. The historical question, therefore, is: from where did Gilbert take this different method of inquiry to demonstrate magnetical phenomena?
3. Gilbert’s De Mundo and De Magnete: two very different books from one and the same author.
We know very little about Gilbert’s life, but he was a very reputable physician in London during the 1580’s eighties and in 1601 he was appointed as Queen Elizabeth I’s royal physician. Gilbert wrote three books, two of them were not finished nor published, but the third was published in 1600. The title of the latter was A New Philosophy, concerning the loadstone, magnetic bodies, and the great magnet, the Earth, demonstrated by many arguments and experiments, best known simply as De Magnete. The two others were titled, Meteorologica and Physiologiae, respectively. After Gilbert’s death in 1603, material from both books was collected from his papers, edited and prepared by Gilbert’s younger half-brother and the books were jointly published posthumously in 1651 with the title De mundo nostro sublunaris.
Many parts of De Mundo were already finished before De Magnete was published. In De Mundo, Gilbert developed a new Natural Philosophy and Meteorology against Aristotlein in which the essential element was Earth, as the only true element of the sublunar world and the “common mother” of all else. So, Gilbert rejected the Aristotelian theory of the four elements by insisting that fire, air, and water were not basic elements. In trying to refute the Aristotelian theory of elements and establish his “Earth” as a replacement for fire, air, water, and earth, Gilbert was frequently inconsistent in his arguments. For example, Aristotle considered his four elements as theoretical terms, in the sense that they were not directly observable as pure elements in the natural world. He assumed that we observe composite bodies. Gilbert, however, considered that each of Aristotle’s four elements were distinctly observed elements. Gilbert did not explain how his one basic substance could give off effluvia or what made this basic substance changes from a pure magnetic Earth to a less pure form. Of the four properties, which Aristotle had been associated with matter, Gilbert considered only three as qualities, namely, heat, moisture, and dryness. Another deficient set of arguments in De Mundo was that Gilbert did not define either the essence or the place in his cosmology of the qualities he accepted. From a modern point of view, Gilbert was merely criticizing Aristotle’s theory of matter without positive evidence for his own. He offered against Aristotle’s theory of matter a different theory of matter, constructed with the same kind of arguments that Aristotle offered for his own theory.
The final three books of De Mundo have the subtitle “Nova meteorologia contra Aristotelem,” and include Gilbert’s theory of comets, clouds, the rainbow, the nature of sea, etc. For Gilbert, meteorology was the interpretation of all things that are suspended in the air or are carried or appear in the heights (Gilbert apud Kelly, 1965, p. 46). It is very likely that Gilbert became interested in connections between the weather and the position and influence of the planets because it was part of a Galenic physician’s training. Physicians were trained to treat a patient when the qualities ascribed to each planet best matched the balance of qualities in the patient’s temperament. Gilbert’s earliest work was a notebook of dated records of the weather, correlated with astrological data (Pumfrey 2002, p. 19). He concluded that Aristotle’s explanations were wrong, and a new meteorology was needed. For example, he criticized Aristotle’s theory of comets because some observations located some of them beyond the Moon. Also, the observation of the New Star of 1572 helped Gilbert to support his denial of the existence of planetary spheres and the spheres of fixed stars. Gilbert also explained the rainbow and created drawings of it, through which he showed the position and colors of both the primary and secondary rainbows. For him, the reflection of the illuminated vapor near the Earth from some dark object formed the primary bow, but the secondary bow was due to the reflection of vapor near a cloud. Although he mentioned many factors which did and did not affect the rainbow, he was not specific about the details of how they affected it or to what degree.
It is interesting to mention that the central epistemological arguments in De Mundo criticizing Aristotle’s theory of matter and meteorology are lacking empirical proof. Except in some cases of measurements for some comets and the observation of the New Star of 1572, Gilbert did not provide in De Mundo positive evidence for his theory. However, De Magnete is another kind of book completely and represents another kind of book and another kind of inquiry. The major difference that we find between the two books is that De Magnete, Gilbert repeated over and over that he had “experimentally demonstrated” different magnetic phenomena. De Mundo is lacking this force of demonstrative arguments. De Magnete’s subtitle clearly indicates the epistemological nature of the book: “A New Philosophy …demonstrated by many arguments and experiments.” The major epistemological difference between the two works concerned Gilbert’s notion of experimental demonstration. At the beginning of the author’s preface, Gilbert says that “Since in the discovery of secret things and in the investigation of hidden causes, stronger reasons are obtained from sure experiments and demonstrated arguments than from probable conjectures and the opinions of philosophical speculators of the common sort” (Gilbert 1958, p. xlvii). Even though his new style of philosophizing subscribes to the traditional requirement of demonstrative knowledge, it rests on a very different idea: sure experiments are the correct procedure to use in order to gain true beliefs and certainty about the natural world. In this sense, Gilbert says that, “Our generation has produced many volumes about recondite, abstruse, and occult causes and wonders, and in all of them amber and jet are presented as attracting chaff; but never a proof from experiments, never a demonstration do you find in them. (Gilbert 1958, p. 77).
One of the most important phenomena that Gilbert claimed to have demonstrated is that Earth rotates. He said that: “We have already proven that all true parts of the earth do move circularly, and that all magnetic bodies are borne round in a circle” (Gilbert 1958, p. 335). Gilbert said that, “We, therefore, having directed our inquiry toward a cause that is manifest, sensible, and comprehended by all men, do know that the earth rotates on its own poles, proved by many magnetical demonstrations to exist” (Gilbert 1958, p. 328). And finally Gilbert concludes emphatically, “It is therefore plain that no argument of sufficient force has yet been formed by philosophers to refute the earth’s motion” (Gilbert 1958, p. 343). For Gilbert, common experience was not a secure source from which to obtain reliable knowledge about magnetism mainly because it had been traditionally mixed with fantasies, figments, and unresolved paradoxes. The traditional idea of magnetism as an occult quality is derived mainly from the inability of Aristotelian explanations to elucidate clearly within a framework of its four causes and qualities.
His epistemological shift was based upon the idea that experiments have a wide range of demonstrative uses. They do not just permit us to disclose recondite true causes but also to prove, demonstrate and show true conclusions about magnetic phenomena. He stresses certainty of experimental results as true facts and the strength of logical argumentation as a foundation of facts. In Gilbert, common experience no longer has the role of providing secure information about magnetic phenomena.
At the beginning of chapter XVII of the Book I, he maintained that
Before we expound the causes of the magnetic movements and bring forward our demonstrations and experiments touching matters that for so many ages lain hid¾the real foundations of terrestrial philosophy¾we must formulate our new and till now unhearing-of view of the earth, and submit it to the judgment of scholars. When it shall have been supported with a few arguments of prima facie cogency, and these shall have been confirmed by subsequent experiments and demonstrations, it will stand as firm as aught that ever was proposed in philosophy, backed by ingenious argumentation, or buttressed by mathematical demonstrations (Gilbert 1958, p. 64).
Gilbert synthesized three interrelated senses of “demonstration” that he used throughout his work. First, he claimed that there is a reliable method of inquiry into phenomena long considered as occult. Experimental demonstrations are able to disclose hidden knowledge that sense experience cannot reveal; so, the main source of natural knowledge is no longer sense experience but experimental experience. Secondly, according to Gilbert, experimental demonstration was also a means to confirm experimental conclusions and many scholars could prove these conclusions again and again, even if the conclusions were quite unbelievable. Experimental demonstration had a role in showing that knowledge acquired by means of experiments is truthful. And finally, Gilbert considered mathematical demonstration as support for empirical conclusions. This kind of demonstration refers not only to geometric diagrams used in De Magnete to show different calculations to determine different magnetic properties, as the terrestrial declination at one specific point, but to his idea that round magnets, like the Earth or terrellas, have a spherical geometry which is shown by experiments. In this sense, Gilbert used demonstration throughout his work to “show,” “exhibit,” or “display” certain magnetic phenomena.
4. Gilbert’s experimental inquiry supported by navigational evidence
There are two historical questions that have epistemological significance: Where did Gilbert take the idea of experimental demonstration? and, Why were De Mundo and De Magnete so different in their epistemological status? I believe that these questions are strongly interrelated. As we saw above, the end of the sixteenth century was an epoch of controversy about the idea of demonstrative knowledge. The first thing that we must keep in mind is that even though Gilbert studied mathematics at Cambridge, he was not a mathematician, so, he did not look for mathematical demonstrations in his work. He was also reluctant to argue by syllogistic demonstrations mainly because he thought Aristotle’s theory of matter to be inadequate and foolish. Consequently, it is reasonable to believe that he took his methodological norms and epistemological point of view from a different area of mathematics and Aristotelian natural philosophy, but from where? I maintain it is highly probable that it was from Galen’s texts.
Gilbert knew Galen’s works well. During that epoch, Galen was a great authority among physicians. Also, Gilbert mentioned Galen twelve times in his De Magnete. Even though Gilbert rejected Galen’s theory of matter, it is very plausible that he had learned the method of discovery from Galen. Galen made a great effort to spell out in detail how reason and observation are to be used in either case. In this sense, he articulated ideas concerning the issue of a rational method of discovery, an ars inveniendi. Such a method of invention or discovery we find by the name of analysis. Galen’s writings in Latin translation played an increasing role in the medical schools of the universities of that time and had an influence far beyond the faculties of medicine. Two treatises were studied with particular care, the Ars medica (Tegni) and “On the Method of Healing,” which also came to be known respectively as the Ars Parva and the Ars Magna. At the beginning of the Ars Parva, Galen mentioned three approaches to teaching medicine: the analytic, which proceeds towards some intended goal; the synthetic, which conversely begins with what is discovered by analysis and proceeds from there; and the Platonic method of division, which Galen uses as his own method of presentation in the rest of the book. Galen taught that the role of reason and observation in knowledge is twofold. Reason and observation are instrumental, in that they serve to arrive at the truth, but they also play a critical role in that they are used to decide or to confirm the truth of a view at which one has already arrived. Despite its obscure remarks about analysis and synthesis, Ars Parva was a text that was widely lectured about and commented upon. Thus, it gave ample opportunity for reflection on the method of scientific discovery and of scientific demonstration within the framework of Galen’s notion of research and finding causes. Roughly speaking, this position makes the claim that there is a systematical, logical method of discovery which, in fact, has as its aim to spell out the rational method of discovery of the appropriate treatment for a given disease (Frede 1985, p xxxiv).
Evidence that Gilbert followed a method of analysis and synthesis in his experimental explorations of magnetic philosophy is his theory of magnetic variation. Variation was the name for the magnetic phenomena by which there is a difference of the angle between magnetic north and true north at a particular point on the Earth’s surface. Gilbert says that “The variation takes place not so much because of these elevated but less perfect parts of the earth and these continental lands, as because of the inequality of the magnetic globe and of the true earth-substance which projects farther in continents than beneath sea-depths. We have therefore to inquire how the demonstration of this new natural philosophy may be drawn from unquestionable experiments” (Gilbert 1958, p. 233). How did Gilbert develop this new theory, and how did he attempt to prove? Gilbert’s first step was to attribute to the Earth new phenomena discovered in the laboratory that had never been suspected to exist on the Earth. He experimented with his terrellas, small rounded magnets on which he positioned small magnetic needles called versorium. Some of these terrellas were perfectly spherical while others had protuberances that imitated major terrestrial continents and massive mountains and peaks. Gilbert showed in De Magnete two different terrellas in order to illustrate this case, neither of them were perfectly spherical. The first terrellae had a “depression comparable to the Atlantic Ocean,” while the second appears to have been ingeniously turned on a lathe to imitate the continents. In both cases, Gilbert showed that a needle deviating from the pole in patterns that replicated the variation of a real compass at sea. “Gilbert’s theory of variation shows that he was moving towards a method of analysis and synthesis that created an ‘ideal, real world’. […] Gilbert knew perfectly well that neither the Earth nor his terrellae were perfect spherical magnets, but this was the domain in which his analysis of the components of magnetic virtue took place. The real world was generated by synthesising the components of ideal verticity and perturbation” (Pumfrey, 2002, p 149). But it was insufficient to use a method without reliable data, specifically in Gilbert’s De Magnete, without geomagnetic information.
Gilbert used a considerable amount of evidence from geomagnetism that was gathered by sailors. Without these data Gilbert simply could not sustain his analogy in the experiment about magnetic variation. From where did Gilbert obtain geomagnetic information? He integrated natural philosophy with “high” mathematics such as astronomy, and “low” mathematics such as navigation. It is also clear that some of Gilbert’s mathematician and astronomer friends helped in some parts of De Magnete. Chapter XII of De Magnete has the following title, “Of finding the amount of the variation; what the quantity is of the arc of the horizon from its arctic or Antarctic intersection by a meridian to the point toward which the needle turns.” For this chapter, Gilbert gathered geomagnetic information about variation from all over the world. It contains variation data from northern regions, regions below the Equator, the Artic Ocean, the South Sea, the Mediterranean Sea, the Eastern Ocean, and from the interior of the great continents. To day, there is historical evidence for the idea that this chapter, specifically, was written by Edward Wright, a graduate of Cambridge University in mathematics, who designed navigational instruments and lectured on mathematics. Wright, Ridley, and Barlow were three men with whom Gilbert discussed his work at length, and all of them knew that Gilbert couldn’t understand Copernicus’ mathematics. But book VI of De Magnete gives the impression of having been written by someone at ease with Copernicus, even with complicated explanations of precession.
We have seen that Gilbert made use of observational, inductive and provable evidence in a different way according to his epoch. Regarding observational evidence, a single man did not make observation but it is a cooperative enterprise. If we recognize that Gilbert did not write De Magnete alone, that in some of the critical parts, he was helped by experts in others areas, many traditional interpretative troubles about him disappear, and what emerges is a modern notion of evidence. His history is an interesting case of cooperative research, experimental designs, mutual support from colleagues. Also, for Gilbert demonstrative knowledge was not mathematical nor syllogistic but experimental. It was an abandonment of the confusion of a method of proof as a method of discovery. For Gilbert, the method of discovery was theoretically derived from a medical framework, but practically performed by experimental devices. Regarding provable evidence, his experimental results had demonstrative force not just because of his logical consistency with common observable phenomena (which was the notion of evidence he inherited from sixteenth-century Aristotelians), but because he worked with geomagnetic evidence from all parts of the explored world. Experiments allowed him to discover true phenomena that are occult to simple observation, like the rotation of the Earth, and they provided experimental proofs impossible to achieve through unaided observation. But for Gilbert, carrying out experiments meant abandoning Aristotle’s theory of matter as well as obtaining geomagnetic evidence from all over around.
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 El surgimiento de la noción de evidencia. Un estudio de epistemología histórica sobre la idea de evidencia científica, in press. 2004.
 The process of formation of what we could call the modern notion of evidence was a long one. It runs from the end of the sixteenth century to the middle of the eighteenth century. What we could understand as the modern notion of evidence should be formulated by these three aspects of the problem of evidence mentioned above, namely, roughly speaking, that during the epoch mentioned above, observational evidence was gathered by sophisticated instruments and/or experiments; that it have been made conceptual criteria to satisfactorily formulate a conception of inductive support (inductive evidence); and that there were formulated different criteria for theory proof, that is, at the end of the seventeenth century the notion of provable evidence was formulated in terms of the support that unexpected predictions of a theory provide for the same theory. And these characteristics of evidence were practically inexistent phenomena in antiquity.
 Heat was defined as the act of attenuating moisture which originated from motion and light. Cold was the absence of this act. Since all moisture was an effluvium from the Earth and dryness a lack of this effluvium, neither moisture nor dryness was a thing itself or an operating property of any body.
 Many authors published books about the art of navigation in Gilbert’s epoch. John Tapp was a mathematical practitioner of that day who was also a publisher of navigational books. He filled a real need when he began the regular publication of an almanac which contained all of the tables he thought would be useful and necessary to seamen. In 1596, he edited and published a book entitled, The Art of Navigation, which was an English translation by Richard Eden of Cortes’ work which had been published first in 1579. A Regiment of the Sea by William Bourne was published in 1574. In it, Bourne details the use of many navigational instruments. The book also contains the first mention of the log-line. Seaman’s Secret was written by John Davis and published first in 1595. Davis had spent much of his life at sea. He was recognized by the leading men of his day for his skill and knowledge of navigation. He was the inventor of the back-staff, sometimes called the Davis Quadrant. He explored the northern coast of America looking for the north-west passage, keeping a daily journal. In his Seaman’s Secrets he used many extracts from that 1593 journal. Edmund Gunter was a professor of astronomy at Gresham College in London. He published works based on computations of the first logarithmic tables of sines, secants and tangents. He developed some instruments for navigation and surveying which were of great importance. His sector was actually the fore-runner of the modern slide-rule. Robert Hues was educated at Oxford University and wrote on the use of Emery Molyneux’s Globes (terrestrial and celestial) in 1594. It is thought that he might have given direct mathematical instruction to the colonists of New Virginia since his patron was the Earl of Northumberland, which would have given him a direct connection to those early settlers.
 In 1599, he published a book entitled, Certaine Errors in Navigation, which contains important sections on navigational instruments and their use. He made many astronomical observations and drew up tables of computation some of which reappeared in his chapter for De Magnete. Thanks to a letter written by a friend of Gilbert’s named Ridley, we know that even though De Magnete explains how to find variation, Gilbert himself was not the actual author of this subject. However, he did discover the cause of variation. In 1616, Ridley published a defense of Gilbert against William Barlow, who was an opponent of Gilbert’s magnetic Copernicanism. In it, Ridley says that: “[Wright] was a verie skilfull and painefull man in the Mathematickes, a worthy reader of that Lecture of Navigation for the East-India Company…[T]his man took great paines in the correcting the printing of Doctor Gilberts booke, and was very conversant with him, and considering of that sixt booke [of De Magnete] which you [Barlow] no way beleeve, […]” (Ridley apud Pumfrey, 2002 p. 176)